A rectified factor network based biclustering method for detecting cancer-related coding genes and miRNAs, and their interactions

Abstract

Detecting cancer-related genes and their interactions is a crucial task in cancer research. For this purpose, we proposed an efficient method, to detect coding genes, microRNAs (miRNAs), and their interactions related to a particular cancer or a cancer subtype using their expression data from the same set of samples. Firstly, biclusters specific to a particular type of cancer are detected based on rectified factor networks and ranked according to their associations with general cancers. Secondly, coding genes and miRNAs in each bicluster are prioritized by considering their differential expression and differential correlation values, protein-protein interaction data, and potential cancer markers. Finally, a rank fusion process is used to obtain the final comprehensive rank by combining multiple ranking results. We applied our proposed method on breast cancer datasets. Results show that our method outperforms other methods in detecting breast cancer-related coding genes and miRNAs. Furthermore, our method is very efficient in computing time, which can handle tens of thousands genes/miRNAs and hundreds of patients in hours on a desktop. This work may aid researchers in studying the genetic architecture of complex diseases, and improving the accuracy of diagnosis.

1. Introduction

Detecting cancer-related genes, including coding genes and microRNAs (miRNAs), as well as their interactions is a crucial task in cancer research, which could help researchers focus further efforts on the most promising biomarkers [1]. For this purpose, various computational methods have been developed, which could be classified into three categories: single gene, network based and gene module methods. Single gene based methods rely on gene expression profile analysis [2, 3]. For example, Endeavour [2] assesses the BLAST scores of candidates against the known cancer genes and prioritize candidates that are homologous to seed biomarker genes. Makhijani et al. [4] and Torrente et al. [5] identified cancer-related genes by compiling a large number of gene expression datasets and choosing common differentially expressed genes (DEGs) as cancer-related genes. Similar methods were also used in cancer-related miRNAs identification. For example, researchers started to explore the involvement of miRNAs in cancers through computational analyses of their expression data with statistical tests such as Student’s t-test [6], Wilcoxon signed-rank test and ANOVA [7, 8].

Network-based methods rely on the guilt-by-association paradigm, i.e., to infer functions of poorly characterized genes from their associations with other well-described genes. The association can be in the form of gene co-expression and gene-gene interaction between candidate genes and known cancer genes [9–11]. In the past few years, several network-based methods for analyzing cancer-related coding genes [12] or cancer-related miRNAs [13] were proposed. For instance, NetICS [14] is a graph diffusion-based method for prioritizing cancer genes by integrating diverse molecular data types on a directed functional interaction network. NetICS prioritizes genes by their proximities to upstream aberration events, and to downstream differentially expressed genes. GenePANDA [10] assesses whether a gene is likely a candidate disease gene based on its relative distance to known disease genes in a functional association network. SIiR-NBI [15] prioritizes miRNAs as potential biomarkers on the basis of a heterogeneous network connecting drugs, miRNAs and genes. KATZ [16] uses the functional similarity scores to denote the associations based on the distances between the miRNAs and disease nodes. Recently, module-based methods are widely used, as many cancers are believed to be caused by the dysfunctional regulation in a set of functionally related genes rather than a single gene. For example, FGMD [17] uses a hierarchical clustering algorithm on gene and isoform expression data to identify functional gene modules, and ranks them by the ratio of known cancer genes in each module. MGOGP [18] uses predefined gene modules and known cancer genes as heuristics to prioritize cancer-related genes. Zhou et al. [19] applied a systems biology approach by combining differential expression analysis and weighted gene co-expression network analysis (WGCNA) to detect the colon cancer-related miRNA and gene modules.

However, limitations of current methods still exist. Most studies handle coding genes and miRNAs separately, ignoring the regulatory relationships between miRNAs and coding genes. In addition, most methods rely on a single source of data type, due to the computational complexity, especially in large datasets. Although the large-scale data enabled better identification of new cancer-related genes or miRNAs, few methods can handle large amounts of datasets in a time-efficient way. New comprehensive and time-efficient methods are increasingly needed as more and more data are becoming available.

