BACKGROUND
a gene signature is a group of genes whose expression pattern represents the status of a gene expression disease  <cit> .
by using the microarray technology, which has developed rapidly in last ten years, various gene signatures are developed for various complex diseases, especially the cancer.
since researchers found that gene-expression signatures are able to predict clinical outcome of breast cancer in  <dig>  <cit> , it have become a hot topic and attracted the attention of both biologists and oncologists.
signatures for various phenotypes, such as poor prognosis  <cit> , invasiveness  <cit> , recurrence  <cit> , and metastasis  <cit> , have been experimentally derived from patient groups and biological hypotheses.
however, distinct signatures share very few genes, even though they paradoxically occupy a common prognosis space.
for both cancer biologists and oncologists, a critical problem is whether these disjoint genetic signatures can provide a unified insight on the relationship between gene expression and clinical outcome.
obviously, complex heterogeneity of signatures caused by different probe design, different platforms, or inadequate patient samples, becomes an obstacle when trying to integrate various signatures of breast cancer.
gene ontology enrichment, pathway analysis, and some genome-scale methods are proposed to explain the lack of overlap  <cit> .
in literature  <cit> , the authors list five possible explanations for the small overlap between signatures:
<dig>  heterogeneity in expression due to different platform technologies and references;
<dig>  differences in supervised protocols with which signatures are extracted;
<dig>  although the genes are not exactly the same, they represent the same set of pathways;
<dig>  differences in clinical composition between datasets ;
<dig>  small sample size problems that cause inaccurate signatures.
through a large-scale analysis that performed on  <dig> breast cancer samples from affymetrix platform, the authors of literature  <cit>  conclude that the small signature overlap is most likely due to small sample size problem .
however, the conclusion might be specific to the datasets and the specific techniques used in their work.
by comparison of three prognostic gene expression signatures for breast cancer, literature  <cit>  suggested that the small overlap between the different prognostic gene signatures is because these different signatures represented largely overlapping biological processes .
by taking into account the biological knowledge that exists among different signatures, the authors of  <cit>  found that different signatures are similar at biological level, rather than gene level .
much work has been done in an effort to understand the small overlap between gene signatures, but so far there is no widely accepted explanation.
meanwhile, computational biologists have developed protein interaction networks that effectively have been used to analyze protein interactions underpinning share sub-phenotypes among otherwise seemingly disparate disease, such as retinitis pigmentosa, epithelial ovarian cancer, inflammatory bowel disease, amyotrophic lateral sclerosis, alzheimer disease, type  <dig> diabetes, coronary heart disease  <cit>  and head and neck tumor metastasis  <cit> .
for an individual expression signature in breast cancer, protein interaction networks are successfully used to predict prognosis  <cit>  and detect subnetwork signatures of metastatic disease  <cit> .
more recently, in  <cit> , on genome-wide coexpression networks for different disease states, the authors used univariate cox model and relief algorithm to select the genes that are the most predictive of clinical outcome to construct gene signature for lung cancer.
a 13-gene lung cancer prognosis signature with significant prognostic stratifications is identified by this method.
by single protein analysis of net-works and conservative permutation re-sampling, a small, but more biological significant breast cancer signature consisted by  <dig> genes is identified from a protein interaction network include  <dig> cancer-related genes curated from literatures  <cit> .
in reference  <cit> , by integrating biological knowledge and different signatures, the authors derived a unified signature that is more robust than original signatures.
however, to integrate different breast cancer signatures, most existing methods need cancer domain knowledge, such as cancer-related literature used in  <cit> .
this limited the application of these methods.
in this paper, we describe a method to integrate different breast cancer signatures by using graph centrality in a context-constrained pin for human breast cancer which is constructed by integrating disjoint gene signatures reported in previous literatures.
unlike most existing methods, the method proposed in this paper is able to integrate distinct gene signatures without cancer domain knowledge.
by gene ontology  enrichment analysis, kyoto encyclopedia of genes and genomes  enrichment analysis and relating our results to previous biological studies, we show that the genes in centrality-based signatures are tightly related to breast cancer and are able to predict clinical outcome.
methods
to identify reliable gene signature of breast cancer by integrating various gene signatures, we propose a graph centrality based method to identify disease genes from a constrained pin and the overview of this method is provided in figure  <dig>  briefly, as shown in figure  <dig>  the method proposed here has three steps:
<dig>  collect genes from different breast cancer gene signatures, and discard the genes that exist in only one signature.
<dig>  project the genes collected in step  <dig>  to human pin to construct a context-constrained pin that consisted.
therefore, to some extent, all genes in this context-constrained network are related to breast cancer.
however, we don't know which genes are the most important ones to the breast cancer and can be used to predict clinical outcome.
