Network enrichment analysis: extension of gene-set enrichment analysis to gene networks
© Alexeyenko et al.; licensee BioMed Central Ltd. 2012
Received: 17 November 2011
Accepted: 9 August 2012
Published: 11 September 2012
Gene-set enrichment analyses (GEA or GSEA) are commonly used for biological characterization of an experimental gene-set. This is done by finding known functional categories, such as pathways or Gene Ontology terms, that are over-represented in the experimental set; the assessment is based on an overlap statistic. Rich biological information in terms of gene interaction network is now widely available, but this topological information is not used by GEA, so there is a need for methods that exploit this type of information in high-throughput data analysis.
We developed a method of network enrichment analysis (NEA) that extends the overlap statistic in GEA to network links between genes in the experimental set and those in the functional categories. For the crucial step in statistical inference, we developed a fast network randomization algorithm in order to obtain the distribution of any network statistic under the null hypothesis of no association between an experimental gene-set and a functional category. We illustrate the NEA method using gene and protein expression data from a lung cancer study.
The results indicate that the NEA method is more powerful than the traditional GEA, primarily because the relationships between gene sets were more strongly captured by network connectivity rather than by simple overlaps.
List of acronyms and their meanings
Altered gene set
A list of differentially expressed genes in experiment
Functional gene set
A list of genes that were previously known to be related
Gene enrichment analysis
A method of counting overlaps between AGS and FGS
Gene set enrichment analysis
A method using the maximum overlap between AGS and FGS
Network enrichment analysis
A method of measuring network connectivity between AGS and FGS
Fixed network enrichment analysis
A NEA method when AGS is a list of k top-ranking genes
Maximum network enrichment analysis
A NEA method to avoid dependence on k
In parallel with the development of GEA and expression measurement technology, biological knowledge about gene and protein interaction is also growing rapidly. Gene networks readily connect well- and poorly annotated proteins, and combine various biological mechanisms. A few examples of current applications include: inference concerning the functions of previously unannotated genes , extension of GO terms and pathways , finding novel disease genes  and prioritization of disease gene candidates .
There are currently a number of network-based methods that characterize gene sets rather than individual genes. Similarly to GEA, some methods can be considered network enrichment analysis (NEA). Such approaches have revealed network patterns that are enriched compared to those expected by chance. For example, using an information-theoretic method, Huttenhower et al. analytically derived scores to quantify network relations between distinct biological processes from GO terms. Shojaie and Michailidis  suggested a linear model approach within an orthogonal microarray design and employed both the gene expression data and a previously known gene network to detect GO terms most influential in the transcriptome perturbation. Unfortunately, this method would require extensive modification and statistical analyses for every new application.
The existing network-based methods have not fully integrated the topological information in the gene network and the functional information about biological processes. JActiveModules  is a popular and easy to use software, as it is run on the state-of-the-art network browser platform Cytoscape . The idea is to find modules in the global network based on the significance of gene alteration (usually differential-expression p-values). Note here that these modules are not biologically characterized by any known FGS. A similar method was suggested in Liu at al. , using their own software. As in JActiveModules, network modules enriched in DE genes are first identified, and these modules serve as the AGSs. The biological characterization of the identified modules proceeds in the same way as GEA: known FGSs are assessed for being over-represented in the AGSs using Fisher’s exact tests. Hence, the network topology influences the formation of AGS, but not the relationships between AGS and FGS. Another similar approach was implemented in the Ingenuity Pathway Analysis software (IPA; http://www.ingenuity.com). Lists of differentially expressed  or alternatively spliced genes  were found to be associated with certain biological processes within limited ‘gene networks’ (using IPA terminology). To our knowledge, none of the methods developed so far offers a straightforward and transparent interpretation comparable to GEA. Such a method should exploit the topological properties of the networks, in particular the interactions between the AGS and FGS, and should provide a proper statistical inference.
