CoXpress: differential coexpression in gene expression data
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Abstract
Background
Traditional methods of analysing gene expression data often include a statistical test to find differentially expressed genes, or use of a clustering algorithm to find groups of genes that behave similarly across a dataset. However, these methods may miss groups of genes which form differential coexpression patterns under different subsets of experimental conditions. Here we describe coXpress, an R package that allows researchers to identify groups of genes that are differentially coexpressed.
Results
We have developed coXpress as a means of identifying groups of genes that are differentially coexpressed. The utility of coXpress is demonstrated using two publicly available microarray datasets. Our software identifies several groups of genes that are highly correlated under one set of biologically related experiments, but which show little or no correlation in a second set of experiments. The software uses a resampling method to calculate a pvalue for each group, and provides several methods for the visualisation of differentially coexpressed genes.
Conclusion
coXpress can be used to find groups of genes that display differential coexpression patterns in microarray datasets.
Keywords
Cluster Algorithm Hierarchical Cluster Analysis Acute Myeloid Leukaemia Acute Lymphoblastic Leukaemia Microarray DatasetAbbreviations
 ALL
acute lymphoblastic leukaemia
 AML
acute myeloid leukemia
 TALL
T lineage leukaemias
 E2APBX1
B lineage leukemias that contain t(1;19)
 BCRABL
B lineage leukemias that contain t(9;22)
 TELAML1
B lineage leukemias that contain t(12;21)
 MLL rearrangement
B lineage leukemias that contain rearrangements in the MLL gene on chromosome 11, band q23
Background
Microarrays have become a standard tool for the exploration of global gene expression changes at the cellular level [1]. Data analysis often includes the use of a statistical test, such as a ttest or analysis of variance, to find genes differentially expressed in one set of conditions when compared to another, or the use of clustering algorithms in order to find groups of genes which behave similarly over a number of experiments [2]. However, these techniques may not detect differential coexpression patterns that exist between two biological states.
Statistical tests, such as the ttest or ANOVA, identify genes that are differentially expressed under one or more conditions. The output of such tests is a simple list of genes, with an associated test statistic and pvalue [3]. There is no indication of which genes may be interacting with one another. Alternatively, clustering algorithms are often used to find groups of genes which display similar expression profiles across a dataset, and these clusters are subsequently analyzed visually for patterns of interest [4, 5]. Eisen et al used hierarchical cluster analysis to determine groups of coexpressed genes, and found that genes within those groups were functionally related [4], and the use of hierarchical cluster analysis is now a standard technique for analysing microarray data [2, 6]. Yeung et al [7] assessed the use of hierarchical clustering to find groups of coregulated genes. Various clustering algorithms were used on a number of datasets, and the results evaluated by determining those genes that share a common transcription factor. Of the algorithms tested, MCLUST [8] and two hierarchical methods (based on the pearson correlation coefficient) showed the highest coincidence of correlated and coregulated genes.
However, genes which show highly correlated patterns of expression in one biological state, but not in another, may not be highly correlated across the entire dataset, and therefore would not be associated with one another if a clustering algorithm is used. Variation may exist in the expression of a gene in different groups of individuals due to the presence of subpopulations, and this may lead to that gene being grouped incorrectly. Furthermore, clustering algorithms do not provide methods to identify groups that are behaving differently in different biological conditions.
Recent work has concentrated on alternative approaches to the discovery of coexpressed genes. Li [9] describes a method whereby genes whose expression is associated with differential coexpression patterns in other pairs of genes may be discovered, and Lai et al [10] describe a conceptually similar method whereby pairs of genes that display differential coexpression patterns between the normal and cancerous state may be discovered. Other approaches have centred on the construction of large gene coexpression networks. Lee et al [11] analysed 60 human microarray data sets to construct gene coexpression networks conserved across multiple data sets, and Stuart et al [12] constructed a gene coexpression network across different organisms, indicating that such relationships are evolutionarily conserved. However, neither of the above attempted to find group of genes differentially coexpressed between different conditions. Choi et al [13] tackled this problem by constructing normal and tumour coexpression networks from a variety of public datasets, comparing the results to find differences in coexpression patterns associated with cancer. In all of these cases, the networks were built by comparing genes pairwise, using some variation of the pearson correlation coefficient, to determine if a coexpression link exists between the two genes. These links were then joined to form a coexpression network.
Cluster analysis and network construction can be thought of as alternative methods for finding coexpressed genes. Whereas networks concentrate on conserved, pairwise comparisons, there is no guarantee that genes that are close in the network, but are not directly linked, have correlated expression profiles. Alternatively, cluster analysis produces groups of genes that are correlated above a certain level, defined by where the tree is cut and the clustering algorithm, but there is no indication of which particular pairs of genes are interacting. Kostka and Spang [14] described the first method to investigate differentially coexpressed groups of genes, using an additive model for scoring genegene coexpression and then a stochastic search algorithm to find groups of genes showing differential coexpression patterns. Jen et al [15] have produced ACT, the Arabidopsis Coexpression Tool, which allows users to calculate coexpression across userdefined data sets and uses a correlation cutoff to define groups of genes.
Here we describe coXpress, a simple and easy to use package that allows users to explore differential coexpression in an intuitive way. The package is aimed at biologists who want to analyse differential coexpression in their data set, which can be achieved in just 4 simple commands once the data has been loaded. CoXpress uses hierarchical cluster analysis to explore the relationship between genes, cutting the tree to form groups of genes that are coexpressed. This is an intuitive approach that many biologists are familiar with. CoXpress then uses a resampling approach to find those groups that are coexpressed in one set of experiments and not in another. The package should be used as first step in the analysis of coexpression, and is designed to complement the approaches described above.
Implementation
CoXpress is released as a package for R. R is a freely available, opensource statistical package [16] that is widely used in the biological community. R has very powerful statistical and graphical capabilities, and many addon packages are freely available. The bioconductor project [17, 18] provides a huge number of addon packages for R, covering a wide range of biological data analysis applications, and the implementation of coXpress in R provides seamless integration with many of these packages. CoXpress is written in the native R language and has been fully tested on both windows and linux. R is available for windows, linux, unix and MacOS (including MacOS X).
The input for coXpress is a matrix of data, with rows representing genes and columns representing microarrays. The R data.frame object is most convenient, and can be created by reading in a text file (using the read.table function), an Excel spreadsheet (using the RODBC library) or from existing R objects, created by the packages from the bioconductor project such as affy [19], limma [20] or marray [18].
The genes are first clustered based on their expression values in a subset of experiments (termed subset 1), using the cluster.gene function. This function wraps the dist, cor and hclust functions that are built in to R, and thus provides a simple interface to hierarchical clustering. When a correlation coefficient is used as the distance measure, the distance measure is calculated as 1  r, where r is the pearson correlation coefficient. The resulting tree is cut at a userdefined value, using the cutree function, to form groups of genes that are coexpressed in subset 1. These groups are then examined in both subset 1 and a second set of experiments, defined by the user, which we will term subset 2.
Groups of size 1 are ignored as there can be no coexpression. Groups of size two are handled by the cox.pairs function. The cox.pairs function uses the cor.test function in R to test if the genes are significantly correlated in subset 1 and subset 2. Thus, a pair of genes significantly correlated in subset 1 and not significantly correlated in subset 2 can be described as differentially coexpressed.

