GeneSignDB (http://compbio.dfci.harvard.edu/genesigdb/) 17 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. 94 distinct human breast cancer signatures are obtained, which are reported in 58 different literatures. Since the genes which are included in only one gene signature may be generated by chance, we discard these unreliable genes.

A complete human PIN is constructed by integrating protein interaction data from Human Protein Reference Database (HPRD) and BioGRID interaction database 1819. After removal of duplicate edges and self-interactions, we got a PIN that is consisted by 51057 distinct interactions among 11465 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 2924 proteins and 4698 interactions.

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 20. 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(V,E), the six measurements of centrality used in this study are defined as following:

• Degree centrality(DC): The degree centrality DC(i) of vertex i is the number of edges connecting node i and its neighbors 21.

D C ( i ) = D e g ( i ) ,

where Deg(i) is the degree of vertexes i.

• Betweenness centrality(BC): The betweenness centrality BC(i) of a node i is the average fraction of shortest paths that pass through the node i 22.

B C ( i ) = ∑ s ∑ t σ s t ( i ) σ s t , s ≠ t ≠ i ,

where σ_st denotes the total number of shortest paths between s and t and σ_st(i) denotes the number of shortest paths from s to t that pass through the node i.

• Closeness centrality(CC): The closeness centrality CC of node i can defined as 23:

C C ( i ) = 1 ∑ j ≠ i c p ( i , j )

CC is a global metric which describes how the given node i connects to other nodes.

• Subgraph centrality(SC): The subgraph centrality SC(i) of node i can be defined as 24:

S C = ∑ l = 0 ∞ μ l ( i ) l ! ,

where μ_l(i) denotes the number of closed walks of length l which starts and ends at node i.

• Eigenvector centrality(EC): The eigenvector centrality EC(i) 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(i) = e₁(i), where e₁ corresponds to the largest eigenvalue of A 25.

• Information centrality(IC): The information centrality IC(i) of node i in a is defined as 26:

I C ( i ) = [ 1 n ∑ j 1 I i j ] - 1 ,

where n is the number of nodes in graph G and I_ij = (r_ii + r_jj - r_ij) - 1, where r_ij 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 = (r_ij) = [D - A+ J] - 1. For computational purposes, I_ii is defined as infinite. Thus, 1 I i i = 0 .

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.

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 27282930. Basically, the p-value is defined as following:

P = 1 - ∑ i = 0 k - 1 C i G - C n - i G n ,

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 6 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(P) with the annotation 31.

Gene set enrichment analysis for KEGG pathways is very similar to the one for GO annotations. In Equation 6, 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 32.

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.

As mentioned in Methods section, 94 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 3260 genes, and the smallest signature only contains 4 genes. The median size of these signatures is 46.

To evaluate the similarity among these gene signatures, we analyze the overlap among the 94 gene signatures (see Table 1). The analysis result is very consistent with the results reported in literature 15. A very small overlap is found among different signatures. 4143 (58.6% of the total number) genes are found in only one signature, but only 24(0.4%) genes overlapped 10 or more signatures, and none of the genes overlapped all 94 signatures. The lack of overlapping is an obstacle to integrate various signatures of breast cancer.

All genes included in the 94 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 2924 proteins and 4698 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 1. In a recent similar study performed by Chen et.al, based on a context-constrained network that obtained from literatures, 10 published gene signatures are integrated and a 54-genes signature is obtained 15. This result is named as "Chen's signature" in the rest of this paper. For comparison, we also select 54 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 2.

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 54 genes identified by EC and SC are the same. By contrast, overlap between our results and Chen's gene signature is only 5-8(9.3%-14.8%, p-value < 0.05).

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, TP53 gene, which is already known as a tumor suppressor, is always the most important gene. Another similar example is breast cancer type 1 susceptibility protein (BRCA1). As we expected, our result also shows that BRCA1 plays an important role in the breast cancer. Other similar examples include epidermal growth factor receptor (EGFR), E1A binding protein p300(E300), Androgen receptor gene(AR) and so on (see Table 2).

However, another well-known breast cancer gene, BRCA2, is not included in any signature identified by the six centrality measurement. This is because BRCA2 is included in only one original signature and was discarded when we constructed the context-constrained PIN. On the one hand, the absence of BRCA2 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 BRCA2 in out signature indicates that our method can be improved by refining the signature genes collection method.

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 3, 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 2. The most dense networks are consisted by the disease genes that are identified by EC and SC.

As shown in Table 4, 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.

Biological process GO enrichment analysis is performed on each gene signatures (see Table 5). For each signature, the GO biological process with highest p-score and corresponding p-score are presented in Table 5. Unlike the genes identified in Chen's study 15, 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".

The structure of GO terms is a tree-like structure (see Figure 3. The term "regulation of biological regulation", which is located at the same level of "cell cycle", is the ancestor of "positive regulation of macromolecule metabolic process". According to G2SBC database 33, only 190 breast cancer genes are annotated by "Cell Cycle", but 1159 breast cancer genes are annotated by "regulation of biological process". This indicates that the gene signatures identified by graph centrality are probably more tightly related to breast cancer.

According to the p-score, both the two types of enrichment analysis suggested that EC and SC are probably the best choices to identify disease genes from context-constrained network and integrate different gene signatures. As reported in literatures, SC also has superior performance in the discovery of essential proteins in protein interaction network 34 and essential proteins tend to have higher correlation with dominant and recessive mutants of disease genes 35. This is possibly the reason that SC and EC outperformed other centrality measurements. We also note that the PINs that are consisted by the disease genes identified by EC and SC are denser than that of other centrality measurements(see Table 3). This indicates that breast cancer genes have tight and complicated relationship with each other.

Since SC and EC outperform in functional enrichment analysis, we tested the SC and EC based gene signatures in a genome-wide microarray dataset: GSE7390 36. This microarray dataset is downloaded from NCBI GEO database and includes 198 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 198 patients in GSE7390 were divided into two main clusters (Additional File 2), the first cluster includes 118 samples, and the second cluster includes 80 samples. The mean value of each attribute of the samples in each cluster are listed in Table 6. As shown in Table 6, 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.

In the first cluster of patients, 104 of them were ER+; and in the second cluster of patients, only 30 of them were ER+. The p-value calculated by ANOVA is 2.47 × 10^-13. 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 97 patients were longer than 2000 days; and in the second cluster, that number is only 55. The p-value is 0.04254. Normally, p-value that smaller than 0.05 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.