With the increasing availability of multi-dimensional biological datasets for the same samples (i.e., gene expression, miRNAs, and copy numbers), it becomes possible to systematically understand the regulatory mechanisms in cancer [20]. Many studies have been conducted in this way [21]. For example, Freiesleben et al. [22] combined analyses of miRNAs and gene expression profiles in uncovering pathways potentially involved in multiple sclerosis. Zhang et al. [23] developed a multiple nonnegative matrix factorization framework to integrate gene and miRNA expression data for identifying miRNA-gene regulatory comodules. Liu et al. [24] used data from mRNA and miRNA microarray datasets to identify potential pancreatic cancer-related genes. It is important to discover a set of co-expressed genes and miRNAs representing a functional gene module [25]. Research shows that joint analysis of expression data on the same set of samples from multiple omics sources has potential to achieve more comprehensive results than separate analyses [26, 27]. On the other hand, many co-expression relationships are condition specific. Biclustering was developed to cluster a subset of genes that have similar expression in a subset of conditions [28]. For example, Fiannaca et al. [29] used a biclustering approach (ISA algorithm) to simultaneously select a subset of features that characterizes a subset of samples based on a “local similarity” criterion for analyzing the differential expression of miRNAs in breast cancer samples. As a result, they found 12 different miRNA clusters, associated to specific groups of patients. They concluded that clustering miRNAs according to subclass of tumours can help better define a potential role of miRNA as prognostic, diagnostic and therapeutic markers. However, the biclustering problem is NP-Complete [30] and very time-consuming to compute. A promising method to address this issue is the recently developed unsupervised learning approach Rectified Factor Networks (RFN), which is a generalized alternating minimization algorithm based on the posterior regularization method. RFN can efficiently construct very sparse, non-linear, high-dimensional representations of the input via their posterior means [31]. To speed up computation, RFN performs a gradient step both in E-step and M-step with GPU implementations. RFN can easily get thousands of biclusters from a very large matrix in a short time.

In this paper, we propose a new method rfnGMI (rectified factor network for cancer-related coding Gene, MiRNA and their Interactions detection), which applies RFN on the analysis of the combined expression profiles of miRNAs and coding genes from the same set of samples (Supplemental File, rfnGMI.py). By analyzing combined expression profiles of coding genes and miRNAs, a set of functional related coding genes and miRNAs are clustered together by RFN, and the regulatory relationships between miRNAs and coding genes can be identified. To detect cancer-related coding genes, miRNAs and their interactions, only biclusters specific to a studied cancer type (breast cancer in this study) are considered. The selected biclusters are prioritized by considering their differential expression and differential correlation values, protein-protein interaction (PPI) data, and overlaps with general known cancer marker coding genes and miRNAs. To get more robust result, a rank fusion process is used to obtain the final comprehensive rank by combining multiple ranking results together.

2. Methods and Materials

The overall design of our method is shown in Fig. 1. rfnGMI mainly comprises of five parts: (A) datasets preprocessing, (B) RFN-based cancer-specific bicluster detection and prioritization, (C) prioritization of bicluster coding genes and miRNAs, (D) rank fusion process, and (E) cancer-related gene-miRNA interactions detection.

Fig. 1. Overview of our method with five components.

A. Data processing and input. The RNA-Seq expression datasets of both coding genes and miRNAs in the same sets of samples were downloaded from TCGA and processed. B. RFN-based breast cancer-specific bicluster detection and prioritization. In this step, biclustering method (RFN) is iteratively applied on Z-score transformed expression matrixes E_C (cancer) and E_N (normal). Each time only one most significant bicluster was selected. C. Prioritization of bicluster coding genes and miRNAs. In the selected biclusters, we measured the importance of a coding gene or miRNA by considering four aspects of information: a) The differential expression value of the coding gene or the miRNA (de_i). b) The sum of the differential correlation value between the coding gene or the miRNA and all other genes in the bicluster (dc_i). c) Whether the coding gene or the miRNA is a known cancer-related gene (kc_i). d) Whether the coding gene or the miRNA has direct PPI interactions with known cancer-related coding genes and miRNAs (DI_i). D. Rank fusion process. We used a rank fusion process to get the final rank of all the coding genes and miRNAs in the selected biclusters (B₁,B₂,…,B_N). E. Detection of cancer-related coding gene-miRNA interactions based on cancer-specific biclusters.