In this paper we present a method of network enrichment analysis that systematically implements the network approach to describe novel gene sets with biologically meaningful functional categories. The method integrates two kinds of biological information: functional information (currently available for a minority of genes) and network connectivity of nearly all protein-coding genes. In contrast to traditional GEA, our NEA method quantifies the over/under-representation of the functional group members among the neighbors in the gene network rather than in the AGS itself. For statistical inference, we developed a fast network randomization algorithm in order to obtain the distribution of any network statistic under the null hypothesis of no association between an AGS and FGS. We demonstrate applications of NEA on high-throughput gene and protein expression datasets from a lung cancer study, and compare its performance and power with those of GEA. We provide an R package called ‘nea’, freely available at http://http:/www.meb.ki.se/~yudpaw. For pedagogic purposes, in Section C of the Additional file 1, we also provide a fully worked-out example of analysis of lung cancer data from Bild et al.’s .
Data from a lung cancer study
For illustration we used expression data from a cohort of 123 lung cancer patients who underwent complete surgical resection at the Institut Mutualiste Montsouris (Paris, France) between 30 January 2002 and 26 June 2006. The recruitment of participants was carried out in compliance with the Helsinki Declaration, and this study was approved by the ethics committee of the Institut Gustave Roussy (Paris). All involved patients gave a written informed consent. From each patient, snap-frozen tumor and corresponding normal tissues were collected. We assayed the samples for gene expression, performed using dual-color human array from Agilent containing 41,000 gene probes; a dye-swap was employed for each sample and the log-ratio value was combined by averaging. Scanned microarray images were analyzed by using Agilent Feature Extraction software version 10.5.1.1. A loess normalization was then performed using the normalizeWithinArrays function from R package limma .
For a subset of 16 tumor samples we also obtained protein expression profiles. From each sample 160 μ g of protein was taken off and precipitated using four volumes of ice cold acetone. The precipitated samples were dissolved in iTRAQ dissolution buffer and digested according to manufacturers instructions (Applied Biosystems). Three proteomics platforms were used: Applied Biosystems’s MALDI TOF-TOF, Agilent’s Accurate-Mass Q-TOF and a hybrid LTQ-Orbitrap from Thermo Fischer Scientific. From these platforms, a total of 4,406 proteins were detected in at least one sample.
Altered gene sets
where log(T/N) is the log intensity-ratio of tumor vs normal expression. For the AGS with a fixed size, we considered the top 100 (k = 100) genes per individual.
The AGS from the protein expression data was defined similarly: for each sample we kept proteins whose expression exceeded the corresponding average across 16 samples. The number of proteins in the AGSs has a median of 424 (range 257 to 654).
NEA statistics and randomization
The immediate statistical question is whether an observedd AF (k) ord AF is significantly higher or lower than expected under the null hypothesis of no biological relation. This assessment is not trivial, as we need to respect the network topology. Crucially, it is not adequate to compare the AGS with a random list of genes. The scale-free property of most biological networks means that the degree distribution is highly skewed, with a few network hubs but a large number of sparsely connected nodes. (The degree of a node is defined as the number of neighbors connected to that node). Randomly replacing a network hub by a sparsely connected gene does not make sense. A hub gene may have a few links to genes in a FGS simply by chance, whereas for a non-hub gene the same number of links would indicate an important biological pattern.
In some simple cases, analytical calculations of the null distribution are possible, for example using the hyper-geometric distribution . However, for general networks, e.g. when gene groups may share members, theoretical analyses are not feasible. In such a situation, for example, Li et al. chose to limit their analysis to only cases where the gene groups did not overlap, which is a serious limitation.
A general approach in generating the null distribution of the network statistic is based on a network randomization that preserved the degree distribution. This approach was applied, for example, by [19–22]. The basic algorithm rewires the whole network by systematic swapping of network links so that the degree of each node is preserved, while its network neighbors are replaced. The algorithm is as follows:
• Step 0: Randomly select a pair of edges (A-B and C-D).