1 ≤ r ≤ +1
where 1 represents positive correlation, 1 represents negative correlation and 0 represents no relationship. The tstatistic is used here to summarise the "difference from zero" of a group of pairwise correlation coefficients. The exact formula for this is:
where x is the vector of unique, pairwise correlation coefficients, $\overline{x}$ is the mean of x and se(x) denotes the standard error of x. A group of highly correlated genes will have a mean correlation close to 1 and a small standard error, resulting in a large value for t. However, a group of uncorrelated genes will have a mean close to 0 and a relatively large standard error, resulting in a small value for t. The observed t statistic is compared against m random t statistics in order to calculate a probability of randomness.
Results
The AML/ALL leukaemia dataset
The utility of coXpress is demonstrated using gene expression data from the leukaemia microarray study of Golub et al [21]. This dataset represents gene expression measurements from 38 tumour mRNA samples, 27 acute lymphoblastic leukaemia (ALL) cases and 11 acute myeloid leukaemia (AML) cases. The HU6800 Affymetrix array was used, which contains 6800 probesets. The dataset has been filtered such that genes with negative values in any sample have been removed, resulting in 2568 genes.
Using coXpress, the genes were first clustered according to their expression levels in the 27 ALL samples, using the cluster.gene function. The distance measure used was 1  r, where r is the pearson correlation coefficient. The resulting tree was cut at a distance of 0.4, representing a correlation coefficient of 0.6, using the cutree function.
These groups were then examined in both the ALL and AML cases using the coXpress function. The observed t statistics in all cases were compared with the t statistics generated by randomly resampling the dataset 10,000 times for each group size. The resulting table contains one row for each group.
To test the robustness of the method to outliers, a bootstrapping approach was used. Each group was retested 1000 times, each time randomly selecting 75% of the observations for each leukaemia subtype (20 AML cases and 8 AML cases). The number of times each group was found to be differentially coexpressed by the coXpress method was recorded.
Differentially coexpressed groups from the Golub dataset
group  N  t1  t2  pr.g1  pr.g2  mean.corr1  mean.corr2  robustness 