<dig>  to determine the relationship between genes and breast cancer, we calculated graph centrality of each gene in this constrained pin.
since the constrained pin is built based on breast cancer gene signatures, graph centrality of genes in this network indicates their relationship to breast cancer.
output given number of genes with highest graph centrality as the new unified breast cancer signature.
details of the three steps are described in following three subsections and then validation methods are presented.
collecting genes from different signatures
genesigndb   <cit>  is a curated gene signatures database that collected gene signatures for various species and diseases.
keywords "breast cancer" for disease and "human" for species are used to search gene signatures for human breast cancer in genesigndb.
<dig> distinct human breast cancer signatures are obtained, which are reported in  <dig> different literatures.
since the genes which are included in only one gene signature may be generated by chance, we discard these unreliable genes.
construction of context-constrained pin
a complete human pin is constructed by integrating protein interaction data from human protein reference database  and biogrid interaction database  <cit> .
after removal of duplicate edges and self-interactions, we got a pin that is consisted by  <dig> distinct interactions among  <dig> proteins.
then, the genes we collected in the first step are projected to the complete human pin and a constrained pin for human breast cancer is obtained.
this constrained pin contains  <dig> proteins and  <dig> interactions.
use graph centrality to quantify the relationship between genes and breast cancer
various definitions of graph centrality have been proposed from different perspectives to evaluate the importance of nodes in a graph.
the concept has been widely used in bioinformatics, such as discovery of essential proteins in protein networks  <cit> .
because it is difficult to infer which definition is best for identifying disease genes in the context-constrained network, we evaluated six different definitions in our work.
for a protein interaction network g, the six measurements of centrality used in this study are defined as following:
• degree centrality: the degree centrality dc of vertex i is the number of edges connecting node i and its neighbors  <cit> .
dc=deg,
where deg is the degree of vertexes i.
• betweenness centrality: the betweenness centrality bc of a node i is the average fraction of shortest paths that pass through the node i  <cit> .
bc= ∑s∑tσstσst,s≠t≠i,
where σst denotes the total number of shortest paths between s and t and σst denotes the number of shortest paths from s to t that pass through the node i.
• closeness centrality: the closeness centrality cc of node i can defined as  <cit> :
cc=1∑j≠icp
cc is a global metric which describes how the given node i connects to other nodes.
• subgraph centrality: the subgraph centrality sc of node i can be defined as  <cit> :
sc= ∑l=0∞μll!,
where μl denotes the number of closed walks of length l which starts and ends at node i.
• eigenvector centrality: the eigenvector centrality ec of node i is defined as the ith component of the principal eigenvector of a, where a is an adjacent matrix.
let λ be an eigenvalue and e be the eigenvector.
then for an equation λe = ae, we can obtain ec = e <dig>  where e <dig> corresponds to the largest eigenvalue of a  <cit> .
• information centrality: the information centrality ic of node i in a is defined as  <cit> :
ic=- <dig>
where n is the number of nodes in graph g and iij =  -  <dig>  where rij is the element of matrix r. let d be a diagonal matrix of the weighted degree of each node and j be a matrix with all its elements equal to one.
then, we get r =  =  -  <dig>  for computational purposes, iii is defined as infinite.
thus, 1iii= <dig>
high centrality of a gene indicates that it is important to the constrained pin and probably plays an important role in mechanism of breast cancer development.
therefore, according to the graph centrality of genes, we get a gene list that is ordered by the genes' importance to human breast cancer.
depending on specific purpose, a given number of top genes can be selected to construct a reliable gene signature of breast cancer.
the reliable gene signature is the integration of the disjoint original signatures.
kegg pathway and gene ontology enrichment analysis
p-value based on the hypergenometirc distribution is widely used as a measurement of the extent to which the clusters are annotated by a specific go term  <cit> .
basically, the p-value is defined as following:
p=1-∑i=0k-1cig-cn-ign,
where c is the size of the gene set containing k gene with a given go term; g is the size of the universal set of known genes and contains n genes with the annotation.
low p in formula  <dig> indicates that the module closely corresponds to the go annotation because the network has a rare chance to produce the module.
to simplify our analysis, we define p-score as the negative of log with the annotation  <cit> .
gene set enrichment analysis for kegg pathways is very similar to the one for go annotations.
in equation  <dig>  c is the size of the gene set containing k genes that exist in a given kegg pathway; g is the size of the universal set of known genes and contains n genes that exist in the pathway.
similarly, p-score can be used to measure the relationship between the gene set and a specific kegg pathway.
in this study, both kegg and go enrichment analysis are performed on david  <cit> .
validate on microarray dataset
to evaluate the signature's ability to predict clincal outcome, we used expression intensity of the genes in the signature to cluster microarray datasets of breast cancer patients with different pathologic parameters.
patients with similar pathologic parameters should be clustered togather.
for a given pathologic parameter, the p-value of the clustering result indicates the signature's ability to predict the pathologic parameter.
in this study, euclidean distance between samples are calculated by using the expression intensity of genes in gene signature.
then hierarchical clustering is used to cluster the microarry datasets of breast cancer patients.
