Computational Genomics
Discovering tightly regulated and differentially expressed gene sets in whole genome expression data
1 Bioinformatics Program, University of California San Diego, La Jolla, CA 92093-0404, USA
2 Department of Computer Science and Engineering, University of California San Diego, La Jolla, CA 92093-0404, USA
*To whom correspondence should be addressed.
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ABSTRACT |
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 TOP ABSTRACT 1 INTRODUCTION2 METHODS3 RESULTS4 DISCUSSIONREFERENCES |
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Motivation: Recently, a new type of expression data is being collected which aims to measure the effect of genetic variation on gene expression in pathways. In these datasets, expression profiles are constructed for multiple strains of the same model organism under the same condition. The goal of analyses of these data is to find differences in regulatory patterns due to genetic variation between strains, often without a phenotype of interest in mind. We present a new method based on notions of tight regulation and differential expression to look for sets of genes which appear to be significantly affected by genetic variation.
Results: When we use categorical phenotype information, as in the Alzheimer's and diabetes datasets, our method finds many of the same gene sets as gene set enrichment analysis. In addition, our notion of correlated gene sets allows us to focus our efforts on biological processes subjected to tight regulation. In murine hematopoietic stem cells, we are able to discover significant gene sets independent of a phenotype of interest. Some of these gene sets are associated with several blood-related phenotypes.
Availability: The programs are available by request from the authors.
Contact: cye{at}bioinf.ucsd.edu
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1 INTRODUCTION |
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TOPABSTRACT1 INTRODUCTION2 METHODS3 RESULTS4 DISCUSSIONREFERENCES |
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1.1 Background
When microarrays were first introduced 10 years ago, researchers were attracted to the high throughput nature of the technology that enabled them to examine the activity of all genes in a cell simultaneously. The original promise of using this technology to quickly generate biologically relevant and verifiable hypotheses has yet to be fully realized. Ironically, much of the initial work has focused on the reduction of whole genome expression data to the identification of individual genes that exhibit differential expression. The most common such studies compare the expression levels of individual genes between two spatial or temporal conditions; or between diseased (e.g. cancerous) and normal cells. Various statistical tests are used to assess the significance of differential expression by comparing individual genes to the rest of the genes. Using these single-gene approaches, researchers have identified many genes critical to the function of various biological processes including the yeast cell cycle (Spellman et al., 1998) and the onset of human breast cancer (Perou et al., 2000).
Because most biological processes involve the complex interaction and regulation of multiple genes, identifying differentially expressed sets of genes has important advantages over identifying individual genes. Many genes may individually exhibit marginal differential expression but may have a significant combined effect on phenotypic outcome. The most common gene set method directly extends single-gene approaches by:
- Ordering the complete list of genes, L, according to their evidence for differential expression.
- Examining the occurrence of a predefined gene set S to determine whether it is overrepresented in the top portion of the list, B, relative to the complete list L.
- Computing a P-value usually based on the Fisher's exact test or its large-sample approximation
2 test.
This approach is reasonable but has at least three shortcomings. First, by considering only those genes that belong to a gene set, others not in the set and their relative positions in the gene list are disregarded. Second, significant genes are arbitrarily selected using a threshold leading to different results from using different thresholds. Third, and most importantly, once B and S have been picked, the actual measure of differential expression (or other scores) associated with each gene is disregarded and any additional information, including correlation between gene expression levels is ignored (Pavlidis et al., 2004).
Exploiting the correlation structure between genes is an alternate approach of utilizing microarray data. It has been shown in previous studies that correlated expression levels between genes are directly associated with functional relationships such as physical interactions and common regulatory mechanisms (Eisen et al., 1998). As such, expression level correlation has been used to identify new functional modules and gene sets.
