Quantifying differential gene connectivity between disease states for objective identification of disease-relevant genes
© Chu et al; licensee BioMed Central Ltd. 2011
Received: 24 November 2010
Accepted: 31 May 2011
Published: 31 May 2011
Network modeling of whole transcriptome expression data enables characterization of complex epistatic (gene-gene) interactions that underlie cellular functions. Though numerous methods have been proposed and successfully implemented to develop these networks, there are no formal methods for comparing differences in network connectivity patterns as a function of phenotypic trait.
Here we describe a novel approach for quantifying the differences in gene-gene connectivity patterns across disease states based on Graphical Gaussian Models (GGMs). We compare the posterior probabilities of connectivity for each gene pair across two disease states, expressed as a posterior odds-ratio (postOR) for each pair, which can be used to identify network components most relevant to disease status. The method can also be generalized to model differential gene connectivity patterns within previously defined gene sets, gene networks and pathways. We demonstrate that the GGM method reliably detects differences in network connectivity patterns in datasets of varying sample size. Applying this method to two independent breast cancer expression data sets, we identified numerous reproducible differences in network connectivity across histological grades of breast cancer, including several published gene sets and pathways. Most notably, our model identified two gene hubs (MMP12 and CXCL13) that each exhibited differential connectivity to more than 30 transcripts in both datasets. Both genes have been previously implicated in breast cancer pathobiology, but themselves are not differentially expressed by histologic grade in either dataset, and would thus have not been identified using traditional differential gene expression testing approaches. In addition, 16 curated gene sets demonstrated significant differential connectivity in both data sets, including the matrix metalloproteinases, PPAR alpha sequence targets, and the PUFA synthesis pathway.
Our results suggest that GGM can be used to formally evaluate differences in global interactome connectivity across disease states, and can serve as a powerful tool for exploring the molecular events that contribute to disease at a systems level.
Network and pathway models have been frequently used to describe complex interaction patterns of genes and other types of molecules, and there is increasing recognition that such networks will facilitate a more clear understanding of cellular physiology . Developed using global expression , proteomic [3, 4], or metabolic  measures, the models can be used to characterize the patterns of interaction (gene-gene, gene-protein, etc) that underlie cellular states. Such models have been used to define the complex pathobiology of numerous cancer types [6–8], neurological conditions , and metabolic disorders . More recently, models constructed through integration of genotype and expression data have been used to identify disease-susceptibility loci that alter network dynamics [11, 12].
Though network models are fairly easy to visualize using graphs, direct comparison of two models (for example, transcriptome networks across disease states), and quantitative measurement of the differences between networks, remains challenging. In recent years there have been growing literature of methodology for such comparisons , either for a global scale estimation of overall network similarity [14–16], or for measures of local difference in connectivity for nodes or modules in the network [17–19]. Among the many methods used to infer gene networks are Gaussian Graphical models (GGM) [20–23], including the empirical Bayes methods for fitting Gaussian graphical models , which performs well in inferring large-p small-n gene networks. As a probabilistic method, GGM provides posterior probabilities of gene-gene interaction for each edge in the network, a quantifiable measure of interaction that incorporates the uncertainty of the model. We recently  applied the method to build an integrative network based on multiple data sources (i.e. SNP genotypes and gene expression data). We now extend this method to integrate clinical phenotypes, such as disease status, in order to facilitate identification of network modules whose connectivity patterns differ by disease status. Our approach enables direct comparison of two co-expression networks and objective identification of network components that consistently exhibit differential connectivity patterns across disease states. For simplicity we will only consider dichotomous phenotypes, though this method could be extended to categorical or continuous traits as well.
where and are the posterior probability estimates for the event that an edge exists between gene j and gene k, in groups C and D, respectively. If and/or are zero, we assign them a very small number on the same scale as the smallest non-zero posterior probability to make sure all odds ratios are well-defined. The posterior odds ratios between the disease groups provide a quantitative measure for difference between network connectivity, and the parts of the network where the postORs differ from 1 are likely the parts most relevant to the disease state (panel (c) in Figure 1). Panel (d) in Figure 2 shows a histogram of the log posterior odds ratio, with most of the edges concentrated around zero and relatively few of them way out in the tails, which represent the edges associated with the disease states. The gap from around ±5 to ±30 roughly corresponds to the sharp climb in the posterior probability seen from panel (c) in Figure 2. This pattern has been observed in all data sets that we have analyzed, though the scales in which the extreme observations fall may vary depending on the sample size and the number of genes in the network. As the sample size increases relative to the number of genes, we observe more extreme values of log postORs, in some cases going up to ±50 or 60.
which is a good approximation of the average postORs for all edges in the set, as most of the posterior probabilities , are close to zero. This gives a reasonable measure of the overall differential connectivity for each gene set.