RESULTS
overlap among breast cancer signatures
as mentioned in methods section,  <dig> breast cancer gene signatures are obtained from public database.
since the different generation methods and the various purposes of these signatures, the size of these signatures are very different.
the biggest signature contains  <dig> genes, and the smallest signature only contains  <dig> genes.
the median size of these signatures is  <dig>
to evaluate the similarity among these gene signatures, we analyze the overlap among the  <dig> gene signatures .
the analysis result is very consistent with the results reported in literature  <cit> .
a very small overlap is found among different signatures.
<dig>  genes are found in only one signature, but only  <dig> genes overlapped  <dig> or more signatures, and none of the genes overlapped all  <dig> signatures.
the lack of overlapping is an obstacle to integrate various signatures of breast cancer.
there is very small overlap among distinct breast cancer signatures.
most genes exist in only one signature, and only  <dig> genes are included in  <dig> or more signatures.
centrality based gene signatures
all genes included in the  <dig> signatures are projected to the human pin described in methods section.
in consideration of the lower reliability of gene signatures, only the genes that are included in two or more different signatures are used to construct the context-constrained pin of breast cancer.
finally, this context-constrained pin contains  <dig> proteins and  <dig> interactions.
then, six graph centralities of each genes in this context-constrained pin are calculated.
higher centrality for a gene indicates that the gene is more important to this network and should be more tightly related to breast cancer.
graph centrality of each gene in the context-constrained pin is calculated and provided in additional file  <dig>  in a recent similar study performed by chen et.al, based on a context-constrained network that obtained from literatures,  <dig> published gene signatures are integrated and a 54-genes signature is obtained  <cit> .
this result is named as "chen's signature" in the rest of this paper.
for comparison, we also select  <dig> most important genes identified by each centrality definitions to construct gene signatures.
full list of genes in these graph centrality based signatures are provided in table  <dig>
<dig> genes with highest graph centrality in the context-constrained pin are selected to consist new breast cancer gene signatures.
the genes in the six signatures identified by six graph centrality measurements are listed in this table.
since all the six graph centrality definitions are designed to measure the importance of a node to a graph, gene signatures identified by the six centrality measurements are similar with each other.
a extremely case is all the top  <dig> genes identified by ec and sc are the same.
by contrast, overlap between our results and chen's gene signature is only 5- <dig>
an interesting result is found in our work.
no matter which centrality measurement is used to evaluate the importance of genes in the context-constrained network, tp <dig> gene, which is already known as a tumor suppressor, is always the most important gene.
another similar example is breast cancer type  <dig> susceptibility protein .
as we expected, our result also shows that brca <dig> plays an important role in the breast cancer.
other similar examples include epidermal growth factor receptor , e1a binding protein p <dig>  androgen receptor gene and so on .
however, another well-known breast cancer gene, brca <dig>  is not included in any signature identified by the six centrality measurement.
this is because brca <dig> is included in only one original signature and was discarded when we constructed the context-constrained pin.
on the one hand, the absence of brca <dig> is also a evidence to prove that the quality of existing breast cancer gene signatures is low, and on the other hand, the absence of brca <dig> in out signature indicates that our method can be improved by refining the signature genes collection method.
relationship among genes in gene signatures
to investigate the relationship among genes in the gene signatures, seven sub pins are constructed by projecting genes in each gene signature to the complete human pin.
as shown in table  <dig>  the sub pins consisted by the genes in the graph centrality based gene signatures are much denser than that consisted by the genes in chen's signature.
we also can observe the significant difference in figure  <dig>  the most dense networks are consisted by the disease genes that are identified by ec and sc.
to investigate the differences between graph centrality based gene signatures and that reported in previous literature, topological size of sub-network consisted by the genes in these gene signatures are calculated and presented in this table.
it should be note that the sub-network consisted by the genes included in chen's gene signature is not a connected graph.
the number in parenthesis is the number of proteins of its biggest connected component.
kegg pathways enrichment analysis
as shown in table  <dig>  the most significant kegg pathway of all six graph centrality-based gene signatures are "pathways in cancer", but that of chen's gene signature is "cell cycle".
chen's gene signature is also annotated by "pathways in cancer", but the p-score is very low.
it is obvious that graph centrality based method is more powerful than span to identify cancer related genes in a constrained pin.