A promising new technique, gene set enrichment analysis (GSEA) uses binary phenotype information (e.g. samples belonging to two classes) and a new statistic similar to the Kolmogorov–Smirnov statistic to evaluate microarray data at the level of gene sets. The method avoids many of the problems of single-gene approaches by determining whether members of a gene set S tend to occur toward the top (or bottom) of the entire gene list L, in which case the gene set is correlated with the phenotypic class distinction. This approach eliminates some of the single-gene biases and detects differentially expressed gene sets whose individual members are not necessarily differentially expressed under the single-gene model. The steps are (1) construct a ranked list L of genes based on correlation between their expression and class distinction using any suitable metric (signal-to-noise ratio), (2) given an a priori defined set of genes S, calculate an enrichment score (ES) that reflects the degree to which a set S is overrepresented at the extremes (top or bottom) of the entire ranked list L, (3) estimate the statistical significance of the ES score by using an empirical phenotype-based permutation test procedure that preserves the complex correlation structure of the gene expression data and (4) correct for multiple testing by normalizing the ES score for each gene set to account for the size and then calculating the FDR for each normalized enrichment score.
The major advantage of GSEA is the ability to identify differentially expressed gene sets while preserving the correlation structure of the gene expression data avoiding a potential source of false positives. Tian et al. (2005) presents a potential solution by performing separate statistical tests based on two different but nevertheless related null hypotheses. Although statistically sound, such an approach makes the computation of a P-value difficult.
1.2 ‘Tightly regulated’ gene sets
Recently, a new type of expression data is being collected which aims to measure the effect of genetic variation on gene expression of pathways (Morley et al., 2004; Bystrykh et al., 2005). In these datasets, expression data are collected from multiple strains of the same model organism under the same condition. The goal of analyses of these data is to identify differences in regulatory patterns due to genetic variation between strains. Previous gene set based methods, including GSEA, identify sets of genes which are highly variable across the strains and correlated with a phenotype of interest. An example of such a pathway is shown in Figure 1a. However, these types of datasets motivate a new notion of differential expression, tightly regulated gene sets, where differentially expressed genes are highly correlated within the strains. In this phenomenon, a set of genes is expressed at a different level of activity in each strain and may represent a different level of activity of a pathway. Figure 1b shows an example of a tightly regulated pathway.
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In this paper, we formalize the notions of tight regulation and differential expression to generate two null hypotheses. First, we present a new method for identifying tightly regulated gene sets based on a correlation statistic. Second, we introduce a more general method of identifying differential expression to specifically handle whole genome expression data over different strains of a model organism without requiring a phenotype. From Figure 1, we see that our two notions of significance for a gene set capture different information. A differentially expressed gene set has contrasting vertical bands. Figure 1a and b both have a high ratio of genes differentially expressed while Figure 1c has only a few genes differentially expressed. A tightly regulated gene set has a smooth horizontal gradient. This pattern is observed in Figure 1b but not in Figure 1a and c.
We apply our methods to three datasets, two of which have been previously analyzed with other gene set based methods allowing us to directly compare our results. The first dataset is a diabetes expression profiling study of a binary phenotype [17 individuals with normal glucose tolerance (NGT) versus 18 individuals with Type 2 Diabetes Mellitus (DM2)]. The second dataset is an Alzheimer's expression profiling study of a continuous phenotype where 31 individuals were quantified by their MiniMental State Examination (MMSE) scores. These individuals are also clinically divided into four categories: control, incipient, moderate and severe. Finally, we apply our methods to a dataset containing expression profiles of hematopoietic stem cells (HSCs) from 22 strains of recombinant inbred mice.
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2 METHODS |
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TOPABSTRACT1 INTRODUCTION2 METHODS3 RESULTS4 DISCUSSIONREFERENCES |
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2.1 Hypothesis testing framework
The overall objective of our approach is to identify gene sets that are differentially expressed and tightly regulated. This gives us two null hypotheses as follows:
- Hypothesis D0: The genes in a gene set show the same pattern of differential expression compared with the rest of the genes.
- Hypothesis T0: The genes in a gene set show the same amount of correlation as the rest of the genes.