2.1. Datasets and preprocessing

Both coding gene and miRNA RNA-Seq raw count datasets of the normal and breast cancer under the same sets of samples were downloaded from The Cancer Genome Atlas (TCGA) (https://tcga-data.nci.nih.gov/tcga/). After removing genes or miRNAs with zero expression values across all samples, we had the expression data of 20,492 genes and 503 miRNAs over 758 cancer samples, 20,381 genes and 503 miRNAs over 94 normal samples (Supplemental File, Sample_Reference_ID.txt). For gene differential expression analysis, we used DESeq2 R package [32] and the raw count expression datasets. DESeq2 expects raw count data as the input, which is important for DESeq2’s statistical model to hold. For bicluster detection, RFN needs Gaussian mean-centered data. Hence, we firstly removed genes and miRNAs with 0 expression values across all samples. Then we applied a log2 transformation of the raw read counts and then calculated the z-score. The z-score represents the number of standard-deviations that a gene expression value is away from the mean of all the values in the same group.

Cancer-related genes and miRNAs were retrieved and combined from several sources. From [33], we collected 110 breast cancer-related genes, and from the breast cancer website (https://www.breastcancer.org/) we collected 17 breast cancer specific genes. After removing genes excluded in the expression datasets, we had 115 breast cancer-related genes, which were used to validate our method. From the COSMIC database [34], we collected 604 general cancer genes (excluding the 115 breast cancer-related genes) as known cancer genes. From the miRCancer database (http://mircancer.ecu.edu/index.jsp) [35], we collected 120 breast cancer-related miRNAs and 225 other cancer-related miRNAs as general known cancer miRNAs. We downloaded all the PPIs from the Human Protein Reference Database (HPRD) [36], which included 39,240 interactions among 9617 proteins, among which 3794 genes had direct interactions with the 604 known cancer-related genes.

2.2. Cancer-specific bicluster detection

We used the unsupervised matrix decomposing based biclustering method RFN to detect cancer-related biclusters [31]. RFN is a revised version of Factor Analysis for Bicluster Acquisition (FABIA), one of the most successful biclustering methods [37]. In contrast to the concept of a bicluster as a set of co-expressed genes under a set of conditions [38], biclusters in RFN are identified by decomposing the expression matrix into clusters that each corresponds to a subset of samples and a subset of features that exhibit a unique latent structure to those subsets. The RFN model is shown in Eq. 1.

$$v=Wh+\epsilon$$ (1)

where v ∈ R^m are visible units (observations) of expression level on n samples and m genes (coding genes and miRNAs), h ~ N(0, I) is the prior of the hidden units, ε ~ N(0,Ψ) is the noise of v. The parameters are weight matrix W ∈ R^m×l and the noise covariance matrix Ψ ∈ R^m×m. l is the predefined number of biclusters.

The objective function O of RFN is defined in Eq. 2.

$$O=\frac{1}{n}{\sum }_{i=1}^n\log p(v_i)-\frac{1}{n}{\sum }_{i=1}^n{D}_{KL}(Q(h_i|v_i)\Vert p(h_i|v_i))$$ (2)

where Q is a variational distribution, D_KL is the Kullback-Leibler distance, and p(v_i) and p(h_i|v_i) are the prior and posterior, respectively.

The constrained posterior of a bicluster is obtained by multiplying the input matrix by a vector, and subsequently rectifying and normalizing the code unit. To make the feature membership vectors and sample membership vectors sparse, a Laplace prior on the parameters of the original RFN model and a component-wise independent Laplace prior for the weights W are introduced. To get the final biclusters of the input matrix we used threshold values H _thr and W _thr to filter out genes and samples in each bicluster as in [37].

