The novel multi-dimensional 'omics data analysis software SIGMA² is built on the framework of a facile visualization tool called SIGMA, which can display alignment of genomic data from a built-in static database 7. The arsenal of functionalities introduced in SIGMA² is shown in Table 1.

SIGMA² is built to handle a variety of analysis techniques typically used in the high-throughput study of cancer, allowing the combinatorial integration of multiple 'omics disciplines. The hierarchy, which underlies the program, groups data into genome, epigenome, and transcriptome is shown in Figure 2A and the overall functionality map is given in Figure 2B and listed in Table 2. With each 'omics dimension, data sets may be imported representing any of the major types of biological measurements being assayed, for example, (i) examining both DNA copy number and LOH assays within the genomic bundle, (ii) examining both DNA methylation and histone modification status within the epigenomics bundle, and (iii) examining both gene expression profiles and microRNAs expression assays within the transcriptomic bundle. Each assay may branch into data sources from a multitude of technology platforms.

SIGMA² treats all data in the context of genome position based on the relevant human genome build using the UCSC genome assemblies. An interval-based approach is used to sample across different array platforms and assays and data from each interval are merged together. Briefly, this is done by querying data at fixed genomic intervals for each platform and subsequently taking an average of the measurements within each interval. The algorithm is listed in Figure 3.

Standard tab-delimited text files are used for the input of data for all of the assay types. For genomic data, specifically array CGH, normalization is recommended using external algorithms such as CGH-Norm and MANOR 1920. Segmentation analysis can be performed within SIGMA², but results from external analysis can be imported and used in the consensus calling feature. The algorithms which can be called within SIGMA² currently include DNACopy and GLAD 2122. Multiple sample batch importing is available to facilitate efficient loading of datasets. To utilize this, the user must create an information file which describes each sample in the dataset. Formatting requirements of the information file are specified in the manual. Alternatively, for Affymetrix SNP array analysis, data should also be pre-processed and normalized using the appropriate software, such as CNAG before importing into SIGMA² 23. Genotyping calls should be made prior to importing, using the "AA", "AB" and "BB" convention. If the genotype call does not exist, "NC" must be specified. For epigenomic data, data from affinity based-approaches (MeDIP 6 and ChIP 24) should contain a value representing the level of enrichment and the genomic coordinates for each spot. Similarly, for bisulphite-based approaches 25, a percent of converted CpGs should be provided along with the genomic coordinates for each spot. Finally, for transcriptome data, gene expression data from Affymetrix experiments can be directly imported and processed as CEL files and are normalized using the MAS 5.0 algorithm implemented in the "affy" package of R. For any assay type, custom data can be imported whereby the user provides a map of the platform based on the given genome build, and the unique identifier for the map must be used for the data generated from those experiments.

The main user interface in SIGMA² utilizes a tabbed window-pane which allows the user to open multiple visualizations simultaneously (Figure 4). The left part of the window manages the analyses and projects which belong to the current user and button shortcuts for the main functionality are spread along the top of the window. Using an example of an array CGH profile from the Agilent 244K platform, we demonstrate the step-wise interrogation of a region of interest 26. Briefly, using the highlighting toolbar button, the user can select a region of interest and subsequently, by clicking the right mouse button, the user can search for annotated genes within the specified genomic coordinates.

The first, and most basic, level of analysis is from a single assay type. For array CGH, multiple options for segmentation algorithms are available within the program and results from externally run segmentation can be imported as well. However, each segmentation algorithm has its advantages and disadvantages depending on the type of data used and the quality of data at hand. A unique feature of SIGMA² is the ability to take a consensus of multiple algorithms using "And" or "Or" logic between algorithms. Moreover, a level of consensus can be specified (Figure 5A). For example, if an experiment is analyzed using five approaches, the user can select areas of gain and loss which were detected by one algorithm, at least three algorithms, all five algorithms, etc. For LOH, basic analysis using the number of consecutive markers that exhibit LOH is used to determine its status. Affinity-based approaches for DNA methylation and histone modification states or bead-based percentage of CpG island methylation is analyzed by either direct thresholding or z-transform thresholding. For any of the different assay types, when examining across a number of samples, a frequency of alteration can be calculated and plotted.