2.2 Identifying tightly regulated pathways
We use the Kendall Tau to look for tightly regulated gene sets. Unlike the Pearson and Spearman correlations, there is an intuitive, graphical interpretation of the Kendall Tau. Given two genes, we create two ranked lists of the strains based on the expression levels of each gene. In graph theoretic terms, we are creating a bipartite graph with the strains representing the two sets of vertices. Each strain from one ranked list is connected to the same strain in the other ranked list by an edge.
Formally, given two genes i and j each with n expression values, one from each strain, the Kendall Tau is defined as:
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2.3 Identifying differentially expressed pathways
2.3.1 ANOVA and variance
For datasets that include categorical phenotype information, we use a linear mixed effects ANOVA model to rank the genes based on their F statistic. We use the MAANOVA R package and specify the gene-specific model as:
where the indicies track array (i), gene (g) and measurement (r); G is the average intensity associated with a particular gene; S is the effects associated with different samples or conditions (i.e. normal versus type 2 diabetes patients); I is the individual random effect of multiple individuals from a particular sample (i.e. five diabetes patients); and 
is the residual. We compute the following F statistic:
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For datasets that do not have clear categorical phenotype information, we look for differential expression based on the variance of the gene expression values of each gene. This is mostly applicable to whole genome expression data of different individuals from the same model organism.
2.3.2 The Mann-Whitney test
To compute over-representation of a gene set in a ranked list, either derived from a linear ANOVA model or by computing the variance of the expression levels, we use the Mann–Whitney statistic. This non-parametric test uses the entire list to compute the statistic, an advantage over Fisher's exact test or the 2 approximation. Given a ranked list of genes, we expect genes from those gene sets exhibiting differential expression to cluster at the top of the list.
Formally, given a m x n matrix representing a microarray experiment with m strains and n genes, we first rank the genes based on their differential expression. We now take each gene set of interest S and compute the Mann–Whitney score where genes belonging to the set are compared with genes not in set. The alternate hypothesis is that those genes belonging to our gene set tend to show up higher on the list than other genes. The null hypothesis is that genes belonging to our gene set should be evenly distributed with respect to all other genes. We use the R statistics package to compute the Mann–Whitney statistic and its associated P-values which are based on normal approximations (R Development Core Team, 2005).
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3 RESULTS |
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TOPABSTRACT1 INTRODUCTION2 METHODS3 RESULTS4 DISCUSSIONREFERENCES |
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To find correlated gene sets, we measure the amount of correlation between each pair of genes in the set. We use as a statistic the sum of the square of the correlation coefficients. For a gene set S, we first compute the correlation coefficients (Kendall Tau) for each pair of genes, cij. Then, we square each coefficient and sum the squares,
. Finally, we normalize this statistic by the number of elements in the gene set. To assess the significance we generate 2000 gene sets with the same number of genes as S, and recompute the statistic. A P-value is computed based on these iterations. When we have groupings of individuals based on phenotype, for example, normal versus diabetic or severe versus incipient Alzheimer's, we use an ANOVA-based approach to look for differentially expressed gene sets. First, we construct a mixed-effect ANOVA model treating the effects due to disease state and variation among individuals as two fixed effects. Our null hypothesis is that gene expression does not vary between the groups. With this model, we use a F-statistic to measure how differentially expressed each gene is between the groups. If we do not have phenotypic groupings, as is the case for our murine expression data, we use the variance to measure differential expression for each gene. We rank each gene based on one of the two statistics for differential expression and use the Mann–Whitney statistic to detect significant gene sets, i.e. those with many genes occupying the top of the list.
Given these two statistical tests for tight regulation and differential expression, we can identify statistically significant gene sets using either statistic. When we computed these two statistics on the diabetes dataset, we were encouraged to see that there is very little correlation between the P-values (
= 0.136).
3.1 Example I: diabetes—NGT versus DM2
As a proof of concept, we first reanalyze the diabetes dataset originally reported in (Mootha et al., 2003). This dataset consists of whole genome expression profiles from 35 individuals, 17 of whom have NGT and 18 of whom have DM2. We consider the same 323 gene sets reported in (Mootha et al., 2003) compiled from various databases including BioCarta, GenMAPP and GO.