3  34  155.6977  0.175907  0  0.4439  0.70126  0.002587  901 
62  7  59.75635  1.06598  0  0.876  0.7201  0.09352  1000 
121  11  54.77229  1.835753  0  0.065  0.679399  0.085609  926 
21  12  51.18428  0.83765  0  0.8032  0.659053  0.03528  1000 
79  7  50.37868  0.830252  0  0.2021  0.724548  0.063511  914 
78  10  50.376  1.040897  0  0.1614  0.655953  0.049546  950 
131  8  42.89021  1.744949  0  0.0787  0.668891  0.144298  760 
157  7  41.89854  0.1536  0  0.5177  0.696409  0.01012  1000 
472  7  36.4184  0.56951  0  0.6958  0.642614  0.04193  1000 
193  7  32.0097  0.06639  0  0.4814  0.707166  0.00404  974 
Most changed pairwise correlation coefficients between the ALL and AML subsets in group 62
GeneA  GeneB  Cor Group 1  Cor Group 2 

X82200_at  U72936_s_at  0.75613  0.68659 
D87127_at  U72936_s_at  0.772053  0.49596 
HG1400HT1400_s_at  U72936_s_at  0.741713  0.50531 
D87127_at  Y08614_at  0.741222  0.47561 
X82200_at  Y08614_at  0.783967  0.40329 
X82200_at  Z26491_s_at  0.773757  0.39009 
D14043_at  HG1400HT1400_s_at  0.654386  0.48988 
D14043_at  Y08614_at  0.687928  0.39583 
D87127_at  Z26491_s_at  0.624918  0.39106 
D14043_at  D87127_at  0.739456  0.24224 
Least changed pairwise correlation coefficients between the ALL and AML subsets in group 62
GeneA  GeneB  Cor Group 1  Cor Group 2 

D14043_at  X82200_at  0.710406  0.11507 
HG1400HT1400_s_at  Z26491_s_at  0.730394  0.014146 
Y08614_at  HG1400HT1400_s_at  0.802284  0.131596 
Y08614_at  U72936_s_at  0.720434  0.05055 
X82200_at  HG1400HT1400_s_at  0.687068  0.222248 
D87127_at  X82200_at  0.727349  0.375199 
D14043_at  Z26491_s_at  0.718968  0.484247 
Z26491_s_at  U72936_s_at  0.679597  0.511949 
D87127_at  HG1400HT1400_s_at  0.577312  0.440534 
D14043_at  U72936_s_at  0.708798  0.586629 
The GOHyperG function of the GOstats package [22] was used to find GO terms overrepresented in the differentially coexpressed groups. Group 3, with 34 members, is enriched for GO terms for lymph node development, cell organisation and biogenesis, and protein biosynthesis and transport. Group 62, which has 7 members, is enriched for GO terms for methyltransferase activity, DNA modification, protein transport and DNA and protein methylation. Group 121, with 11 members, is enriched for GO terms for nucleotidase activity, and RNA splicing, processing and metabolism.
The ALL subtype dataset
This dataset is from the Acute Lymphoblastic Leukaemia study by Yeoh et al [23]. Six subtypes of ALL leukaemias are represented in 248 cases. The six subtypes are TALL, E2APBX1, BCRABL, TELAML1, MLL rearrangement, and hyperdiploid >50. The HG_U95Av2 Affymetrix microarray was used which contains 12,600 probesets. The dataset has been filtered such that genes with negative values in any sample have been removed, resulting in 1516 genes present in the dataset.
Using coXpress, the genes were first clustered according to their expression levels in the BCRABL samples, using the cluster.gene function. The distance measure used was 1  r, where r is the pearson correlation coefficient. The resulting tree was cut at a distance of 0.5, representing a correlation coefficient of 0.5, using the cutree function. These groups were then examined in both the BCRABL and TALL subsets.
Differentially coexpressed pairs in the ALL subtype dataset
group  N  r1  p1  r2  p2 

14  2  0.658202  0.007638  0.58144  4.33E05 
201  2  0.655991  0.007916  0.44687  0.002664 
143  2  0.67791  0.00548  0.30901  0.043776 
Groups of N ≥ 3 were analysed in the BCRABL and TALL subsets using the coXpress function. The observed t statistics in all cases were compared with the t statistics generated by randomly resampling the dataset 10,000 times for each group size. The resulting table contains one row for each group.
To test the robustness of the method to outliers, a bootstrapping approach was used. Each group was retested 1000 times, each time randomly selecting 75% of the observations for each leukaemia subtype. The number of times each group was found to be differentially coexpressed by the coXpress method was recorded.
Differentially coexpressed groups from the ALL subtype dataset
group  N  t1  t2  pr.g1  pr.g2  mean.corr1  mean.corr2  robustness 