To assess the theoretical performance of our approach, we performed a series of simulation studies. For each simulation study we first generate two partial correlation matrices representing networks observed in two groups of samples (i.e. "cases" and "controls"), and then generate synthetic expression data sets from them. We then attempt to recover the network using GGM and calculate the postORs for all pairs of genes. To simulate networks most closely resembling real world network data, we set out to develop a set of relatively sparse networks with few strong connections. When generating the partial correlation matrices for the "case" network we therefore follow the same approach in , whereby we estimate a connectivity network using an expression dataset generated from peripheral blood CD4+ lymphocytes , take the top G genes with the highest correlation, retain correlation coefficients of the top q significant edges and shrink all remaining correlation coefficients to zero. We take G = 100 and q = 77 in our simulation study, which corresponds to about 1.5% of all possible edges (all with posterior probability over 0.95). The "control" networks are from the null model, where the expression data are generated from an independent multivariate distribution and none of the genes are connected. We simulate the expression data with 200 samples in each group and repeat the entire procedure 10 times.
Breast Cancer Study
We now demonstrate the application of our method to real data sets. The main results will be focused on the comparison between two independent gene expression data sets from breast cancer tissues of varying histological grade available through the Gene Expression Omnibus (GEO series GSE2990 and GSE6532). The GSE2990 series consists of Affymetrix Human Genome U133A Array data for 189 breast tumor samples from the National Cancer Institute database , from which we selected 100 estrogen receptor-positive (ER+) samples with histological grades 1 (n = 61) and 3 (n = 39). The GSE6532 series contains several independent validation sets generated using Affymetrix U133PLUS2 GeneChips and described in , from which we used the 33 samples from Guy's Hospital, UK (17 grade 1 and 16 grade 3). These data sets were selected based on sample sizes and availability of clinical phenotypes. Using the R package genefilter, we applied the non-specific gene ltering  on both data sets. The resultant data set consisted of 1,445 RefSeq-annotated genes with interquartile ranges (IQR) in the upper 50% for both data sets.
We applied our method sequentially to define, in each dataset, the differences in network connectivity patterns observed across breast cancers of different histological grades. The two datasets were analyzed separately to enable unbiased evaluation of the reproducibility of findings by our method when applied to biologically independent datasets. We observe a similar pattern to those seen in the simulation studies, with most edges concentrated around zero and relatively few in the extremes. Focusing on the edges with extreme postOR probabilities of differential connectivity between grades (Empirical p-values < 0.001 based on permutation), we found significant overlap across studies. When considering genes exhibiting high degrees of connectivity - so-called hubs  defined as genes with at least 30 independent edges - 10 of 33 hubs demonstrating differential connectivity patterns in dataset GSE2990 were also observed in the second dataset GSE6532 (Fisher's exact test, p-value = 1.5 × 10 -5). This high degree of overlap between two independent data sets suggests that the observed differential network connectivity patterns are a reproducible property of complex biological processes such as cancer progression.
Hub list for breast cancer study (GSE2990 and GSE6532) histological grade 1 and 3
Prior evidence for role in breast cancer biology
Up-regulated in endometrial cancer by the inducer of myometrial infiltration ERM/ETV5 ; Protective role against oxidative-stress induced apoptosis in endometrial cancer ; Down-regulated in ovarian tumors following cisplatin treatment 
Overexpression in breast cancer tumor tissue, with elevated blood serum levels in patients with metastatic disease 
Overexpressed in subset of estrogen-receptor positive breast cancer; Ectopic overexpression confers a highly invasive phenotype in primary mammary epithelial cells; AGTR1-positive tumor growth reduced by 30% with receptor blockade in xenograft model 
Breast tumor transfection of MMP12 reduced endothelial cell invasion and capillary tube formation 
BEX2 is overexpressed in a subset of primary breast cancers and mediates nerve growth factor/nuclear factor-kappaB inhibition of apoptosis in breast cancer cell lines. 
siRNA-mediated knockdown of S100A8/A9 expression significantly reduced H-Ras-induced invasion/migration; Induction confers the invasive/migratory phenotype ; Immunopositivity correlates with mitotic activity, MIB-1 index, HER2 overexpression, node metastasis, and poor prognosis ; Associated with transformation and progression of breast cancer cells which is reversed by treatment with silencing inhibitors ; Down-regulated in invasive tumors 
Differentially expressed in hill-type cancer cells 
We next examined whether these same genes could be identified using more standard analytic approaches (making our method redundant) or whether our approach provides truly independent information. When we applied traditional differential expression analysis (linear regression as implemented in the R package limma: Linear Models for Microarray Data, ) to the datasets, we found that only two of the 10 hub genes - AGTR1 and NAV3 - were themselves differentially expressed by histological grade (FDR adjusted p-value ≤ 0.05). Moreover, none of the 10 differentially connected hub genes were identified as relevant grade-related genes in the original report by . These comparisons suggest that differential connectivity mapping can identify disease relevant genes that would not be found using more traditional approaches. The lack of differential expression for most of the hubs themselves argues that the observed differential connectivity patterns are not primarily due to primary alterations of hub gene expression, but rather due to more subtle changes in expression of numerous genes interacting with these hubs.