• Step 1: ‘Rewire’ the two edges in such a way that A becomes connected to D, while B connects to C. In case one or both of these new links already exist in the network, this step is aborted and a new pair of edges is selected.
Repeated applications of the above steps lead to a randomized version of the original networks. However, for a large network it is not clear at what point a sufficient level of rewiring has been achieved, and the algorithm is also inefficient as it rejects too many rewired links that are generated earlier.
The key to a fast and transparent algorithm is to first represent the network in terms of a binary adjacency table, with each node represented by a row and a column, and the cell entry ‘1’ represents connected nodes, and ‘0’ otherwise. The table is symmetric, and its margin is equal to the degree distribution of the nodes. Thus our goal is to generate a randomized table with fixed margins, similar to the hypergeometric sampling model associated with the Fisher’s exact test, but with the additional constraints of symmetry and binary entries. Adapting the hypergeometric sampling model to these constraints, the network randomization is achieved by the following sequential algorithm:
• Step 0: Start with a list of nodes 1,…,N, ordered by degreeδ1 ≥ ⋯ ≥ δ N > 0.
• Step 1: Assign theδ1 links of the largest node to the other nodes randomly but with probability weighted byδ2, …, δ N .
• Step 2: Remove node 1, and reduce by 1 the degree of each node connected to node 1.
• Step 3: Construct a new list of remaining nodes with positive degrees, then reorder and renumber them 1,…,N, and go to Step 1. Stop if there is no remaining node with positive degree.
Construct a random network: for i = 1,⋯,N, takeδ i nodes randomly with equal weights as neighbors of the i th node. The choices of neighbors are made independently across different nodes.
Test the network: compute the resulting degree distribution and accept the network if it has the required degree distribution, otherwise reject it.
Likewise, the probability that the node with degreeδ i has a link with the largest node is . This is exactly the same as the weights in our algorithm. Thus, our weighting scheme simply offers a short-cut to produce truly unbiased random networks. A similar proof was used in . Our proposed algorithm is computationally very efficient, since each node needs to be visited at most once. The average number of nodes that need to be visited depends on the degree distribution. In our application with ∼16,000 nodes and ∼1.5 M links (see the subsection on gene network below), this average was ∼8,200 nodes. On a 3 GhZ PC with 4 Gb RAM, using native R commands, the algorithm takes ∼60 seconds.
where and s AF (k) are the mean and standard deviation of . We use the term NEA when referring to both FNEA and MNEA. These scores can be used as a measure of activation of the FGS, thus providing a biological characterization of the AGS. Assuming a normal distribution, one could convert the scores to p-values, which are convenient for combining results of network analyses with information from other findings, such as genome-wide association studies, small-scale experiments, mutation analysis, etc.
where is the estimated proportion of null results. Monotonicity is then imposed by taking the cumulative minimum over all p-values ≥p k .
Comparative procedures: GEA and GSEA
where (a b c d) are the table frequencies. This can be seen as the z-statistic associated with the log odds-ratio. If some observations in the table are zero, then they are replaced with 0.5 to prevent z from being undefined.
whereg j is the j th-ranked gene in the AGS,N R is the number of genes in R. As with the GEA, however, GSEA also does not use any network topology in its inference. To assess the significance of observed enrichment score, a permutation test procedure was originally developed for group comparisons. In our application the AGS is defined for each person, so the permutation is performed within each person.
We compiled a comprehensive network by merging 4 networks: (1) the data integration network of functional coupling , re-generated with updated datasets on protein-protein interactions (IntAct), gene expression (GEO) and sub-cellular localization (GO). This network contains 1,515,318 links, with each gene identified by the ENSEMBL gene ID; (2) curated pathways (KEGG KGML files, as of June 2010), consisting of 25,765 links; (3) known protein complexes (KEGG and CORUM, as of June 2010), consisting of 54,046 links; (4) coherent annotations (coherence was estimated by a custom software as simultaneous presence of two genes in a series of overlapping GO terms, weighted for compactness of the latter), consisting of 20,412 links.