When we compare our methods with GSEA, we notice some interesting similarities and differences. Table 1 shows all significant gene sets using our method (sorted by the average rank of their P-values) and the GSEA method (P < 0.05). The gene set implicated in the original GSEA paper (Subramanian et al., 2005) and a follow up (Tian et al., 2005), OXPHOS, is the second highest scoring gene set using our approach while it is only marginally significant using the GSEA approach (P < 0.01). In addition to OXPHOS, we identify several more gene sets related to oxidative phosphorylation, including MAP00190 and KEGG: electron transport chain. Figure 2 shows a clustering of the top scoring gene sets. The represented biological processes include oxidative phosphorylation, proteasome degradation, carbon fixation and metabolism and cell–cell signaling. Some of these processes, including carbon fixation and pyruvate metabolism, are known to be differentially perturbed in diseased individuals (Randle et al., 1964). Others, especially the signaling pathways, are interesting potential biological targets because not only are they differentially expressed in diseased individuals, they are also tightly regulated, which suggests that a small number of regulatory elements govern the behavior of the pathway and the outcome of the phenotype.
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3.2 Alzheimer's data
Another dataset analyzed by Tian et al. (2005) considers a group of Alzheimer's patients. Blalock et al. (2004) performed gene expression experiments on 22 Alzheimer's disease (AD) patients and 9 controls. In addition to the clinically diagnosed categories of incipient, moderate and severe, each of these patients also have a Mini Mental Status Exam score which is a reliable index of AD-related cognitive status at a given point in time.
Using a database of gene sets compiled from BioCarta, KEGG, GENMAPP and GO (Tian et al., 2005), we perform two separate analyses to identify differentially expressed genes. First, we use ANOVA and the discrete phenotype to rank genes based on their differential expression with respect to the groupings. Second, we rank the genes based on the variance of their expression values. For each ranked list, we then use the Mann–Whitney test to identify top scoring gene sets. To identify tightly regulated gene sets, we use the same sum of squares correlation statistic as before and compute P-values based on 2000 permutations.
All methods used in this analysis detected an overwhelming number of significant gene sets, many of which appear to have housekeeping functions. Table 2 shows representative gene sets from the top 25 clusters and their respective statistics. We find some of the same gene sets identified in (Tian et al., 2005) including cation transporter activity (GO:0008324). Interestingly, an accompanying gene set, calcium ion transport (GO:0006816) is not discovered by our methods. Closer examination reveals that although the calcium ion transport gene set is slightly differentially expressed (P < 0.096), it is not tightly regulated (P < 0.96). In other words, although most of the proteins involved in calcium ion transport are channel proteins, the regulation might actually occur at the level of the ATP-dependent molecular transporter. This hypothesis is supported by the identification of numerous gene sets involved in metabolism including the cation-transporting ATPase activity gene set (GO:0019829). Several mitochondrial-related gene sets are also discovered supporting the pathogenesis of AD due to defects in these gene sets (Hinerfeld et al., 2004). Gene sets involving gluconeogenesis and glycolysis, two processes known to be involved in neurodegenerative disorders, are also among the top scoring sets.
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Finally, of note is that many KEGG pathways involving neurodegenerative diseases, including the Alzheimer's pathway and the Neurodegenerative Diseases pathway are differentially expressed under one criterion (ANOVA) but not under another (variance). These pathways include many genes such as APP, APOE and PSEN whose activity has been well documented to be associated with Alzheimer's.
3.3 Mouse HSC data
Finally, we apply our gene set analysis methods to an expression profiling study of HSCs from 30 BXD mice strains. We do not use the ANOVA model for differential expression because we do not have a definitive grouping of the individuals based on any one phenotype. Instead, we look for evidence of differential expression using the variance of the corrected expression levels. To compare our approach to the GSEA method, we compute the correlation between each gene and a known blood phenotype, the cycling of HSC after 7 days using the Fisher's Z-score. We use the gene sets from Tian et al. (2005).
