BACKGROUND
genes and their protein products carry out cellular processes in the context of functional modules and are related to each other through a complex network of interactions  <cit> .
understanding an individual gene or protein's network properties within such networks may prove to be as important as understanding its function in isolation  <cit> .
because of this, numerous studies have focused on the large scale modeling of genomic and proteomic data.
utilizing network theory, these studies have yielded insights into biological systems.
for example, both protein interaction networks and gene co-expression networks exhibit a strong modularity reflecting functional partitioning.
both of these network types have been frequently observed as having a scale-free topology, with the existence of highly connected hub nodes  <cit> .
scale-free networks are resistant to random perturbations but sensitive to targeted removal of highly connected nodes  <cit> .
comprehensive efforts to determine the functional consequences of individual gene deletions in yeast provide the opportunity to study the relationship between individual gene network properties and gene deletion lethality  <cit> .
for example, physical interaction studies in yeast have allowed comparison of connectivity to gene essentiality based on gene deletion.
<cit> .
typical of scale-free networks, there were few highly connected proteins within the network, and the deletion of a protein with a large number of binding partners is more likely to be lethal in yeast.
thus, the relative position of nodes within a protein interaction network is strongly affiliated with distinct biological properties of individual proteins.
similarly, analysis of unweighted gene co-expression networks have revealed a relationship between connectivity and essentiality across all genes  <cit> .
correlation of gene expression across a wide variety of experimental perturbations has been shown to cluster genes of similar function  <cit> .
since this guilt-by-association approach may lead to false positive groupings, approaches have been refined by comparing orthologs across divergent species indicating that highly conserved co-expression is a strong predictor that two genes will function in similar pathways  <cit> .
this indicates that functionally related genes are under similar expression constraints.
the gene co-expression networks that are based on these relationships have been shown in multiple species to be frequently scale-free and exhibit a small world architecture similar to protein interaction networks even though they are generally more strongly connected  <cit> .
it is still unclear however, to what degree the network properties of individual genes within a co-expression network can predict relative gene importance for a particular process.
to assess this, we have constructed three networks based on a weighted measure of connectivity  <cit>  of correlated gene expression in yeast using three separate microarray data sets.
we assessed relationships between essentiality and connectivity of each gene within the whole network.
further, we define 'modules'  and determine that in some instances, the relative importance of genes within these modules can be inferred from network connectivity.
we demonstrate that genes which have high connectivity  within a weighted co-expression network are significantly more likely to be essential for yeast viability.
furthermore, we demonstrate a relationship between connectivity and a measure of sequence conservation.
finally, we show that certain critical modules are conserved from one network to another, and that in many cases it is possible to extend the relationship between connectivity and essentiality or between connectivity and conservation within given modules.
thus, analysis of gene co-expression networks provides insight into the functional importance of individual genes within modules of co-expressed genes.
RESULTS
network validation and properties
in order to test the relationship between gene connectivity within the co-expression network and gene essentiality, we first constructed three networks corresponding to three microarray datasets.
the yeast microarray data were derived from experiments designed to analyze dna damage  , cell cycle  , and environmental response    <cit> .
each network was constructed as conceptually shown in figure  <dig>  nodes were defined as individual genes.
the co-expression network is based upon the correlation relationships between individual genes across a dataset .
from the microarray data, the absolute value of the pearson correlation is the initial measure of gene co-expression similarity .
this co-expression similarity was then transformed into an adjacency matrix  by raising the similarity to a certain power based on a scale free topology criterion as described previously  <cit> .
the powers selected were  <dig> ,  <dig> , and  <dig> .
these data can also be visualized as a drawn network .
each of the datasets resulted in the construction of distinct networks but with global similarities.
the differences in the modularity of the three networks is demonstrated by comparing the heat maps of the topological overlap matrices .
a topological overlap matrix is an indicator of the similarity of all the nodes in question and is defined in detail in the methods section of this manuscript.
approximations of all three of the networks are also drawn in figures 3b, 4b and 5b using the fruchterman-reingold algorithm as implemented in pajek  <cit>  and demonstrate obvious modularity with aggregation of genes into strongly co-expressed groups.
individual gene connections can be difficult to visualize in such complex graphs as presented.
thus, in order to probe the structure of the network, we first sought to determine characteristics of the general network topology.
