There is a wealth of techniques for identifying significant differential gene expression. These techniques can be categorized into three approaches; viz., individual genes, gene pathways and gene classes approaches.

• Individual genes

These techniques search for individual genes that are differentially expressed. For example, the fold change, t-test and Significance Analysis of Microarrays (SAM) [1]. The output of such algorithms is a list of genes that are deemed differentially expressed.

• Gene pathway deduction

Methods of this genre attempt to infer biological information from data without using pre-existing biological information. Bayesian learning [2] and Boolean network learning [3] are representatives of this approach. The researcher will obtain a set of gene networks connected and inferred solely from the gene expression data.

• Gene classes

These techniques test how gene classes behave as a whole. These techniques either pre-process or post-process their information with existing biological background knowledge to guide their analysis of the microarray data. Examples include over-representation analysis (ORA) [4], Functional Class Scoring (FCS) [5], GSEA [6], NEA [7] and ErmineJ [8]. Results from such methods are normally a list of pathways or gene groups that are differentially expressed according to the algorithms.

The commonly acknowledged challenge of these techniques is obtaining reproducible results. For instance, in differentially expressed gene discovery, there should be a substantial overlap in the gene lists from different datasets of the same disease. This is inferred from the premise that similar underlying conditions cause the onset of certain diseases. However it has been shown that there is little concurrence among such gene lists [9–11].

For example, [11] demonstrated this inconsistency using SAM. For a pair of datasets involving prostate cancer [12, 13], he calculated the percentage overlap of differentially expressed genes between them. The top 10 genes had a percentage overlap of 30% while the top 100 genes had a percentage overlap of 15%. The same calculations were repeated for lung cancer [14, 15] and DMD [16, 17] datasets, yielding similar low percentages.

In addition, the functional gene lists, pathways or classes determined by such methods do not provide sufficient descriptive information about the interplay and relationship of genes [18]. Hence the generated hypotheses are usually too general, rendering them ineffective in guiding further research and treatment [19].

In this article we present our technique, SNet, to identify subnetworks which are expressed significantly within a phenotype of a microarray experiment. Furthermore, we demonstrate the consistency—and thus reproducibility—of the identified subnetworks by achieving a high overlap (51.18% to 93.01%) between significantly differentially expressed genes (found within the identified subnetworks) of different microarray experiments of the same disease. Finally, we show that the significant genes found by t-test/GSEA formed much smaller subnetworks (<5 genes) than ours. These experiments demonstrate the consistency, reproducibility, descriptive power, interpretability and significance of subnetworks obtained using our technique.

We hypothesize that specific biological processes within pathways are relevant to specific diseases. Thus our approach concentrates on identifying these biological processes that we termed “subnetworks”. These subnetworks should be largely the same across independent datasets of the same disease. Because the probability of such a subnetwork of highly expressed genes randomly occurring is sufficiently low, we are able to conclude that these subnetworks have a strong biological relevance with respect to the disease. Furthermore, such a subnetwork provides intricate information on the interplay and relationship between the genes, which will be advantageous in guiding subsequent research. This technique also removes sporadic genes that appear solitary within a biological pathway (because of their higher possibility of being a false positive).

We define the term “subnetwork” as “a set of genes and relationships where all genes in the subnetwork are reachable by all other genes in the (undirected) subnetwork. Reachability between genes is established by the existence of an undirected path between the genes of the subnetwork.” This is analogous to the definition of “connected components” in graph theory [20].

Only two types of gene-gene relationships are considered: inhibition and activation. This information regarding the relationship of two genes within a pathway is already inherent within the database and our goal is to find out if the microarray data complies with these relationships. In the example in Figure 1, we see the genes ATM, CHK1, CHK2 and MDM2 with the relationships: ATM activating CHK1, CHK2 and MDM2 inhibiting p53. Thus we define the term “relationship” between a pair of genes X and Y as a situation where either X “activates” Y or X “inhibits” Y.