Table 3 shows representative gene sets from the top 25 scoring clusters. Many of these gene sets represent housekeeping genes but we note some interesting candidates. The hypoxia signaling pathway, which includes genes such as HIF-1, a well known transcription factor that targets growth factors such as VEGF and EPO shows evidence of differential expression (P < 0.001) and tight regulation (P < 0.006). The growth factors in turn promote HSC development and differentiation. Although GSEA does not find the hypoxia signaling pathway (P < 0.688), it is able to find the KEGG insulin signaling pathway which contains the SHIP inositol phosphatase, Inpp5d, an important negative regulator of cytokine and immune receptor signaling. Absence of SHIP has been shown to affect the homeostasis and regeneration of murine HSCs (Helgason et al., 2003). Interestingly, insulin, IGF-1 and hypoxia have all been shown to stimulate HIF-1 leading one to speculate as to the complex nature of the regulatory network (Fukuda et al., 2002). We also find the KEGG gap junctions pathway Figure 1b (ranked #25) which contains connexin 43, a gene that is involved in multiconnexin-expressing stromal support of hematopoietic progenitors and stem cells (Cancelas et al., 2000). The information exchange mediated by stromal and HSC interaction has been implicated in stem cell differentiation and development (Orlic et al., 2001; Rosendaal et al., 1994).
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Both GSEA and our method find two gene sets related to active transport (GO:0015399 and GO:0015077) which are not known to be related to any blood phenotypes. When we perform the GSEA analysis using two other phenotypes (stem cell frequency and concurrence of peripheral blood CD4%), we find some interesting results. Using stem cell frequency as the phenotype, these two gene sets are ranked 6 and 9 having P-values of P < 1.98E-09 and P < 1.48E-08, close to those found using the HSC turnover phenotype. However, when we use the concurrence of peripheral blood phenotype, the two gene sets are ranked 554 and 451 with P-values of P < 0.69 and P < 0.40. From the GSEA results, we see that these two gene sets are correlated with some phenotypes but not others. This result supports what we were able to find using expression data alone.
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4 DISCUSSION |
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TOPABSTRACT1 INTRODUCTION2 METHODS3 RESULTS4 DISCUSSIONREFERENCES |
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We have introduced a new method for analyzing gene sets based on the intuitive notions of tight regulation and differential expression. We first presented an approach to look for tightly regulated gene sets using correlation statistics. By considering the correlation structure of gene sets, we are restricting ourselves to only those gene sets that have pathway-like properties. This allows us to use gene sets from sources such as Gene Ontology, where biological pathways are not well represented, to their full potential. This is evident when we analyzed the Alzheimer's dataset. We found that while many gene sets associated with calcium ion channels are differentially expressed but not tightly regulated, other gene sets associated with the ATP-dependent calcium transporter are both differentially expressed and tightly regulated. This result suggests a regulatory mechanism at the level of the transporter and not the channel proteins.
We have also presented a more general framework for finding differentially expressed gene sets which is more appropriate for genome wide expression data over genetically similar individuals or strains of model organisms where clear phenotypic classes are absent and regulatory pattern differences are due to genetic variation. Our approach allows us to detect these subtle differences in expression of individuals which can then be used to look for associated phenotypes (Ghazalpour et al., 2005) as well as eQTLs in genetic variation studies (Bystrykh et al., 2005). In murine HSCs, we were able to find two active transport gene sets independent of phenotype information. Their correlation with phenotypes were then verified using a popular gene set based approach.
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Acknowledgments |
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C.Y. and E.E. are partially supported by National Science Foundation Grant No. 0513612. Part of this investigation was supported using the computing facility made possible by the Research Facilities Improvement Program Grant Number C06 RR017588 awarded to the Whitaker Biomedical Engineering Institute, and the Biomedical Technology Resource Centers Program Grant Number P41 RR08605 awarded to the National Biomedical Computation Resource, UCSD, from the National Center for Research Resources, National Institutes of Health. Additional computational resources were provided by the California Institute of Telecommunications and Information Technology (Calit2).
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