we considered two models.
to quantify the fit to the scale free topology model or to the truncated exponential model, we used the model fitting index r-squared of the corresponding linear model involving the log transformed variables  <cit> .
the pattern of network connectivity in these datasets approximated a scale-free topology .
these results are similar to the general trend with genetic perturbation networks and other gene co-expression networks  <cit> .
however, gene co-expression networks may better fit an exponential power law  <cit> .
for two of the three constructed yeast networks , the distribution of connectivity  of genes best fits a power law p ~ k-γ and the other  best fits an exponentially truncated power law p ~ k-γ e-αk  <cit> .
we point out that in general that regardless of the overall structure, the major trend is that the high connectivity genes are few in number, and that most genes have low connectivity .
global network connectivity relationships
network modeling in biological systems  <cit>  stresses the relative importance of highly connected nodes.
thus, the small number of high connectivity genes within the gene co-expression networks defined here are expected to be more important.
to test the relative importance of each gene across the entire network, we determined the relationship between connectivity and gene essentiality.
all the genes for a network were first ranked according to their weighted connectivity and then placed into  <dig> equal sized bins according to their position in this ranking.
the weighted connectivity of a given gene is defined as the sum of its connection strengths with all other genes in the network .
the percentage of essential genes in each bin was then plotted against the mean connectivity in each bin .
we also calculated the spearman correlation coefficient based on the ranked unbinned data and found that there is a relationship between the connectivity and the proportion of essential genes in each of the three datasets  for each network.
while the binned plots are well suited for visualizing the results, we calculated the correlation coefficients on the raw, unbinned data to arrive at a valid p-value.
to study whether our conclusions were being unduly influenced by data outliers, we removed genes whose connectivity was more than two standard deviations away from mean connectivity but found no substantial variation in the reported relationships.
thus, there is a clear relationship between connectivity of genes, in these weighted gene co-expression networks, and gene essentiality across the whole network.
these results are robust with respect to experimental conditions since the three separate datasets all have the same functional relationship between connectivity and gene essentiality.
these results are consistent with a single whole network generated from gene co-expression data and using an unweighted network  <cit> , as well as networks based on protein-protein interactions  <cit> .
yeast co-expression networks fit an evolutionarily plausible model in which network connection distribution is a natural consequence of gene duplication, mutation and deletions  <cit> .
the emergence of approximate power-law distribution  is intimately linked to the growth of the network in which new nodes are preferentially attached to highly connected already established nodes  <cit> .
a direct consequence of this network growth model is that high connectivity 'hub' genes are more likely to be highly conserved across different species.
stated another way, within a gene co-expression network the oldest nodes would be more likely than the newer nodes to be in hub positions.
with this in mind, we examined the relationship between connectivity and the relative evolutionary sequence conservation of a node  against n. crassa c. elegans, d. melanogaster, h. sapiens, and m. musculus).
high connectivity genes are plotted in figure 2g–2i relative to the average of the blastp hit in four other eukaryotic genomes.
as before, we calculated the spearman correlation for the ranked, but still unbinned, data and found that there is a relatively weak but highly significant correlation indicating that high connectivity genes are more evolutionarily conserved .
our results were robust with respect to the removal of outlier genes .
this relationship is similar to that reported for gene perturbation networks  <cit>  and in evolutionarily conserved gene co-expression relationships  <cit> .
identification of modules
in order to identify modules, we performed hierarchical clustering on the topological overlap matrix derived from these networks as described in the methods section.
in doing so, we identified modules that involve conserved processes for rrna processing, protein synthesis, and ubiquitination  using an ease analysis  <cit> .
one prediction about network constructions is that certain critically important modules ought to be repeatedly detected in independent datasets.
within the network modules  produced by the different datasets for gene ontology enrichment,  <dig> distinct modules that were common to the  <dig> different data sets were detected .
comparing the modules that had an enrichment in rrna processing, protein synthesis and the ubiquitin pathway terms across the dd, cc and er datasets resulted in a highly significant overlap of  <dig> genes .
similarly, the protein synthesis module also had significantly more overlap than expected by chance in which  <dig> genes were present in all three modules .
the ubiquitin module had the least overlap of common genes  probably because of its smaller size in general.
these three processes are well known to be fundamental processes and have been described before in great detail, and so we decided to investigate the nature of these overlapping regions further.