to investigate the relationship between the gene signatures and cancer-related pathways, kegg pathway enrichment analysis is preformed on these signatures.
go enrichment analysis
biological process go enrichment analysis is performed on each gene signatures .
for each signature, the go biological process with highest p-score and corresponding p-score are presented in table  <dig>  unlike the genes identified in chen's study  <cit> , which is annotated by term "cell cycle", five centrality-based gene signatures are annotated by "positive regulation of macromolecule metabolic process" and only the gene signature identified by bc is annotated by "response to organic substance".
to investigate the relationship between the gene signatures and cancer-related biological processes, gene ontology enrichment analysis is preformed on these signatures.
the structure of go terms is a tree-like structure .
this indicates that breast cancer genes have tight and complicated relationship with each other.
validate of the prognostic potential of the subgraph centrality based gene signature
since sc and ec outperform in functional enrichment analysis, we tested the sc and ec based gene signatures in a genome-wide microarray dataset: gse <dig>  <cit> .
this microarray dataset is downloaded from ncbi geo database and includes  <dig> breast cancer patients width different pre-diagnosed pathologic parameters.
we analyze the relationship between the sc based signature genes and hormone receptor status using hierarchical clustering.
the  <dig> patients in gse <dig> were divided into two main clusters , the first cluster includes  <dig> samples, and the second cluster includes  <dig> samples.
the mean value of each attribute of the samples in each cluster are listed in table  <dig>  as shown in table  <dig>  the tumor size and npi score of the first cluster is smaller than those of the second cluster.
disease-free survival time, overall survival time, distant metastasis-free survival time, 10-year overall survival probability and time to distant metastasis of the patients in the first cluster is longer than those of the patients in the second cluster.
in another word, the condition of patients in the first cluster is much better than the second cluster of patients.
mean value of each clinical outcome recorded in the microarray dataset of the samples in each cluster is presented in this table.
in the first cluster of patients,  <dig> of them were er+; and in the second cluster of patients, only  <dig> of them were er+.
the p-value calculated by anova is  <dig>  × 10- <dig>  we also explored the relationship between the signature genes and the time to distant metastasis.
in the first cluster, the time to distant metastasis of  <dig> patients were longer than  <dig> days; and in the second cluster, that number is only  <dig>  the p-value is  <dig> .
normally, p-value that smaller than  <dig>  means the result is statistic significant and is not generated by chance.
such small p-value of the clustering result indicates that the sc based signature is able to predict the clinical outcome very well.
discussion and
CONCLUSIONS
identification of genes which play important roles in the development of cancer is a critical problem needed to solve in current research of various cancers.
gene expression signatures provide a way to find significant cancer genes in given groups of patients.
due to the low overlap between heterogeneous signatures, how to integrate them is becoming a serious problem.
fortunately, as shown in this paper, graph centralities, especially ec and sc, are useful tools to integrate existing different cancer gene signatures.
as well-known, weighted protein interaction network can be constructed by integrating functional annotations, and centrality is also can be extended to weighted network easily  <cit> .
more promising results should be found in the weighted protein interaction network.
besides this, other topological parameters from graph theory may improve this method as well.
competing interests
the authors declare that they have no competing interests.
authors' contributions
gc conceived and carried out this work under the guidance and supervision of jw.
jw, gc and ml drafted the manuscript together.
yp participated in revising the draft.
all authors have read and approved the manuscript.
supplementary material
additional file 1
graph centrality of genes in the context-constrained pin.
in this study, graph centrality of each gene in the context-constrained pin is calculated and used to quantify the relationship between genes and the breast cancer.
the calculation results are provided in this additional file.
click here for file
additional file 2
sc-based gene signature based hierarchical clustering analysis of breast cancer microarray dataset by using sc-based gene signature.
according to the gene signature identified by sc, hierarchical clustering analysis is performed on the breast cancer microarray dataset, gse <dig>  which include  <dig> breast cancer patients with various pathologic parameters.
click here for file
acknowledgements
this work is supported in part by the national natural science foundation of china under grant no.
<dig> and no.
<dig>  the ph.d. programs foundation of ministry of education of china no.
<dig>  the freedom explore program of central south university no.