For data from different array platforms, but assaying the same biological measurement, the algorithm for integration is used to derive common data. This feature is most applicable to DNA copy number data due to the number of array CGH platforms. This allows for better utilization of publicly available data and thus, increasing sample size for statistical analysis. Similar to the multiple sample analysis of data on the sample platform, a frequency of altered states can be generated and plotted. Figure 5A shows the concerted analysis of a sample profiled on the Affymetrix 500K SNP array, Agilent 244K CGH array and the whole genome tiling path BAC array (Figure 5B).

Within a given 'omics dimension, multiple assay types can be analyzed in combination. For example, it is useful to investigate copy number and LOH and the interplay between DNA methylation and different states of histone modification. Typically, in regions of copy number loss, LOH is also observed. However, LOH can also occur in regions which are copy number neutral, indicating a change in allelic status which is not interpretable by one dimension alone. Here, we show a sample for which copy number and LOH information exists, a region of copy number loss associated with LOH (Figure 6). In terms of epigenetics, DNA methylation and states of histone methylation and acetylation have been known to be biologically relevant. With high throughput technologies available to assay these dimensions, this type of analysis will become more prevalent.

The most common analysis of multiple 'omics dimensions is the influence of the genome on the transcriptome. A number of software packages have started to incorporate approaches to examining gene dosage and gene expression 8927. In SIGMA², there are multiple functionalities which allow the user to link DNA copy number to gene expression. For a single group of samples, with matching DNA copy number and gene expression profiles, the user can determine associations through two main options: a) using a correlation-based approach, correlating the log ratios with the normalized gene expression intensities and b) using a statistical-based approach comparing the expression in samples with copy number changes against those without copy number change utilizing the Mann Whitney U test, analogous to approaches taken in previous studies 27. Spearman, Kendall or Pearson correlation coefficients can be calculated for option a). Similarly, this functionality is also available for correlating epigenetic profiles and gene expression.

In addition to single group analysis, two-dimensional genome/transcriptome analysis can be applied to two-group comparison analysis. For example, if patterns of copy number alterations are compared between two groups and a particular region is more frequently gained in one group than another, the expression data can subsequently compared between the groups of sample to determine if there is an association between gene dosage and gene expression. That is, we would expect the group with more frequent copy number gain to have higher expression than the other group. Notably, this functionality does not require both copy number and expression data to exist for the same sample, but allows the user to select an independent dataset for expression data comparisons (Figure 7).

Finally, for two groups of samples, the user can compare the distribution of changes between two groups to determine if the patterns are statistically different using a Fisher's Exact test. For DNA copy number, it is the distribution of gain and losses; for DNA methylation or histone modification states, the proportion of samples that meet the threshold of enrichment for each group (low or high); and for LOH, proportion of samples with LOH for a region for each group.

This type of analysis can be performed with a single sample or multiple samples, thus allowing combinatorial ("and") analysis for large datasets. In addition, the user can also identify "or" events, where a change in any of the dimensions can be flagged. This is more important in multi-sample datasets as one dimension may not capture complex alterations of a particular region.

Using the breast cancer cell line HCC2218, we show the integration of genomic, epigenomic, and transcriptomic data. Interestingly, when we examine the ERBB2 gene on chromosome 17, we show concurrent amplification, LOH, loss of methylation and drastic increase in gene expression (Figure 8). ERBB2 has shown to be an important gene in breast cancer development and therapeutic intervention. This demonstrates the value in integrating multiple dimensions to understand complex alteration patterns in disease samples where multiple causes can lead to a single effect.

High resolution images can be exported for all types of visualizations in SIGMA². Histogram plots of gene expression, heatmaps with clustering of gene expression, karyogram plots and frequency histogram plots are the main types of visualization available. Frequency histogram data which is used to generate the plots can also be exported. Integrated plots with data plotted serially or overlaid are also available for analysis involving multiple genomic and epigenomic dimensions. Genes which are obtained from the conjunctive (And) and disjunctive (Or) multi-dimensional analysis can be exported with their status. Results of statistical analysis such as Fisher's exact comparisons and U-test comparisons of gene expression can be exported against annotate gene lists based on user-specified human genome builds. Currently, April 2003 (hg15), May 2004 (hg17) and March 2006 (hg18) are the available genome builds 18. As new builds are released, support for those builds will be available. Finally, data from multi-platform integration can be exported based on based pair position for additional external analysis if necessary.