47  16  59.8611  2.453073  0  0.0684  0.66915  0.05863  805 
31  10  29.20261  2.194293  0  0.0677  0.64726  0.07787  861 
89  13  42.1617  1.934779  0  0.0904  0.63834  0.04420  885 
41  11  30.19613  1.122452  0  0.2115  0.63042  0.05146  986 
25  12  34.18317  2.531833  0  0.0503  0.62832  0.10027  686 
9  14  30.35473  2.324388  0  0.0655  0.59705  0.06109  829 
71  13  33.96871  2.236447  0  0.0658  0.58783  0.05880  855 
15  19  45.6475  1.865767  0  0.1373  0.58500  0.03853  1000 
103  10  29.54434  1.24949  0  0.9613  0.58393  0.03758  1000 
19  20  45.45846  1.509674  0  0.2093  0.5810  0.02446  1000 
11  16  43.62891  1.402566  0  0.1964  0.57995  0.02908  1000 
114  12  32.84917  1.192507  0  0.205  0.57624  0.03668  995 
32  13  34.2227  1.097651  0  0.2275  0.57004  0.03208  982 
The GOHyperG function of the GOstats package [22] was used to find GO terms overrepresented in the differentially coexpressed groups. Group 47 with 16 members, is enriched for GO terms for hormone catabolism, glucocorticoid receptor signalling and glucocorticoid catabolism. Group 31 with 10 members contains two probes for a gene in the RAS oncogene family, and is enriched for GO terms for oxidoreductase activity and ubiquitin activating enzyme activity. Finally, group 89 with 13 members contains genes annotated as Bcell lymphoma and cancer susceptibility genes, as well as genes enriched for GO terms for endothelial cell migration, regulation of cell motility and migration, angiostatin binding and regulation of blood vessel endothelial cell migration.
Discussion
It is clear that coXpress is capable of finding differentially coexpressed groups of genes in both data sets. The groups presented above are extremely highly correlated in one subset of experiments, yet show little correlation in another subset. Furthermore, these patterns of correlation are shown to be nonrandom in the first subset, and no different from random in the second subset. The results show that it is the overall correlation structures of these groups that have changed significantly and some pairs of genes are still highly correlated in the second subset. It is important that each group is examined using the inspect.groups function in order to determine which of the pairs of genes are still correlated and which are not. The groups found by coXpress could also feed into the network construction technique described by Choi et al [13] to determine which pairwise relationships are conserved and which are not. One would expect the differences between ALL and AML leukaemia in the Golub dataset to be larger than those between different ALL subtypes in the Yeoh dataset, and the fact that coXpress can still find groups with such different correlation structures demonstrates the power of the method.
The use of hierarchical cluster analysis, followed by cutting the tree, is an intuitive approach and one that is familiar to biologists. However, it has limitations. For example, each gene may only be in one group, which does not ring true for biological systems, where many genes have multiple functions. Also, the choice of where to cut the tree is arbitrary. A high cutoff will produce many small groups of genes that are very highly correlated, whereas a lower cutoff will produce fewer groups, of larger size, which are not as highly correlated. In reality the user must use a range of different cutoffs to see which performs best with their dataset. Other clustering algorithms, such as MCLUST [7, 8], have been shown to outperform hierarchical cluster analysis, however, there is no reason why these algorithms could not be used to define the groups of genes prior to running the coXpress function.
There are several directions in which the software can be developed. At present, the user defines which subsets of experiments are analysed, however it is possible that coXpress could suggest, or improve, these groupings using an approach such as random forests or genetic algorithms. This may allow researchers to discover subpopulations in the system under study. Integration of other clustering algorithms with coXpress, such as MCLUST, may also improve the performance of the software. In particular, clustering or grouping algorithms that allow genes to be present in more than one group may be advantageous. Finally, the integration of network construction algorithms would allow researchers to further analyse and visualise the differentially coexpressed groups discovered by coXpress.
Conclusion
We describe coXpress, an opensource R package that allows researchers to analyse differential coexpression patterns in DNA microarray data. CoXpress contains several methods for the discovery and visualisation of differentially coexpressed genes. We show how coXpress can be used to find groups of differentially coexpressed genes in two publicly available microarray datasets. The groups found are shown to be highly correlated in one subset of experiments, yet show little or no correlation in a second subset of experiments. A comparison against random distributions is used to obtain a pvalue for the coexpression of the genes in different subsets.
Availability and requirements

Project Name: coXpress

Project Home Page: http://coxpress.sf.net

Operating Systems: Windows, Linux

Programming Language: R

Other Requirements: R, gplots, gtools, gdata (for heatmaps), hu6800, hgu95av2, plotrix (for examples)

License: GNU GPL
Notes
Acknowledgements
This work was funded by the core strategic grant of the Institute for Animal Health, provided by the BBSRC.
Supplementary material
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