The appeal of systems-based or interacteome mapping approaches for the study of disease is steadily increasing with the recognition that non-linear epistatic interaction underlies all but the simplest of biological processes. However, formal identification of biologically relevant interaction patterns imbedded in complex network connectivity maps has been a challenging problem. Several studies have looked at global comparison of the networks based on annotated database, such as GO or KEGG [14–16]. Unlike our method, those previous studies assume complete knowledge of the networks (i.e. they do not accommodate uncertainty in the observed connectivity between nodes). In many instances, however, complete certainty is unattainable. Moreover, these methods are largely global, but do not provide information regarding regional differences (i.e. measures of difference in connectivity between any two nodes in the network). Without a measure of variability of the model, it is not easy to distinguish disease-related genes from those that have neutral roles. There are several methods for comparing region differential connectivity between two networks, based on pair-wise gene co-expression relationships, either at the gene cluster/module level [17, 19, 47, 48] or at the individual gene level . Here we have presented a novel approach that enables direct comparison of two different networks derived from Gaussian graphical model. The key feature of the GGM approach is that the network inference is based on partial correlation (i.e. conditional dependence), which distinguishes direct interactions from indirect ones [24, 49]. The postORs from empirical Bayes approach provide an easily interpretable quantitative measure for differential connectivity, allowing search for local differential connectivity either for individual genes, gene pairs, or on a cluster/module level. The method performed well in detecting differential network connectivity in simulations of moderate sample size, compared to other simple methods with Pearson correlations or partial correlations only. In fact, even though the sensitivity was modest, both the simulation studies and the real breast cancer datasets suggest that our approach detects many of the strongest associations with very high specificity.
Application of differential connectivity mapping to the breast cancer data sets provides several important insights, both regarding the utility of this approach to other disease states, and with respect to the importance of network connectivity underlying disease processes such as cancer. With regard to the performance of the method, we first found substantial reproducibility (~30%) in the observed connectivity patterns across the two breast cancer datasets, then similar results were found in the third data set, suggesting network connectivity as a robust, measurable property of complex biological processes. Second, many of the most compelling findings from our analysis (the 10 hubs observed in both datasets) have been previously implicated in breast cancer or other estrogen-responsive cancers, suggesting that the approach is highly specific with regard to biologically relevant findings. Third, as the hubs genes are not always expressed, the majority of the 10 hub genes were not detected using the traditional differential expression approach. Differential connectivity mapping complements differential gene expression analysis and can be used to identify those genes.
Perhaps most importantly, careful review of the specific genes identified suggests that hubs manifesting differential connectivity (or one or more of their connected edges) may represent important candidates for therapeutic targeting. In addition to EGR1 (discussed above), of the 10 hub genes identified, there is experimental evidence for at least three that their targeted manipulation alters the malignant and invasive potential of breast cancer. Matrix metalloprotease 12 (MMP12), a protease that converts plasminogen to angiostatin (a potent inhibitor of angiogenesis), inhibits angiogenesis when overespressed in breast cancer tissue . S100A8, a calcium-binding protein that complexes with S100A9 and whose expression is suppressed by functional BRCA1 , is induced by H-Ras to promote malignant potential (tumor cell invasion and migration). Contradictory reports suggest that these malignant properties are either attenuated  or enhanced  upon siRNA-mediated knockdown of S100A8/A9 expression, suggesting S100A8 as a targetable regulator of malignant potential. Similarly, AGTR1 (one of only two differentially-connected hubs that was also itself differentially expressed across tissue grades) is a potent inducer of invasive phenotypic properties when overexpressed in primary mammary epithelial cells . These effects are inhibited by the AGTR1 antagonist losartan, and FDA-approved medication commonly prescribed for the management of essential hypertension. Consistent with these observations, treatment of xenograft models of breast cancer with losartan reduces tumor growth in AGTR1-positive, but not AGTR1-negative, breast cancers . It is intriguing to speculate whether manipulation of NAV3, the only other gene that displayed both properties of differential connectivity and differential expression across tissue grade, would have similar effects in altering the malignant potential of breast cancers.
In conclusion, we have developed a highly specific method for the identification of genes that demonstrate differential connectivity across disease states. Though applied here to transcriptome data, this method can be applied more broadly to other types of biological network models, and can serve as a novel approach for the identification of high priority target nodes underlying complex biological processes.
The authors acknowledge support of the National Institutes of Health through grants R01 HL086601, RC2 HL101543 and R01 HG003646. The authors would also like to thank the anonymous reviewers for the helpful comments and suggestions.
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