gene members were selected that were shared within similar functional modules from the three datasets and searched for in the kegg  <cit>  database.
in the ubiquitin pathway,  <dig> of the overlapping  <dig> genes were found in kegg, and all of these were found to be in the same proteasome structure.
since the overlap for this module was unusually small due in part to the very small size of the er dataset's ubiquitin module, we also looked at the overlap just of the cc and dd ubiquitin modules.
of the  <dig> genes present in both the cc and dd modules, only  <dig> were present in the kegg database.
of those  <dig> members, all of them were in the same proteasome structure.
for the protein biosynthesis module,  <dig> of  <dig> overlapping members were represented in the kegg database, and of these,  <dig> out of a possible  <dig> were components of the kegg annotated yeast ribosome.
notably, if the  <dig> overlapping members were first rank ordered by their average network connectivity, and the bottom quartile removed, then 100% of the remaining members are part of this same yeast ribosome structure, which shows that in this overlap set the high connectivity genes were in fact the members of the yeast ribosome.
finally, the overlap of genes detected in the rrna modules overlap identified purine and pyrimidine synthesis and rna polymerase  <dig> pathways.
these pathways dominate this list with  <dig> out of the  <dig> identified matches to the kegg database.
unlike the previous two results however, multiple pathways are found that represent this module.
the three network modules discussed all contain large protein complexes.
this is in agreement with the recent discovery that there is often a correlation between genes that are expressed together and proteins that bind to each other  <cit> .
however, there is no reason to believe that modules in co-expression networks will always correspond to protein complexes since our module detection method should find any set of genes with high pair-wise correlations.
any experimental perturbation that gives rise to a highly correlated gene set is expected to result in a corresponding network module.
intramodular network connectivity relationships
having identified  <dig> functionally similar modules in the three different datasets, we assessed whether these same modules contain the same information as the entire network.
is the connectivity of a gene within the identified modules correlated with the likelihood that a gene was essential by deletion analysis and also whether it was conserved ?
to test connectivity correlations within these modules, we define the intramodular connectivity  as the sum of all connectivity measures only with genes within the same module.
similar to that performed for the total gene connectivity within the whole network, binned values were plotted to observe the possible relationships .
to evaluate significance, spearman correlation coefficients for the ranked but unbinned data were calculated for relationship of k.in to essentiality and sequence conservation.
interestingly, there was a general trend to similar correlations as that seen within the whole network.
the correlation with sequence conservation was generally weak: the ubiquitin module formed from the dd dataset and the rrna processing modules in the er and cc were the most correlated with k.in.
there was a correlation of k.in and essentiality in all three datasets within the rrna processing module , and for two of the datasets  within the ubiquitin module, and a trend towards a weak anticorrelation within the protein synthesis module .
thus, some of the relationships between connectivity and essentiality or sequence conservation and not detected when the analysis is restricted within the modules.
characterizing modules that contain essential hub genes
the relationship between intramodular connectivity and essentiality is not necessarily universal for any module in any dataset.
whether or not a module contains meaningful information for predicting essentiality depends on the expression data  that were analyzed.
one can view the correlation of k.in and essentiality as a test of the modules importance.
the key issue is that in order for a module to demonstrate this relationship, there must be a sufficient number of essential genes within the module.
as some modules have substantially fewer essential genes than others, there is little power to detect any relationship with k.in within those modules.
we calculated the spearman correlation between the proportion of essential genes within a module and the correlation of k.in with essentiality and show that there is a strong positive correlation .
since in actual applications the goal will be to find unknown 'essential' genes, it would be preferable to have another metric of 'essential' gene enrichment.
in this regard, it is interesting to note that of the three modules studied in the  <dig> datasets , there were  <dig> that had a correlation of k.in with sequence conservation .
of these  <dig> modules, all  <dig> were shown to have a strong relationship of k.in with essentiality in the same modules.
of the  <dig> without a correlation , only one showed a correlation between k.in and essentiality .
thus, the detection of a relationship between intramodular connectivity and sequence conservation may predict those modules with a relationship between k.in and essentiality.
discussion
our results extend the inferences made from protein and metabolic networks to the more prolific datasets available from gene expression data.
these results are made possible due to broad surveys of expression and the comprehensive characterization of the yeast genome with deletion mutants.