The final network contained 1,445,027 functional links between 16,299 distinct HUPO genes (some links were lost as we translated the ENSEMBL IDs to HUPO gene symbols). Note that no evidence from the lung cancer datasets was involved in the network construction. The network is available from http://www.meb.ki.se/~yudpaw.
Functional gene sets
To characterize AGSs by involvement of known biological processes, we compiled a list of genes which are of importance in cancer:
• All 235 pathways in the KEGG database (as of 21 Apr. 2010);
• 16 GO terms that could be related to hallmarks of cancer ;
• 7 cancer-related pathways and otherwise defined FGS from publications reporting on large-scale cancer genome projects;
• EMT, epithelial-mesenchymal transition (a pathway behind metastatic development, manual curation by S. Souchelnytskyi);
• Acidic switch (a pathway behind tumor-specific pH-shift, i.e. tumor’s ability to grow in hypoxic environment, manual curation by A. de Milito).
In total the list included 5,698 distinct HUPO gene symbols assigned to 264 FGSs (overlaps are allowed). The list of pathways with their meanings and references are given in Section B of the Additional file 1 Report. The complete list of genes for each FGS is available as an RData file at http://http:/www.meb.ki.se/~yudpaw.
Result and discussion
To assess the level of connectivity, we generated a series of randomized networks that preserved the degree distribution of all genes. The estimated number of links expected by chance was 51.6 and the FNEA z-score was 4.97. In the other 15 patients with proteomics data, the z-score associated with EMT ranged from 1.81 to 9.83, so that the current sample was ranked 6 out of 16. In total, 15 z-scores out of 16 exceeded 1.96. Importantly, two of the EMT proteins, VIM and FN1, were themselves found in eight and ten sample AGSs, respectively. As a result, GEA also detected some relationship between these tumors and EMT, but only 6 of the GEA scores exceeded 1.96. Looking at Figure 2B explains the higher sensitivity of NEA: network connections lead to ACTA2, CDH1, SIP1, and other EMT genes that were themselves not found in the AGS. In addition, FN1 and VIM contributed with many links.
Performance on known gene-sets
To demonstrate the biological validity of NEA, we analyzed gene sets altered in our lung cancer dataset versus known gene groups relevant to this disease. For each sample, we set the AGS to be the top 100 genes DE between tumor and normal tissues, so we had a total of 123 AGSs. Ding et al. compiled a comprehensive list of 623 genes – known tumor suppressors, growth factors etc. – and screened them for somatic mutations in lung adenocarcinoma tissues. Among the 623 genes, 26 genes were declared ‘confident’ drivers in the sense that they are mutated at significantly high frequency. We performed NEA on (i) the full set of 623 genes, (ii) the set of 26 confident driver genes, and (iii) the set of 153 genes for which there were at most one mutation was detected by . Another functional group was the pathway of non-small cell lung cancer from KEGG database.
Additionally, we downloaded a list of genes somatically mutated in lung cancers from the COSMIC database , which is potentially less biased towards previously known cancer drivers. The list of 764 genes not included in Ding et al. was split into two parts: (i) 110 genes that mutated more than once and (ii) 654 genes reported only once. The latter can be regarded as a negative control. To get an unbiased comparison, we took 50 randomly sampled sets consisting of 110 genes from the 654 genes. The latter lists were expected to contain many spuriously reported passenger genes, so we expect fewer links to our lung cancer AGSs.