<dig>  and the u.s. national science foundation under grants ccf- <dig>  ccf- <dig>  and cns- <dig>
this article has been published as part of bmc systems biology volume  <dig> supplement  <dig>  2011: biocomp  <dig> - the  <dig> international conference on bioinformatics & computational biology: systems biology.
the full contents of the supplement are available online at http://www.biomedcentral.com/1752-0509/5?issue=s <dig>

 a gene signature is a group of genes whose expression pattern represents the status of a gene expression disease. by using the microarray technology, which has developed rapidly in last ten years, various gene signatures are developed for various complex diseases, especially the cancer. since researchers found that gene-expression signatures are able to predict clinical outcome of breast cancer in, it have become a hot topic and attracted the attention of both biologists and oncologists. signatures for various phenotypes, such as poor prognosis, invasiveness, recurrence, and metastasis, have been experimentally derived from patient groups and biological hypotheses. however, distinct signatures share very few genes, even though they paradoxically occupy a common prognosis space. for both cancer biologists and oncologists, a critical problem is whether these disjoint genetic signatures can provide a unified insight on the relationship between gene expression and clinical outcome. obviously, complex heterogeneity of signatures caused by different probe design, different platforms, or inadequate patient samples, becomes an obstacle when trying to integrate various signatures of breast cancer. gene ontology enrichment, pathway analysis, and some genome-scale methods are proposed to explain the lack of overlap. in literature, the authors list five possible explanations for the small overlap between signatures: heterogeneity in expression due to different platform technologies and references; differences in supervised protocols with which signatures are extracted; although the genes are not exactly the same, they represent the same set of pathways; differences in clinical composition between datasets; small sample size problems that cause inaccurate signatures. through a large-scale analysis that performed on breast cancer samples from affymetrix platform, the authors of literature conclude that the small signature overlap is most likely due to small sample size problem. however, the conclusion might be specific to the datasets and the specific techniques used in their work. by comparison of three prognostic gene expression signatures for breast cancer, literature suggested that the small overlap between the different prognostic gene signatures is because these different signatures represented largely overlapping biological processes. by taking into account the biological knowledge that exists among different signatures, the authors of found that different signatures are similar at biological level, rather than gene level. much work has been done in an effort to understand the small overlap between gene signatures, but so far there is no widely accepted explanation. meanwhile, computational biologists have developed protein interaction networks that effectively have been used to analyze protein interactions underpinning share sub-phenotypes among otherwise seemingly disparate disease, such as retinitis pigmentosa, epithelial ovarian cancer, inflammatory bowel disease, amyotrophic lateral sclerosis, alzheimer disease, type diabetes, coronary heart disease and head and neck tumor metastasis. for an individual expression signature in breast cancer, protein interaction networks are successfully used to predict prognosis and detect subnetwork signatures of metastatic disease. more recently, in, on genome-wide coexpression networks for different disease states, the authors used univariate cox model and relief algorithm to select the genes that are the most predictive of clinical outcome to construct gene signature for lung cancer. a 13-gene lung cancer prognosis signature with significant prognostic stratifications is identified by this method. by single protein analysis of net-works and conservative permutation re-sampling, a small, but more biological significant breast cancer signature consisted by genes is identified from a protein interaction network include cancer-related genes curated from literatures. in reference, by integrating biological knowledge and different signatures, the authors derived a unified signature that is more robust than original signatures. however, to integrate different breast cancer signatures, most existing methods need cancer domain knowledge, such as cancer-related literature used in. this limited the application of these methods. in this paper, we describe a method to integrate different breast cancer signatures by using graph centrality in a context-constrained pin for human breast cancer which is constructed by integrating disjoint gene signatures reported in previous literatures. unlike most existing methods, the method proposed in this paper is able to integrate distinct gene signatures without cancer domain knowledge. by gene ontology enrichment analysis, kyoto encyclopedia of genes and genomes enrichment analysis and relating our results to previous biological studies, we show that the genes in centrality-based signatures are tightly related to breast cancer and are able to predict clinical outcome. methods to identify reliable gene signature of breast cancer by integrating various gene signatures, we propose a graph centrality based method to identify disease genes from a constrained pin and the overview of this method is provided in figure briefly, as shown in figure the method proposed here has three steps: collect genes from different breast cancer gene signatures, and discard the genes that exist in only one signature. project the genes collected in step to human pin to construct a context-constrained pin that consisted. therefore, to some extent, all genes in this context-constrained network are related to breast cancer. however, we don't know which genes are the most important ones to the breast cancer and can be used to predict clinical outcome. to determine the relationship between genes and breast cancer, we calculated graph centrality of each gene in this constrained pin. since the constrained pin is built based on breast cancer gene signatures, graph centrality of genes in this network indicates their relationship to breast cancer. output given number of genes with highest graph centrality as the new unified breast cancer signature. details of the three steps are described in following