in contrast to gene expression data, which are based on the assessment of cells in many different states of perturbation, protein interaction measurements are determined in only a limited set of conditions which by nature only capture a subset of all possible protein-protein interactions.
others  <cit>  have constructed gene perturbation networks by looking at the expression changes when individual genes are eliminated or in relation to transcription factor expression.
microarray based surveys of gene expression allow detailed surveys of gene expression across a wide variety of experimental perturbations.
from these data a strong correlation of gene expression for two genes implies that both genes act within a common functional group and are under similar transcriptional control.
since these networks are not based on direct measurements of protein binding/interaction, the presence of two genes that are highly correlated has a different interpretation than that derived from a protein interaction network.
in a co-expression network, two closely tied nodes would be highly correlated but not necessarily direct binding partners.
in spite of this key difference, numerous other studies have indicated that genes that are correlated with each other across a modest range of experiments tend to function in similar ways and that this functional categorization is strengthened when gene co-expression exists across large evolutionary distances  <cit> .
here, we use a more general weighted gene co-expression network construction method for network construction that can be applied generically to microarray data using simple correlational analyses of individual genes  <cit> .
advantages of weighted networks over unweighted networks based on dichotomizing the correlation matrix include a) that the continuous nature of the gene co-expression information is preserved and b) that the results of weighted network analyses are highly robust with respect to the choice of the parameter β,  <cit> .
we show that there is a strong correlation with the weighted gene co-expression connectivity measure and gene essentiality and sequence conservation.
our analysis demonstrates that individual conserved modules are identifiable within a network.
moreover, the presence of these modules, which were detected in three independent networks, illustrates that these networks have a structure to them which matches known cellular biology.
we have also shown that when sufficient information is available, these correlation modules can provide further information about which of their members are more likely to be important for a given process.
the ability to assess whether or not a module is complete enough to be informative using a test like either of the ones employed here will be important for validating the merit of less understood modules in the future.
our study extends the strong links between the network properties of a gene within co-expression networks and the global importance of each gene to the yeast cell, and may have implications for targeted drug therapy in more complex biological systems like cancer.
for instance, one can infer from an analysis of the single gene deletion data that single targets for inhibition can be partially predicted from expression data.
however, in biological systems an optimal effect is frequently achieved by inhibiting multiple specific targets.
can we extrapolate network positions and relationships to infer effective combinations of targeted therapeutics?
yeast is an excellent model for establishing the rules for applying network theories to practical predictions.
for instance, will double deletions of high connectivity genes within the network which reside in the same module have substantially greater negative consequences to the yeast than double deletions of low connectivity genes?
alternatively, will genes which are connecting distinct modules, and serving as key connections between integrators prove to be better disruption targets?
the modeling of such proposed interactions in yeast is attractive because of the relative tractability of yeast studies and the availability of large scale datasets.
technologies like synthetic genetic arrays which automate double deletion screens or chemical genomic profiling provide an expanding capability to survey the effects of multiple target inhibition or deletion  <cit> .
however, even with these powerful methods, only a small fraction of the millions of possible combinations will be assayed.
for instance in a substantial recent survey of double deletions only  <dig> % of all possible double deletions were tested for synthetic lethality  <cit> .
thus, network based modeling may be a useful adjunct for the design of double knockout experiments or combination inhibition experiments to permit a more efficient search for synthetic lethals.
an interplay between predictive models and targeted large scale inhibition studies may be quite useful for surveying pathway analysis in yeast.
in the long term, such studies may also be critical in the development of therapies for diseases like cancer.
CONCLUSIONS
in conclusion, our study demonstrates that weighted gene co-expression networks can be used to predict both the likelihood of essentiality and the likelihood of conservation for their gene members within the entire network.
furthermore, we show that these networks can be subdivided into identifiable modules, which themselves can often contain enough individual information to indicate which genes are more likely to be crucial for a particular process.
we have indicated a means for testing whether this is true or not.
thus, we have illustrated how this process can be applied to common microarray data for the purpose of predicting both functional assignment as well as the ranking of gene significance in a particular process with which it is found to be associated.
we believe that these kinds of predictions will be helpful for identifying gene targets for therapeutics and for directing multi-drug therapies.