Network enrichment analysis of lung cancer-related gene sets to patient-specific altered gene sets
Functional gene set
FNEA (k = 100)
GEA (k = 100)
Ding et al., 2008
All (623 genes)
Mutated ≤1 (153)
Detected >1 (110)
Detected once (median)∗ (110)
KEGG05223 non-small cell lung cancer (56)
Largest contrast GEA > FNEA
KEGG00362 Benzoate degradation via hydroxylation (3)
KEGG00513 High-mannose type N-glycan biosynthesis (4)
KEGG00780 Biotin metabolism (4)
KEGG00300 Lysine biosynthesis (5)
KEGG00785 Lipoic acid metabolism (4)
Largest contrast FNEA > GEA
GO0001666 Response to hypoxia (163)
KEGG05200 Pathways in cancer (254)
GO0001525 Angiogenesis (129)
KEGG04010 MAPK signaling pathway (286)
KEGG04020 Calcium signaling pathway (183)
As for the COSMIC gene sets, even the set of multiple mutations had lower numbers of significant AGSs than the above results. Also, using FNEA, we could separate those genes that mutated once from those with more than 1 mutation, again potentially distinguishing the sets of passenger and driver mutations.
In general GEA detected only a few individuals with activated cancer pathways; see Table 2. For example, only 1 of the 123 individuals had significant enrichment of 623 cancer genes of , and 2 in the non-small cell lung cancer pathway. GSEA showed higher overall sensitivity compared to GEA, but GSEA appeared to be less sensitive than NEA. For example, for 26 driver genes of  it only identified 16 significant individuals, compared to 74 and 95 for FNEA and MNEA, respectively.
Among the most activated pathways according to GEA, we saw benzoate degradation via hydroxylation, high-mannose type N-glycan biosynthesis, biotin metabolism, lysine biosynthesis and lipoic acid metabolism. However, according to the NEA scores, few individuals were activated in these pathways. Thus, many pathways not known to be activated in cancer were found to be significant in all individuals by GEA, but not by NEA. On the other hand, putative cancer-related pathways, such as response to hypoxia, pathways in cancer, angiogenesis and the MAPK signaling pathway, were activated in most individuals according to NEA, but not according to GEA.
The results indicated that NEA can detect transcriptomic activity of cancer drivers via functional relations in the network, whereas the mutated genes themselves are not known directly. The fact that both frequently mutated genes (26 genes) and rarely mutated genes (most of the other FGSs) scored high suggests that the NEA is potentially more powerful than the mutation frequency analysis . Furthermore, NEA enables investigation at the level of individuals rather than on pooled observations. Indeed, a large number of cancer drivers could not be detected by Ding et al. or other studies due to low mutation frequency observed in the samples.
We also compared z-score distributions from GEA to those from MNEA and FNEA (Additional file 1: Figure S1).In general, there was little correlation between GEA and NEA scores, which would be expected as they are based on different information. In most situations NEA could achieve higher ranges of scores because there are more ways a gene can interact with other genes in a pathway than simply by being an overlap. On the other hand, the correlation between FNEA and MNEA was 0.65; since FNEA is much simpler to compute than MNEA, in practice FNEA could be sufficient for capturing the network enrichment.
Once constructed, the NEA scores from each individual can be used for further analyses. For illustration we employed factor analysis  in order to explore the lower dimensional space that characterized molecular profiles of individual patients. The varimax rotation algorithm is used because it often provides meaningful interpretations for the factor loadings for each variable (FGS). The individual NEA scores of FGSs served as input variables in the factor analysis. In order to make the results more interpretable, the analysis was performed separately for the following three groups of pathways: (a) cancer-related pathways; (b) signaling and cancer-related pathways; and (c) metabolic pathways. These are given in Section B of the Additional file 1 Report.