RFN can easily get thousands of biclusters from a very large matrix efficiently. We iteratively ran RFN many times and each time only one bicluster with the highest absolute mean Z-score value and smallest p-value was selected. After many iterations, a large number of biclusters can be obtained. As in [39], we used the p-value of its most enriched biological pathway as the p-value of a bicluster. Specifically, the probabilities of having x genes of the same function in a bicluster of size n with a total of N genes can be computed using the following hypergeometric function:

$$P(X=x|N,p,n)=\frac{\left(\begin{array}{c}PN\\ x\end{array}\right)\left(\begin{array}{c}(1-p)N\\ n-x\end{array}\right)}{\left(\begin{array}{c}N\\ n\end{array}\right)}$$ (3)

where p is the percentage of that pathway among all pathways in the whole pathway terms. The p-value is defined in Eq. 4.

$$p-value=P(X\ge x)=1-P(X<x)=1-{\sum }_{i=0}^{x-1}\frac{\left(\begin{array}{c}pN\\ i\end{array}\right)\left(\begin{array}{c}(1-p)N\\ n-i\end{array}\right)}{\left(\begin{array}{c}N\\ n\end{array}\right)}$$ (4)

To get breast cancer-specific biclusters, only biclusters detected in breast cancer samples but not in normal samples are kept. As some genes belong to different functional categories, the biclusters extracted from a gene expression matrix should have overlap below a predefined threshold. Here, we used empirical 0.5 as suggested in Orzechowski et al. [40].

The pseudo code of cancer-specific bicluster detection is given below:

In this method, the input is breast cancer and normal combined expression matrix E_C and E_N. The output is breast cancer-specific biclusters. The parameters include n_hidden (number of latent variables to estimate), n_iter (number of iterations to run the algorithm), learnrateW (learning rate of the W parameter), learnratePsi (learning rate of the Psi parameter), dropout_rate (dropout rate for the latent variables), minP (minimal value for Psi), H_thr (the threshold value used to extract features belonging to a bicluster) and W_thr (the threshold value used to extract samples belonging to a bicluster).

2.3. Prioritization of bicluster coding genes and miRNAs

We propose to prioritize breast cancer-related coding genes and miRNAs by integrating four aspects of information (as shown in Fig. 1). Only coding genes and miRNAs in breast cancer-specific biclusters are considered. For a coding gene or miRNA in a bicluster, the average differential correlation value dc_i is defined in Eq. 5.

$$d{c}_i=\frac{1}{N}\sum _{j=1,j\ne i}^N{f}_{ij}$$ (5)

where N is the total number of genes (coding genes and miRNAs) in a bicluster, f_ij=1 if the changes in the correlation relationship between two genes and between two experimental conditions are both significant; otherwise, f_ij=0. Fisher’s z-test is used to test differential correlation between two conditions (normal and cancer). To test whether the two Pearson correlation coefficients in normal and cancer are significantly different, we transformed r_N and r_c into Z_N and Z_C, respectively [41]. The Fisher’s transformation of r_N is defined in Eq. 6.

$$Z_N=\frac{1}{2}\log \frac{1+r_N}{1-r_N}$$ (6)

Similarly, we transform r_C to Z_C. We used Eq. 7 to test the difference between two correlations.

$$Z=\frac{Z_N-Z_C}{\sqrt{\frac{1}{n_N-3}+\frac{1}{n_C-3}}}$$ (7)

where n_N and n_C represent the sample sizes of normal and cancer samples, respectively. We used the local false discovery rate (fdr) in the fdrtool R package to test the significance [41, 42].

We also considered the differential expression of all genes in a bicluster. For each coding gene or miRNA in a cancer-specific bicluster, if it is differentially expressed, we set de_i=1; otherwise, we set de_i=0. To identify differential expression genes that may contribute to the malignant phenotype of breast cancer, the DESeq2 was used [32] under the default parameter setting, and all coding genes and miRNAs with adjust p-value<0.001 are deemed as differentially expressed.