 genes and their protein products carry out cellular processes in the context of functional modules and are related to each other through a complex network of interactions. understanding an individual gene or protein's network properties within such networks may prove to be as important as understanding its function in isolation. because of this, numerous studies have focused on the large scale modeling of genomic and proteomic data. utilizing network theory, these studies have yielded insights into biological systems. for example, both protein interaction networks and gene co-expression networks exhibit a strong modularity reflecting functional partitioning. both of these network types have been frequently observed as having a scale-free topology, with the existence of highly connected hub nodes. scale-free networks are resistant to random perturbations but sensitive to targeted removal of highly connected nodes. comprehensive efforts to determine the functional consequences of individual gene deletions in yeast provide the opportunity to study the relationship between individual gene network properties and gene deletion lethality. for example, physical interaction studies in yeast have allowed comparison of connectivity to gene essentiality based on gene deletion.. typical of scale-free networks, there were few highly connected proteins within the network, and the deletion of a protein with a large number of binding partners is more likely to be lethal in yeast. thus, the relative position of nodes within a protein interaction network is strongly affiliated with distinct biological properties of individual proteins. similarly, analysis of unweighted gene co-expression networks have revealed a relationship between connectivity and essentiality across all genes. correlation of gene expression across a wide variety of experimental perturbations has been shown to cluster genes of similar function. since this guilt-by-association approach may lead to false positive groupings, approaches have been refined by comparing orthologs across divergent species indicating that highly conserved co-expression is a strong predictor that two genes will function in similar pathways. this indicates that functionally related genes are under similar expression constraints. the gene co-expression networks that are based on these relationships have been shown in multiple species to be frequently scale-free and exhibit a small world architecture similar to protein interaction networks even though they are generally more strongly connected. it is still unclear however, to what degree the network properties of individual genes within a co-expression network can predict relative gene importance for a particular process. to assess this, we have constructed three networks based on a weighted measure of connectivity of correlated gene expression in yeast using three separate microarray data sets. we assessed relationships between essentiality and connectivity of each gene within the whole network. further, we define'modules' and determine that in some instances, the relative importance of genes within these modules can be inferred from network connectivity. we demonstrate that genes which have high connectivity within a weighted co-expression network are significantly more likely to be essential for yeast viability. furthermore, we demonstrate a relationship between connectivity and a measure of sequence conservation. finally, we show that certain critical modules are conserved from one network to another, and that in many cases it is possible to extend the relationship between connectivity and essentiality or between connectivity and conservation within given modules. thus, analysis of gene co-expression networks provides insight into the functional importance of individual genes within modules of co-expressed genes.  network validation and properties in order to test the relationship between gene connectivity within the co-expression network and gene essentiality, we first constructed three networks corresponding to three microarray datasets. the yeast microarray data were derived from experiments designed to analyze dna damage, cell cycle, and environmental response. each network was constructed as conceptually shown in figure nodes were defined as individual genes. the co-expression network is based upon the correlation relationships between individual genes across a dataset. from the microarray data, the absolute value of the pearson correlation is the initial measure of gene co-expression similarity. this co-expression similarity was then transformed into an adjacency matrix by raising the similarity to a certain power based on a scale free topology criterion as described previously. the powers selected were,, and. these data can also be visualized as a drawn network. each of the datasets resulted in the construction of distinct networks but with global similarities. the differences in the modularity of the three networks is demonstrated by comparing the heat maps of the topological overlap matrices. a topological overlap matrix is an indicator of the similarity of all the nodes in question and is defined in detail in the methods section of this manuscript. approximations of all three of the networks are also drawn in figures 3b, 4b and 5b using the fruchterman-reingold algorithm as implemented in pajek and demonstrate obvious modularity with aggregation of genes into strongly co-expressed groups. individual gene connections can be difficult to visualize in such complex graphs as presented. thus, in order to probe the structure of the network, we first sought to determine characteristics of the general network topology. we considered two models. to quantify the fit to the scale free topology model or to the truncated exponential model, we used the model fitting index r-squared of the corresponding linear model involving the log transformed variables. the pattern of network connectivity in these datasets approximated a scale-free topology. these results are similar to the general trend with genetic perturbation networks and other gene co-expression networks. however, gene co-expression networks may better fit an exponential power law. for two of the three constructed yeast networks, the