First the mean and variance of FGS scores are given in Figure S2 of the Additional file 1 Report. The cancer-related pathways were neither the most enriched nor the most variable. Many other signaling KEGG pathways exceeded them in terms of these measures. The metabolic pathways seemed as variable across individuals as signaling ones. Looking at metabolic pathways most highly correlated to signaling pathways and cancer hallmarks, we found that these correlations occurred when the same enzymes were assigned to both a metabolic and a signaling pathway. For example, the RNA-specific adenosine deaminase ADAR (atrazine degradation, KEGG00710) was related to (but not a member of) the cell cycle pathway (KEGG04110) due to its molecular function. Similarly, protein phosphatases that enable biological signaling (and hence belong to multiple signaling pathways) are classified as enzymes of the inositol phosphate metabolism (KEGG00562).
We used 16 FGSs that are the known hallmarks of cancer  and 13 processes relevant to tumor growth. The factor loadings revealed that variability of transcription is mostly shaped by Factor 1: PDGF, IGF, and TGF-beta signaling, angiogenesis and epithelial-mesenchymal transition (EMT), Factor 2: apoptosis and ErbB (also known as HER2 or EGFR) signaling, Factor 3: p53 signaling and cell cycle. We found that EMT was significantly enriched in the virtually all tumors (FNEA z score ranged from 2 to 30), so the variability across patients reflects the varying degree of activation. On the other hand, p53 signaling and cell cycle were significantly (z > 2) activated in subsets of individuals (79 and 24 out of 123 individuals, respectively).
To reveal how cancer-related pathways interact with the normal signaling machinery, we studied factor structure of the combined cancer-related pathways and 55 signaling pathways from KEGG. The first factor (21.4% of total variance) combined apoptosis with Jak-STAT pathway and other immunity-related signaling (B-cell, T-cell, toll-like receptor, and other pathways). Factor 2 explained 16.2% of the total variance. Unlike the first analysis, ErbB was placed with pathways MAPK, WNT, VEGF, insulin, gonadotropin-releasing hormone, and calcium signaling. The third factor (10.0%) confirmed joint activity of PDGF, IGF, and TGF-beta signaling, angiogenesis, and EMT pathways. In addition, these were associated with tissue growth pathways: adherens junction (KEGG04520), focal adhesion (KEGG04510), regulation of actin cytoskeleton (KEGG04810), and tight junction (KEGG04530).
Thus, by combining the cancer-related processes with KEGG signaling pathways, we found that the former do contribute significantly to the factor structure of the signaling pathways. We could see how the core cancer processes cross-talk with their signaling counterparts in the tumor transcriptome level.
We previously observed that the signaling and metabolic domains of the global gene interaction network are poorly connected with each other (unpublished data). In order to overview tumor functionality at the metabolic level, we did factor analysis for 119 metabolic KEGG pathways. Factor 1 (19.2% of total variance) was dominated by metabolism of retinol, steroid hormones, ascorbate/aldarate, fatty acids and several amino acids. Factor 2 (10.6%) incorporated various pathways of sugar metabolism and oxidative phosphorylation, while factor 3 (7.4%) combined metabolism of purine, pyrimidine, phosphonate/phosphinate, seleno-aminoacids, cysteine and methionine.
Comparing the gene and protein expression data
Distinct AGSs from the transcriptomics and proteomics data allowed a systematic analysis of both similarities and differences between individual patients at molecular level. For this we compared the NEA scores of individual AGSs versus 264 FGSs for the two omics data; the plots are given in the Additional file 1: Figure S2. Both manifested higher mean scores for the five tissue growth-related pathways: adherens junction (KEGG04520), gap junction (KEGG04540), focal adhesion (KEGG04510), regulation of actin cytoskeleton (KEGG04810), and tight junction (KEGG04530). These pathways were highly enriched in the vast majority of patients. Similarly, the score distribution of metabolic pathways was quite similar between the two platforms in terms of means and variances. Intriguingly, the proteomics AGSs were strongly depleted in cancer-related FGSs, whereas in the transcription domain the cancer genesets showed the opposite pattern. We have no explanation for this observation.