three subsections and then validation methods are presented. collecting genes from different signatures genesigndb is a curated gene signatures database that collected gene signatures for various species and diseases. keywords "breast cancer" for disease and "human" for species are used to search gene signatures for human breast cancer in genesigndb. distinct human breast cancer signatures are obtained, which are reported in different literatures. since the genes which are included in only one gene signature may be generated by chance, we discard these unreliable genes. construction of context-constrained pin a complete human pin is constructed by integrating protein interaction data from human protein reference database and biogrid interaction database. after removal of duplicate edges and self-interactions, we got a pin that is consisted by distinct interactions among proteins. then, the genes we collected in the first step are projected to the complete human pin and a constrained pin for human breast cancer is obtained. this constrained pin contains proteins and interactions. use graph centrality to quantify the relationship between genes and breast cancer various definitions of graph centrality have been proposed from different perspectives to evaluate the importance of nodes in a graph. the concept has been widely used in bioinformatics, such as discovery of essential proteins in protein networks. because it is difficult to infer which definition is best for identifying disease genes in the context-constrained network, we evaluated six different definitions in our work. for a protein interaction network g, the six measurements of centrality used in this study are defined as following: • degree centrality: the degree centrality dc of vertex i is the number of edges connecting node i and its neighbors. dc=deg, where deg is the degree of vertexes i. • betweenness centrality: the betweenness centrality bc of a node i is the average fraction of shortest paths that pass through the node i. bc= ∑s∑tσstσst,s≠t≠i, where σst denotes the total number of shortest paths between s and t and σst denotes the number of shortest paths from s to t that pass through the node i. • closeness centrality: the closeness centrality cc of node i can defined as: cc=1∑j≠icp cc is a global metric which describes how the given node i connects to other nodes. • subgraph centrality: the subgraph centrality sc of node i can be defined as: sc= ∑l=0∞μll!, where μl denotes the number of closed walks of length l which starts and ends at node i. • eigenvector centrality: the eigenvector centrality ec of node i is defined as the ith component of the principal eigenvector of a, where a is an adjacent matrix. let λ be an eigenvalue and e be the eigenvector. then for an equation λe = ae, we can obtain ec = e where e corresponds to the largest eigenvalue of a. • information centrality: the information centrality ic of node i in a is defined as: ic=- where n is the number of nodes in graph g and iij = - where rij is the element of matrix r. let d be a diagonal matrix of the weighted degree of each node and j be a matrix with all its elements equal to one. then, we get r = = - for computational purposes, iii is defined as infinite. thus, 1iii= high centrality of a gene indicates that it is important to the constrained pin and probably plays an important role in mechanism of breast cancer development. therefore, according to the graph centrality of genes, we get a gene list that is ordered by the genes' importance to human breast cancer. depending on specific purpose, a given number of top genes can be selected to construct a reliable gene signature of breast cancer. the reliable gene signature is the integration of the disjoint original signatures. kegg pathway and gene ontology enrichment analysis p-value based on the hypergenometirc distribution is widely used as a measurement of the extent to which the clusters are annotated by a specific go term. basically, the p-value is defined as following: p=1-∑i=0k-1cig-cn-ign, where c is the size of the gene set containing k gene with a given go term; g is the size of the universal set of known genes and contains n genes with the annotation. low p in formula indicates that the module closely corresponds to the go annotation because the network has a rare chance to produce the module. to simplify our analysis, we define p-score as the negative of log with the annotation. gene set enrichment analysis for kegg pathways is very similar to the one for go annotations. in equation c is the size of the gene set containing k genes that exist in a given kegg pathway; g is the size of the universal set of known genes and contains n genes that exist in the pathway. similarly, p-score can be used to measure the relationship between the gene set and a specific kegg pathway. in this study, both kegg and go enrichment analysis are performed on david. validate on microarray dataset to evaluate the signature's ability to predict clincal outcome, we used expression intensity of the genes in the signature to cluster microarray datasets of breast cancer patients with different pathologic parameters. patients with similar pathologic parameters should be clustered togather. for a given pathologic parameter, the p-value of the clustering result indicates the signature's ability to predict the pathologic parameter. in this study, euclidean distance between samples are calculated by using the expression intensity of genes in gene signature. then hierarchical clustering is used to cluster the microarry datasets of breast cancer patients.  overlap among breast cancer signatures as mentioned in methods section, breast cancer gene signatures are obtained from public database. since the different generation methods and the various purposes of these signatures, the size of these signatures are very different. the biggest signature contains genes, and the smallest signature only contains genes. the median size of these signatures is to evaluate the similarity among these gene signatures, we analyze the overlap among the gene signatures. the analysis result is very consistent with the results reported in literature. a very small overlap is found among different signatures. genes are found in only one signature, but only genes overlapped or more signatures, and none of the genes overlapped all signatures. the lack of overlapping is an obstacle to integrate various signatures of breast cancer. there is very small overlap among distinct breast cancer signatures. most genes exist in only one signature, and only genes are included in or more signatures. centrality based gene signatures