distribution of connectivity of genes best fits a power law p ~ k-γ and the other best fits an exponentially truncated power law p ~ k-γ e-αk. we point out that in general that regardless of the overall structure, the major trend is that the high connectivity genes are few in number, and that most genes have low connectivity. global network connectivity relationships network modeling in biological systems stresses the relative importance of highly connected nodes. thus, the small number of high connectivity genes within the gene co-expression networks defined here are expected to be more important. to test the relative importance of each gene across the entire network, we determined the relationship between connectivity and gene essentiality. all the genes for a network were first ranked according to their weighted connectivity and then placed into equal sized bins according to their position in this ranking. the weighted connectivity of a given gene is defined as the sum of its connection strengths with all other genes in the network. the percentage of essential genes in each bin was then plotted against the mean connectivity in each bin. we also calculated the spearman correlation coefficient based on the ranked unbinned data and found that there is a relationship between the connectivity and the proportion of essential genes in each of the three datasets for each network. while the binned plots are well suited for visualizing the results, we calculated the correlation coefficients on the raw, unbinned data to arrive at a valid p-value. to study whether our conclusions were being unduly influenced by data outliers, we removed genes whose connectivity was more than two standard deviations away from mean connectivity but found no substantial variation in the reported relationships. thus, there is a clear relationship between connectivity of genes, in these weighted gene co-expression networks, and gene essentiality across the whole network. these results are robust with respect to experimental conditions since the three separate datasets all have the same functional relationship between connectivity and gene essentiality. these results are consistent with a single whole network generated from gene co-expression data and using an unweighted network, as well as networks based on protein-protein interactions. yeast co-expression networks fit an evolutionarily plausible model in which network connection distribution is a natural consequence of gene duplication, mutation and deletions. the emergence of approximate power-law distribution is intimately linked to the growth of the network in which new nodes are preferentially attached to highly connected already established nodes. a direct consequence of this network growth model is that high connectivity'hub' genes are more likely to be highly conserved across different species. stated another way, within a gene co-expression network the oldest nodes would be more likely than the newer nodes to be in hub positions. with this in mind, we examined the relationship between connectivity and the relative evolutionary sequence conservation of a node against n. crassa c. elegans, d. melanogaster, h. sapiens, and m. musculus). high connectivity genes are plotted in figure 2g–2i relative to the average of the blastp hit in four other eukaryotic genomes. as before, we calculated the spearman correlation for the ranked, but still unbinned, data and found that there is a relatively weak but highly significant correlation indicating that high connectivity genes are more evolutionarily conserved. our results were robust with respect to the removal of outlier genes. this relationship is similar to that reported for gene perturbation networks and in evolutionarily conserved gene co-expression relationships. identification of modules in order to identify modules, we performed hierarchical clustering on the topological overlap matrix derived from these networks as described in the methods section. in doing so, we identified modules that involve conserved processes for rrna processing, protein synthesis, and ubiquitination using an ease analysis. one prediction about network constructions is that certain critically important modules ought to be repeatedly detected in independent datasets. within the network modules produced by the different datasets for gene ontology enrichment, distinct modules that were common to the different data sets were detected. comparing the modules that had an enrichment in rrna processing, protein synthesis and the ubiquitin pathway terms across the dd, cc and er datasets resulted in a highly significant overlap of genes. similarly, the protein synthesis module also had significantly more overlap than expected by chance in which genes were present in all three modules. the ubiquitin module had the least overlap of common genes probably because of its smaller size in general. these three processes are well known to be fundamental processes and have been described before in great detail, and so we decided to investigate the nature of these overlapping regions further. gene members were selected that were shared within similar functional modules from the three datasets and searched for in the kegg database. in the ubiquitin pathway, of the overlapping genes were found in kegg, and all of these were found to be in the same proteasome structure. since the overlap for this module was unusually small due in part to the very small size of the er dataset's ubiquitin module, we also looked at the overlap just of the cc and dd ubiquitin modules. of the genes present in both the cc and dd modules, only were present in the kegg database. of those members, all of them were in the same proteasome structure. for the protein biosynthesis module, of overlapping members were represented in the kegg database, and of these, out of a possible were components of the kegg annotated yeast ribosome. notably, if the overlapping members were first rank ordered by their average network connectivity, and the bottom quartile removed, then 100% of the remaining members are part of this same yeast ribosome structure, which shows that in this overlap set the high connectivity genes were in fact the members of the yeast ribosome. finally, the