Many known cancer-related coding genes and miRNAs provide a valuable source to predict other potential cancer biomarkers or biomarkers of a specific cancer type. It was found that genes interacting with known cancer-related genes were shown to be ten-fold enriched in true cancer-causing modules [43]. Therefore, we used known cancer-related coding genes and miRNAs as heuristics as many others did [10, 14, 44]. If a coding gene or miRNA in a cancer-specific bicluster is a known cancer-related gene or miRNA, we set kc_i=1; otherwise, we set kc_i=0. Furthermore, we consider whether a coding gene has direct interactions with known cancer-related genes in the PPI network. Since genes with direct interactions in the PPI network are likely functional related, genes having direct interactions with known cancer-related coding genes in the HPRD [45] network are more likely cancer-related. We define the average direct interaction number DI_i of a coding gene in a cancer-specific bicluster in Eq. 8.

$$D{I}_i=\frac{1}{N_K}\sum _{j=1,j\ne i}^{N_K}d{i}_{ij}$$ (8)

where N_K is the total number of known cancer-related coding genes in the HPRD network, and di_ij=1 if coding gene i has a direct interaction with coding gene; otherwise, di_ij=0.

For any coding gene i (or miRNA) in a cancer-specific bicluster, we define bicluster coding gene or miRNA importance value IM_i in Eq. 9.

$$I{M}_i=d{c}_i+d{e}_i+D{I}_i+k{c}_i$$ (9)

In this way, we integrate diverse information together and get a more robust measure of the importance value for a coding gene or miRNA. If a gene or miRNA appears in more than one biclusters, we use the biggest value as its importance value.

2.4. Rank fusion process

Rank fusion creates a comprehensive rank by combining multiple rank results together. To do this, firstly, all cancer-specific biclusters are ranked according to their absolute mean Z-score value, and then all coding genes and miRNAs in each breast cancer-specific bicluster are ranked according to their importance values. To get the final global rank, we adapted the rank fusion process used in [18, 46]. The rank fusion method is a recursive process, which decides the rank of the n th gene based on the pre-ranked n−1 ones.

We use n to represent the number of genes to be ranked. b(n,i) represents the number of top n genes located in the bicluster i. t(n,i) is the estimated number of top n genes in the bicluster i. e(n,i) is the expected value that the n+1 th ranked gene comes from the bicluster i. The absolute mean Z-score of a bicluster z(m_i) is used to indicate the probability of a coding gene or miRNA to be breast cancer-related. The relationship among n, b(n,i), e(n,i) and z(m_i) is shown in Eq. 10.

$$\begin{gathered} t(n,i)=nz(m_i) \\ e(n,i)=t(n+1,i)-b(n,i) \end{gathered}$$ (10)

2.5. Cancer-related miRNA-gene interaction detection

To detect breast cancer-related miRNA-gene interactions, only breast cancer-specific biclusters including both coding genes and miRNAs are used. For coding genes and miRNAs in each bicluster, we represent the number of miRNA-gene interactions recorded in the miRTarBase database [47] as KI. The miRTarBase database contains only experimentally validated miRNA-gene interactions. The miRNA-gene interaction significance value p of each bicluster is defined in Eq. 11.

$$p=\frac{n_C}{T}$$ (11)

where T represents number of random samplings. In each sampling we randomly select the same number of coding genes and miRNAs (non-repetitive sampling) in the bicluster considered, and represent the number of miRNA-gene interactions recorded in the miRTarBase database as ki. n_C represents the number of times ki≥KI in T times of sampling. We use a p threshold 0.05 to select significant biclusters, and count the occurrence of all the miRNAs in all the significant biclusters. The miRNAs with highest occurrence and their corresponding gene interactions present in miRTarBase are selected as breast cancer-related miRNA-gene interactions.