all genes included in the signatures are projected to the human pin described in methods section. in consideration of the lower reliability of gene signatures, only the genes that are included in two or more different signatures are used to construct the context-constrained pin of breast cancer. finally, this context-constrained pin contains proteins and interactions. then, six graph centralities of each genes in this context-constrained pin are calculated. higher centrality for a gene indicates that the gene is more important to this network and should be more tightly related to breast cancer. graph centrality of each gene in the context-constrained pin is calculated and provided in additional file in a recent similar study performed by chen et.al, based on a context-constrained network that obtained from literatures, published gene signatures are integrated and a 54-genes signature is obtained. this result is named as "chen's signature" in the rest of this paper. for comparison, we also select most important genes identified by each centrality definitions to construct gene signatures. full list of genes in these graph centrality based signatures are provided in table genes with highest graph centrality in the context-constrained pin are selected to consist new breast cancer gene signatures. the genes in the six signatures identified by six graph centrality measurements are listed in this table. since all the six graph centrality definitions are designed to measure the importance of a node to a graph, gene signatures identified by the six centrality measurements are similar with each other. a extremely case is all the top genes identified by ec and sc are the same. by contrast, overlap between our results and chen's gene signature is only 5- an interesting result is found in our work. no matter which centrality measurement is used to evaluate the importance of genes in the context-constrained network, tp gene, which is already known as a tumor suppressor, is always the most important gene. another similar example is breast cancer type susceptibility protein. as we expected, our result also shows that brca plays an important role in the breast cancer. other similar examples include epidermal growth factor receptor, e1a binding protein p androgen receptor gene and so on. however, another well-known breast cancer gene, brca is not included in any signature identified by the six centrality measurement. this is because brca is included in only one original signature and was discarded when we constructed the context-constrained pin. on the one hand, the absence of brca is also a evidence to prove that the quality of existing breast cancer gene signatures is low, and on the other hand, the absence of brca in out signature indicates that our method can be improved by refining the signature genes collection method. relationship among genes in gene signatures to investigate the relationship among genes in the gene signatures, seven sub pins are constructed by projecting genes in each gene signature to the complete human pin. as shown in table the sub pins consisted by the genes in the graph centrality based gene signatures are much denser than that consisted by the genes in chen's signature. we also can observe the significant difference in figure the most dense networks are consisted by the disease genes that are identified by ec and sc. to investigate the differences between graph centrality based gene signatures and that reported in previous literature, topological size of sub-network consisted by the genes in these gene signatures are calculated and presented in this table. it should be note that the sub-network consisted by the genes included in chen's gene signature is not a connected graph. the number in parenthesis is the number of proteins of its biggest connected component. kegg pathways enrichment analysis as shown in table the most significant kegg pathway of all six graph centrality-based gene signatures are "pathways in cancer", but that of chen's gene signature is "cell cycle". chen's gene signature is also annotated by "pathways in cancer", but the p-score is very low. it is obvious that graph centrality based method is more powerful than span to identify cancer related genes in a constrained pin. to investigate the relationship between the gene signatures and cancer-related pathways, kegg pathway enrichment analysis is preformed on these signatures. go enrichment analysis biological process go enrichment analysis is performed on each gene signatures. for each signature, the go biological process with highest p-score and corresponding p-score are presented in table unlike the genes identified in chen's study, which is annotated by term "cell cycle", five centrality-based gene signatures are annotated by "positive regulation of macromolecule metabolic process" and only the gene signature identified by bc is annotated by "response to organic substance". to investigate the relationship between the gene signatures and cancer-related biological processes, gene ontology enrichment analysis is preformed on these signatures. the structure of go terms is a tree-like structure. this indicates that breast cancer genes have tight and complicated relationship with each other. validate of the prognostic potential of the subgraph centrality based gene signature since sc and ec outperform in functional enrichment analysis, we tested the sc and ec based gene signatures in a genome-wide microarray dataset: gse. this microarray dataset is downloaded from ncbi geo database and includes breast cancer patients width different pre-diagnosed pathologic parameters. we analyze the relationship between the sc based signature genes and hormone receptor status using hierarchical clustering. the patients in gse were divided into two main clusters, the first cluster includes samples, and the second cluster includes samples. the mean value of each attribute of the samples in each cluster are listed in table as shown in table the tumor size and npi score of the first cluster is smaller than those of the second cluster. disease-free survival time, overall survival time, distant metastasis-free survival time, 10-year overall survival probability and time to distant metastasis of the patients in the first cluster is longer than those of the patients in the second cluster. in another word, the condition of patients in the first cluster is much better than the second cluster of patients. mean value of each clinical outcome recorded in the microarray dataset of the samples in each cluster is presented in this table. in the first cluster of patients, of them were er+; and in the