Because of the fine granularity of analysis, the pathway repository must allow us to easily segregate the original microarray data into its relevant pathways, gene relationships and subnetworks. Due to the large amount of data, the pathway repository must also facilitate the development of automated analysis workflows. The repository therefore is required to have the following characteristics:

This set of criteria eliminates contemporary pathway sources such as Ingenuity [21], BioPax [22], and GenMapp [23], and we are left with KEGG. However, KEGG has a number of limitations. Firstly, its collection of pathways is not sufficiently comprehensive [24]. For example, our analysis [25] shows that 78.8% of pathways in Ingenuity and 64.4% of pathways in Wikipathways are not contained in KEGG. Secondly, KEGG still uses an old-fashioned SOAP/XML interface. So we developed PathwayAPI [25] which offered the combined pathway information of KEGG, Ingenuity, and Wikipathways along with a modern JSON-based application programming interface.

Our technique (to be described later) was applied on the disease types listed below with two different datasets analyzed independently for each disease type. The selection of the two datasets for each disease is because they were used to compare gene selection methods in earlier papers [11]. In addition, the two datasets for each disease type are from different platforms, thus providing a more stringent test as they make it harder for the gene selection algorithms to consistently select the same genes independently from the two datasets.

Microarray experiments are crucial because they measure the behaviour of individual genes with respect to diseases or treatments. Results from these experiments are heavily scrutinised to obtain biological insights into the occurrence of diseases or the effectiveness of certain types of treatments. In order to provide more indepth analysis to experiments, contemporary algorithms have incorporated biological information into their analysis so that the analysis can be more descriptive and hopefully useful to the researchers. Our techniques have taken this approach one step further. Firstly, we no longer consider prior biological knowledge as a separate aspect of microarray analysis. Rather, we take into account the integrity of the biological information that is being provided into the algorithm for analysis. Secondly, our algorithm uses both the gene-gene interaction information and pathway information in our analysis. Because of these two enhancements, we are able to generate subnetworks in real-time according to the responses of the microarray experiments. These contributions help us avoid some of the potential caveats present within microarray experiments.

We are certainly not the first to integrate gene-expression data with gene-gene relationships. GNEA [42] is one such example. GNEA uses a global protein-protein interaction network, finds subnetworks that correspond to regions of significantly differentially expressed genes; these subnetworks are called HSNs in the paper. GNEA then determines which gene sets in a library of gene sets are significantly enriched in HSNs. There are two possible shortcomings in this approach. Firstly, in using a single global protein interaction network, GNEA makes the biological assumption that the local behaviour of proteins can be translated in a similar fashion globally and that gene expression levels are in a tight correspondence to protein levels (which is not generally true). A similar issue is raised in [7] where the authors argued that proteins which are very well connected have an extremely high chance of obtaining a low p-value and being ranked as significant. Because of the high connectivity of such proteins, they are liable to be involved in various disjoint biological processes, leading to the error of combining independent subnetworks through these proteins. To prevent such scenarios, we instead implemented our algorithm via identifying localised gene-gene subnetworks within pathways. Secondly, while a gene set that is significantly enriched in HSNs is likely to be relevant, a large gene set may not be found significantly enriched in HSNs even though it may have contained a subset that is significantly enriched. This is also an issue that we find in GSEA.

We obtain a low result overlap from GSEA possibly because the pathways from PathwayApi are very large and GSEA relies on a large portion of a pathway to exhibit a correlated change. Hence when only a subset of a pathway demonstrates differential expression, GSEA may be unable to pick this up. We verified this hypothesis by feeding into GSEA subnetworks that we found from our algorithm into the leukaemia datasets. Indeed GSEA was then able to obtain significant subnetworks that overlapped.

In addition, we show that our technique generates significant subnetworks and genes that are more consistent across datasets compared to the other popular methods available (GSEA, t-test and SAM). The large size of subnetworks which we generate indicates that they are generally more biologically significant (less likely to be spurious). To validate our results, we show that most of our genes from the generated subnetworks have also been considered significant by the t-test. In addition, we have chosen two sample subnetworks and validated them with references from biological literature. This shows that our algorithm is capable of generating descriptive biologically conclusions.