3. Results

3.1. Parameterization of our method

In this paper, an unsupervised learning biclustering method RFN was used to analyze the combined gene and miRNA expression matrixes of breast cancer. The main parameters used to train RFN model are the number of iterations n_iter and the number of hidden layers n_hidden. We sampled n_iter from 10 to 500, and the distance between the input matrix and the matrix we got (by Eq. 1) vs. n_iter is shown in Fig. 2(A) and Fig. 2(B). The distance between the input matrix and the output matrix is defined as: $d(V,Wh)=\underset{i=1}{\overset{N}{\Sigma }}\underset{j=1}{\overset{N}{\Sigma }}\mid V_{ij}-(Wh{)}_{ij}\mid$. We used the none-zero ratio in the matrix that we obtained as the indicator of the performance of RFN model under different numbers of hidden layers. We sampled n_hidden from 60 to 500, as shown in Fig. 2(C) and Fig. 2(D). According to our analysis in Fig. 2, we chose n _iter = 100 and n _hidden = 100 in our analysis.

Fig. 2. Parameterization of RFN.

The distance between the input matrix and the matrix obtained from the RFN model under different iterations in cancer samples (A) and normal samples (B). The none-zero ratio in the matrix under different iterations in cancer samples (C) and normal samples (D).

RFN can handle a matrix of thousands of rows and columns within 1 minute on a Linux desktop. In this study, we applied RFN on combined gene and miRNA expression datasets of breast cancer analysis. In each iteration only one most significant cancer and normal bicluster was selected out, and finally only breast cancer-specific biclusters were used to detected breast cancer-related coding genes, miRNAs and their interactions. We set the iteration time T=1000 in this study, and each iteration took about 30 seconds on a desktop. The basic machine requirements are: a CUDA 7.5 (or higher) compatible GPU, and at least 2 GB memory. The complexity analysis of our method is: Objective function $O:O\left(\min \left\{nlm,n{l}^2\right\}+l^3\right);$ E-step: $O(nl(m+l));$ M-step: $O(ml(m+l));$ the overall complexity with projected Newton/gradient for $(l+m)<n:O(n(m^2+l^2))$; and rank fusion process: O(nl). Where n is the number of features, m is the number of samples and l is the number of clusters.

3.2. Breast cancer-specific biclusters

We used the cancer-specific bicluster detection method shown in the pseudo code to detect breast cancer-specific biclusters. We set T=1000 (number of iterations), and in each iteration we randomly selected the same number of normal and cancer samples (94 samples, no duplicate). At reach run, only biclusters with p-value<0.0001, and at least 4 genes and 3 samples were kept; and only the bicluster with the biggest absolute mean Z-score value (Z-score>0.5) was chosen. As a result, we got 874 and 901 normal and breast cancer biclusters, respectively, of which 529 biclusters were breast cancer-specific. Figure 3 shows the distribution of coding genes and miRNAs in 874 normal and 901 breast cancer biclusters. In both breast cancer and normal samples, most biclusters comprise of a small number of genes and miRNAs. However, in breast cancer samples, some biclusters include many genes and miRNAs than normal, which indicates more miRNA-gene regulations in cancer. This is in consistent with the recent discovery of an increased global miRNA activity in cancer samples [48].

Fig. 3.

Distribution of gene and miRNA counts in normal and cancer biclusters.

We used the topGO R package to get the significantly (Fisher’s exact test p<0.01) enriched Biological Processes (BPs) in each of the 529 breast cancer-specific biclusters. The selected six biclusters with most significant p-values are shown in Table 1. The annotation results show that breast cancer-specific biclusters are closely related to pathways, such as Notch signaling pathway, Wnt signaling pathway, and ERK1 and ERK2 cascade [49], which are known to be commonly activated in cancer development [50, 51].

Table 1.