second cluster of patients, only of them were er+. the p-value calculated by anova is × 10- we also explored the relationship between the signature genes and the time to distant metastasis. in the first cluster, the time to distant metastasis of patients were longer than days; and in the second cluster, that number is only the p-value is. normally, p-value that smaller than means the result is statistic significant and is not generated by chance. such small p-value of the clustering result indicates that the sc based signature is able to predict the clinical outcome very well. discussion and  identification of genes which play important roles in the development of cancer is a critical problem needed to solve in current research of various cancers. gene expression signatures provide a way to find significant cancer genes in given groups of patients. due to the low overlap between heterogeneous signatures, how to integrate them is becoming a serious problem. fortunately, as shown in this paper, graph centralities, especially ec and sc, are useful tools to integrate existing different cancer gene signatures. as well-known, weighted protein interaction network can be constructed by integrating functional annotations, and centrality is also can be extended to weighted network easily. more promising results should be found in the weighted protein interaction network. besides this, other topological parameters from graph theory may improve this method as well. competing interests the authors declare that they have no competing interests. authors' contributions gc conceived and carried out this work under the guidance and supervision of jw. jw, gc and ml drafted the manuscript together. yp participated in revising the draft. all authors have read and approved the manuscript. supplementary material additional file 1 graph centrality of genes in the context-constrained pin. in this study, graph centrality of each gene in the context-constrained pin is calculated and used to quantify the relationship between genes and the breast cancer. the calculation results are provided in this additional file. click here for file additional file 2 sc-based gene signature based hierarchical clustering analysis of breast cancer microarray dataset by using sc-based gene signature. according to the gene signature identified by sc, hierarchical clustering analysis is performed on the breast cancer microarray dataset, gse which include breast cancer patients with various pathologic parameters. click here for file acknowledgements this work is supported in part by the national natural science foundation of china under grant no. and no. the ph.d. programs foundation of ministry of education of china no. the freedom explore program of central south university no. and the u.s. national science foundation under grants ccf- ccf- and cns- this article has been published as part of bmc systems biology volume supplement 2011: biocomp - the international conference on bioinformatics & computational biology: systems biology. the full contents of the supplement are available online at http://www.biomedcentral.com/1752-0509/5?issue=s 
then, we use graph centralities to quantify the importance of genes to breast cancer. compared with previous results by functional enrichment analysis, graph centralities, especially the eigenvector centrality and subgraph centrality, based gene signatures are more tightly related to breast cancer. in summary, graph centralities provide a novel way to connect different cancer signatures and to understand the mechanism of relationship between gene expression and clinical outcome of breast cancer. in this paper, we propose a method to integrate different breast cancer gene signatures by using graph centrality in a context-constrained protein interaction network. the context-constrained pin for breast cancer is built by integrating complete pin and various gene signatures reported in literatures. the genes which are well-known breast cancer genes, such as tp and brca are ranked extremely high in our results. however due to small overlap between different signatures, it is challenging to integrate existing disjoint signatures to provide a unified insight on the association between gene expression and clinical outcome. we validate these signatures on genome-wide microarray dataset and found strong association between the expression of these signature genes and pathologic parameters. various gene-expression signatures for breast cancer are available for the prediction of clinical outcome. moreover, this method is not only can be used on breast cancer, but also can be used on other gene expression related diseases and drug studies. finally, we get reliable gene signatures that are consisted by the genes with high graph centrality. 12- july biocomp - the international conference on bioinformatics and computational biology las vegas, nv, usa
 various gene-expression signatures for breast cancer are available for the prediction of clinical outcome. however due to small overlap between different signatures, it is challenging to integrate existing disjoint signatures to provide a unified insight on the association between gene expression and clinical outcome.  in this paper, we propose a method to integrate different breast cancer gene signatures by using graph centrality in a context-constrained protein interaction network. the context-constrained pin for breast cancer is built by integrating complete pin and various gene signatures reported in literatures. then, we use graph centralities to quantify the importance of genes to breast cancer. finally, we get reliable gene signatures that are consisted by the genes with high graph centrality. the genes which are well-known breast cancer genes, such as tp and brca are ranked extremely high in our results. compared with previous results by functional enrichment analysis, graph centralities, especially the eigenvector centrality and subgraph centrality, based gene signatures are more tightly related to breast cancer. we validate these signatures on genome-wide microarray dataset and found strong association between the expression of these signature genes and pathologic parameters.  in summary, graph centralities provide a novel way to connect different cancer signatures and to understand the mechanism of relationship between gene expression and clinical outcome of breast cancer. moreover, this method is not only can be used on breast cancer, but also can be used on other gene expression related diseases and drug studies. 12- july biocomp - the international conference on bioinformatics and computational biology las vegas, nv, usa 