We have developed a network enrichment analysis that can be considered a natural extension of the gene enrichment analysis in the network context. NEA exploits the rich and growing information on the biological interaction between genes at different levels, including DNA, RNA and protein, and from different species. The statistical power of this approach is higher than GEA, because the number of potential connections between gene groups is expanded from listed genes to all their network neighbors. The analysis is robust if the gene network is sufficiently dense, so that only connections via several network links between gene groups are considered. We provided such a global gene network of functional coupling by integration of high-throughput and literature data of , complementing it with functional links from curated databases of pathways, gene annotations, and protein complexes.
Our NEA method by definition is not limited to any sub-networks or modules defined by the network structure. In comparison, NEA methods that analyze pre-defined network modules then perform GEA within each module separately, and ignore all non-module genes. Algorithmic solutions for identifying network modules are often controversial, and might produce multiple solutions, where each alternative is hard to validate. Furthermore, in our experience with JActiveModules many identified modules are either very small (fewer than 5 genes) or extremely large, likely representing the largest component of the network, thus creating an additional level of uncertainty in the analysis pipeline. This direction of research can be extended beyond existing gene networks, e.g. attempting to identify latent gene structures .
Genes, the members of FGS used in our analyses, often overlap. This problem is common to all enrichment-based methods that employ ready, third-party defined FGS. Solutions can include either resolving ambiguity by rigorous weighted scoring  or creating curated, non-overlapping FGS for specifically for enrichment analyses, such as hallmarks of cancer, domains of enzymatic activity, etc.
Obtaining the distribution of the network statistics under the null hypothesis, which is needed for inference, is challenging, and we believe that this has hindered network-based analyses so far. In this paper, we propose a sequential network randomization algorithm, using the hypergeometric sampling model to obtain a fast procedure for large biological networks. Chen et al. proposed a sequential importance sampling method to approximate the distribution of the statistics related to the randomized 0-1 tables with fixed margins. In contrast to our procedure, they did not randomize the network itself, but an approximation to it as determined by the trial distribution. Hence, finding or constructing a good trial distribution becomes an issue.
We have focused on the number of direct links with equal weights as the key statistic, but some extensions of this are worth pursuing. For example, one might consider other network statistics, such as the number of indirect links, or more generally, allow different weights for the links. In addition to analyzing an AGS in relation to known gene sets, the NEA has a unique feature: it can quantify the enrichment of single genes in the AGS. As such an analysis does not require any prior gene grouping, it can be applied to all genes found in the network. In this case the characterization of the AGS is based on any available knowledge on the enriched individual genes, such as gene description, presence of a certain protein domain, etc.
Finally, in generating the randomized networks we have constrained them only to have the have a specified degree distribution. Let network assortativity be defined as the correlation between the degrees of the two nodes connected by a link. In our randomized networks a large node is more likely to be connected another large node rather than to a small one. In other words the randomized networks tend to be assortative. The network that we use has an assortativity of r = 0.2, indicating that high-degree nodes are more frequently connected to high degree nodes than to low-degree nodes. We observe the same trend for the human STRING network  (link confidence cutoff > 0.5, r = 0.32). This is opposite to what was found by Newman  (r = −0.15), and Maslov and Sneppen  (r < 0). However, the networks used in their studies were relatively small yeast networks and purely based on physical protein interactions. In any case, the impact of ignoring the second-order property on network-based inferences requires further investigation.
AA and WJL contributed equally; VL, JL and YP conceived of this project as principal investigators. VL, JG and PD carried out the microarray experiments; JL and MP carried out the protein experiments. AA, WJL and YP performed the statistical analysis. AA, WJL, MP, JL and YP wrote the paper. All authors read and approved the final manuscript.
This work is supported by a research grant from the European Union under the Chemores project, the Swedish Science Council, INHA UNIVERSITY Research Grant (INHA-44770-01) and the Next-Generation BioGreen 21 Program (No. PJ009019), Rural Development Administration, Republic of Korea. The estimates of assortativity given in the Dicussion were based on a collaborative work with Ted McCormack.
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