overlap of genes detected in the rrna modules overlap identified purine and pyrimidine synthesis and rna polymerase pathways. these pathways dominate this list with out of the identified matches to the kegg database. unlike the previous two results however, multiple pathways are found that represent this module. the three network modules discussed all contain large protein complexes. this is in agreement with the recent discovery that there is often a correlation between genes that are expressed together and proteins that bind to each other. however, there is no reason to believe that modules in co-expression networks will always correspond to protein complexes since our module detection method should find any set of genes with high pair-wise correlations. any experimental perturbation that gives rise to a highly correlated gene set is expected to result in a corresponding network module. intramodular network connectivity relationships having identified functionally similar modules in the three different datasets, we assessed whether these same modules contain the same information as the entire network. is the connectivity of a gene within the identified modules correlated with the likelihood that a gene was essential by deletion analysis and also whether it was conserved? to test connectivity correlations within these modules, we define the intramodular connectivity as the sum of all connectivity measures only with genes within the same module. similar to that performed for the total gene connectivity within the whole network, binned values were plotted to observe the possible relationships. to evaluate significance, spearman correlation coefficients for the ranked but unbinned data were calculated for relationship of k.in to essentiality and sequence conservation. interestingly, there was a general trend to similar correlations as that seen within the whole network. the correlation with sequence conservation was generally weak: the ubiquitin module formed from the dd dataset and the rrna processing modules in the er and cc were the most correlated with k.in. there was a correlation of k.in and essentiality in all three datasets within the rrna processing module, and for two of the datasets within the ubiquitin module, and a trend towards a weak anticorrelation within the protein synthesis module. thus, some of the relationships between connectivity and essentiality or sequence conservation and not detected when the analysis is restricted within the modules. characterizing modules that contain essential hub genes the relationship between intramodular connectivity and essentiality is not necessarily universal for any module in any dataset. whether or not a module contains meaningful information for predicting essentiality depends on the expression data that were analyzed. one can view the correlation of k.in and essentiality as a test of the modules importance. the key issue is that in order for a module to demonstrate this relationship, there must be a sufficient number of essential genes within the module. as some modules have substantially fewer essential genes than others, there is little power to detect any relationship with k.in within those modules. we calculated the spearman correlation between the proportion of essential genes within a module and the correlation of k.in with essentiality and show that there is a strong positive correlation. since in actual applications the goal will be to find unknown'essential' genes, it would be preferable to have another metric of'essential' gene enrichment. in this regard, it is interesting to note that of the three modules studied in the datasets, there were that had a correlation of k.in with sequence conservation. of these modules, all were shown to have a strong relationship of k.in with essentiality in the same modules. of the without a correlation, only one showed a correlation between k.in and essentiality. thus, the detection of a relationship between intramodular connectivity and sequence conservation may predict those modules with a relationship between k.in and essentiality. discussion our results extend the inferences made from protein and metabolic networks to the more prolific datasets available from gene expression data. these results are made possible due to broad surveys of expression and the comprehensive characterization of the yeast genome with deletion mutants. in contrast to gene expression data, which are based on the assessment of cells in many different states of perturbation, protein interaction measurements are determined in only a limited set of conditions which by nature only capture a subset of all possible protein-protein interactions. others have constructed gene perturbation networks by looking at the expression changes when individual genes are eliminated or in relation to transcription factor expression. microarray based surveys of gene expression allow detailed surveys of gene expression across a wide variety of experimental perturbations. from these data a strong correlation of gene expression for two genes implies that both genes act within a common functional group and are under similar transcriptional control. since these networks are not based on direct measurements of protein binding/interaction, the presence of two genes that are highly correlated has a different interpretation than that derived from a protein interaction network. in a co-expression network, two closely tied nodes would be highly correlated but not necessarily direct binding partners. in spite of this key difference, numerous other studies have indicated that genes that are correlated with each other across a modest range of experiments tend to function in similar ways and that this functional categorization is strengthened when gene co-expression exists across large evolutionary distances. here, we use a more general weighted gene co-expression network construction method for network construction that can be applied generically to microarray data using simple correlational analyses of individual genes. advantages of weighted networks over unweighted networks based on dichotomizing the correlation matrix include a) that the continuous nature of the gene co-expression information is preserved and