Our final contribution lies in our ability to create connected components (of known pathways) in real time based on microarray data. This allows us to obtain connected components according to the microarray data. Both GNEA and GSEA use fixed gene sets and determines if these gene sets are significant or not. These techniques assume that a gene set is significant only if a substantial proportion of the genes within the gene set is significant. This assumption might not be valid because there are instances where only part of a gene set becomes significant; and it would probably go unnoticed if most of the rest of the genes are unaffected. Our ability to create connected components based on the microarray data of the phenotypes—and use these as gene sets—ensures that we have sufficient granularity to capture portions of pathways or gene sets that are affected.

Overview Let the phenotype of interest be d and the remaining phenotypes be labelled as ¬d. We first extract genes which are highly expressed within this phenotype d from the microarray experiment. This set of genes is next segregated into their respective subnetworks using apriori biological information from the pathway repository [25]. This gives us a list of subnetworks cc (whose genes are highly expressed) within d. A score (depending on the size of the subnetwork and its consistency among the patients) is next calculated and assigned to each subnetwork. Finally we estimate the p-value of every single subnetwork within the list and keep those which are significant. This is elaborated in the following steps:

Step 1: Subnetwork extraction We create a ranked gene list for each patient within a phenotype according to the gene expression level of that patient. From this ranked gene list we extract only the top α% of genes for each patient. This condensed gene list is referred to as G _{P i} for the i ^th patient P _i . We next iterate across gene lists G _{P i} only for patients of phenotype d, extracting only genes which appear in more than β% of the patients of phenotype d. This creates a list of genes GL which turns up highly expressed across most of the patients of phenotype d. Finally, using the programmatic interface of PathwayAPI, gene list GL is segregated into the respective subnetworks. In our experiments, α is taken to be 10 and β to be 50.

To segregate GL into the different subnetworks, we first split gene list GL into its pathways and the gene-gene relationships within these pathways. (We highlight that a gene is allowed to appear in more than one pathway.) Next, by treating each gene as a vertex and each gene-gene relationship as an edge, we can easily locate the connected components (subnetworks) formed by these edges (gene-gene relationships) and vertices (genes) in each pathway. This process is illustrated in Figure 4.

Step 2: Subnetwork scoring For each subnetwork sp within cc and for each patient P _i (regardless of phenotype), we compute the overall expression level of sp in P _i by

(1)

Here, g denotes a gene in the subnetwork sp that is highly expressed (top α%) in patient P _i ; k is the number of patients of phenotype d who have gene g highly expressed (top α%); and n is the total number of patients of phenotype d.

Let P₁, …, P _n be patients of phenotype d; and P _{n +1}, …, P _m be patients of other phenotypes ¬d. We assign two score vectors Ssp _{sp , d} and Ssp_sp,¬d respectively for these two groups of patients, where

(2)

The t-statistics is now calculated between these two vectors, creating a final score for each subnetwork sp within cc. We call this score Ssp _{sp , t} .

Step 3: Subnetwork significance We repeat Steps 1 and 2 for all the phenotypes in the dataset to extract a list of subnetworks SN. The significance of the observed subnetworks is estimated by randomly permuting the phenotypes labels, re-extracting the subnetworks and recomputing their t-statistics scores. This generates a null distribution for the score and size of the subnetworks. The p-value of each subnetwork is then calculated relative to this null distribution. The null hypothesis being that for a subnetwork obtained of size |sp| and score Ssp_sp,t, the subnetwork is not significant. An example of such a distribution is seen in Figure 5. In detail, the procedure is as follows:

A Randomly swap the phenotype labels of the patients, recreating the subnetworks and recalculating their t-statistics scores.

B Repeat [A] for 1,000 permutations. This creates a two dimensional histogram of the scores and sizes of the subnetworks.

C Estimate the nominal p-value of each subnetwork by using the histogram created in point [B].

Finally, we consider subnetworks whose p-value was sufficiently small (≤ 0.05) to be significant. Doing so would provide us with an independent set of significant subnetworks SN for each dataset. Using our algorithm, we have managed to show that we are able to obtain consistent significant subnetworks across different datasets of the same disease.