b) that the results of weighted network analyses are highly robust with respect to the choice of the parameter β,. we show that there is a strong correlation with the weighted gene co-expression connectivity measure and gene essentiality and sequence conservation. our analysis demonstrates that individual conserved modules are identifiable within a network. moreover, the presence of these modules, which were detected in three independent networks, illustrates that these networks have a structure to them which matches known cellular biology. we have also shown that when sufficient information is available, these correlation modules can provide further information about which of their members are more likely to be important for a given process. the ability to assess whether or not a module is complete enough to be informative using a test like either of the ones employed here will be important for validating the merit of less understood modules in the future. our study extends the strong links between the network properties of a gene within co-expression networks and the global importance of each gene to the yeast cell, and may have implications for targeted drug therapy in more complex biological systems like cancer. for instance, one can infer from an analysis of the single gene deletion data that single targets for inhibition can be partially predicted from expression data. however, in biological systems an optimal effect is frequently achieved by inhibiting multiple specific targets. can we extrapolate network positions and relationships to infer effective combinations of targeted therapeutics? yeast is an excellent model for establishing the rules for applying network theories to practical predictions. for instance, will double deletions of high connectivity genes within the network which reside in the same module have substantially greater negative consequences to the yeast than double deletions of low connectivity genes? alternatively, will genes which are connecting distinct modules, and serving as key connections between integrators prove to be better disruption targets? the modeling of such proposed interactions in yeast is attractive because of the relative tractability of yeast studies and the availability of large scale datasets. technologies like synthetic genetic arrays which automate double deletion screens or chemical genomic profiling provide an expanding capability to survey the effects of multiple target inhibition or deletion. however, even with these powerful methods, only a small fraction of the millions of possible combinations will be assayed. for instance in a substantial recent survey of double deletions only % of all possible double deletions were tested for synthetic lethality. thus, network based modeling may be a useful adjunct for the design of double knockout experiments or combination inhibition experiments to permit a more efficient search for synthetic lethals. an interplay between predictive models and targeted large scale inhibition studies may be quite useful for surveying pathway analysis in yeast. in the long term, such studies may also be critical in the development of therapies for diseases like cancer.  in conclusion, our study demonstrates that weighted gene co-expression networks can be used to predict both the likelihood of essentiality and the likelihood of conservation for their gene members within the entire network. furthermore, we show that these networks can be subdivided into identifiable modules, which themselves can often contain enough individual information to indicate which genes are more likely to be crucial for a particular process. we have indicated a means for testing whether this is true or not. thus, we have illustrated how this process can be applied to common microarray data for the purpose of predicting both functional assignment as well as the ranking of gene significance in a particular process with which it is found to be associated. we believe that these kinds of predictions will be helpful for identifying gene targets for therapeutics and for directing multi-drug therapies. 
here we investigate the properties of weighted gene co-expression networks formed from multiple microarray datasets. we show strong positive correlations between gene connectivity within the whole network and gene essentiality as well as gene sequence conservation. highly connected hub proteins, largely responsible for maintaining network connectivity, have been found to be much more likely to be essential for yeast survival. application of these techniques can allow a finer scale prediction of relative gene importance for a particular process within a group of similarly expressed genes. we demonstrate the preservation of a modular structure of the networks formed, and demonstrate that, within some of these modules, it is possible to observe a strong correlation between connectivity and essentiality or between connectivity and conservation within the modules particularly within modules containing larger numbers of essential genes.
 genes and proteins are organized into functional modular networks in which the network context of a gene or protein has implications for cellular function. highly connected hub proteins, largely responsible for maintaining network connectivity, have been found to be much more likely to be essential for yeast survival.  here we investigate the properties of weighted gene co-expression networks formed from multiple microarray datasets. the constructed networks approximate scale-free topology, but this is not universal across all datasets. we show strong positive correlations between gene connectivity within the whole network and gene essentiality as well as gene sequence conservation. we demonstrate the preservation of a modular structure of the networks formed, and demonstrate that, within some of these modules, it is possible to observe a strong correlation between connectivity and essentiality or between connectivity and conservation within the modules particularly within modules containing larger numbers of essential genes.  application of these techniques can allow a finer scale prediction of relative gene importance for a particular process within a group of similarly expressed genes. 