TopGO annotation results of top six ranked cancer-specific biclusters

Bicluster ID	GO	Term	Annotated	Expected	P
8	GO:0007219	Notch signaling pathway	156	2.93	0.00074
	GO:0030177	positive regulation of Wnt signaling pathway	80	1.5	0.00076
11	GO:0042775	mitochondrial ATP synthesis coupled electron transport	49	1.57	0.00015
	GO:0061324	canonical Wnt signaling pathway involved in positive regulation of cardiac outflow tract cell proliferation	2	0.06	0.00103
	GO:0006397	mRNA processing	396	12.7	0.00046
	GO:0006270	DNA replication initiation	29	0.93	0.00209
24	GO:0070371	ERK1 and ERK2 cascade	154	2.32	0.00011
	GO:0043410	positive regulation of MAPK cascade	378	5.69	0.00062
83	GO:0006521	regulation of cellular amino acid metabolic process	58	0.63	0.00041
	GO:0006977	DNA damage response, signal transduction by p53 class mediator resulting in cell cycle arrest	66	0.72	0.00574
	GO:0035313	wound healing, spreading of epidermal cells	11	0.12	0.00605
	GO:0006312	mitotic recombination	38	0.41	0.00804
	GO:0033014	tetrapyrrole biosynthetic process	39	0.42	0.00864
317	GO:0043627	response to estrogen	156	5.02	0.00462
	GO:0016338	calcium-independent cell-cell adhesion via plasma membrane cell-adhesion molecules	24	0.77	0.00676
402	GO:0060124	positive regulation of growth hormone secretion	8	0.11	0.00013
	GO:0043627	response to estrogen	156	2.11	0.00028
	GO:0030001	metal ion transport	677	9.17	0.00035
	GO:0007155	cell adhesion	1287	17.43	0.00027
	GO:0007186	G protein-coupled receptor signaling pathway	1129	15.29	0.00277
	GO:0046676	negative regulation of insulin secretion	30	0.41	0.0076

3.3. Breast cancer-related genes and miRNAs

We used the rank fusion method to get the overall ranking of all genes and miRNAs as well as gene-miRNA interactions from all cancer-specific biclusters. To obtain the comprehensive rank, firstly, all breast cancer-specific biclusters were ranked according to their importance values; secondly, all coding genes and miRNAs in each breast cancer-specific biclusters were ranked according to their respective importance values. The top ranked 20 genes and miRNAs related to breast cancer selected by our method are shown in Table 2. Among them, genes MYEOV, OLFML3, MRPL21, TPCN2 and CDCA7, miRNAs hsa-mir-155, hsa-mir-455, hsa-mir-144 and hsa-mir-106b are all known breast cancer-related genes, and miRNAs. PIWIL2, PNMT, TEKT4 and hsa-mir-133a-1 have direct literature support in their relationships with breast cancer, as listed in the table.

Table 2.

Top 20 ranked genes and miRNAs related to breast cancer

Rank	Symbol	Name	PubMed
1	PCDHB5	Protocadherin Beta 5	PMID: 20829831
2	PIWIL2	Piwi Like RNA-Mediated Gene Silencing 2	PMID: 20490325
3	MYEOV	Myeloma Overexpressed	PMID: 12448002
4	PNMT	Phenylethanolamine N-Methyltransferase	PMID: 12727839
5	AKAP14	A-Kinase Anchoring Protein 14	NA
6	OLFML3	Olfactomedin Like 3	NA
7	TMEM164	Transmembrane Protein 164	NA
8	MRPL21	Mitochondrial Ribosomal Protein L21	NA
9	TEKT4	Tektin 4	PMID: 24823476
10	hsa-mir-133a-1	NA	PMID: 29207145
11	hsa-mir-155	NA	PMID: 29207145
12	ZNF689	Zinc Finger Protein 689	NA
13	CDH15	Cadherin 15	NA
14	hsa-mir-455	NA	PMID 29257232
15	TPCN2	NA	NA
16	ALLC	Allantoicase	NA
17	ACAP1	ArfGAP With Coiled-Coil, Ankyrin Repeat and PH Domains 1	NA
18	hsa-mir-144	NA	PMID: 27785072
19	hsa-mir-106b	NA	PMID: 28518139
20	CDCA7	Cell Division Cycle Associated 7	PMID: 30151890

‘NA’ indicates that no literature support was found for its involvement in breast cancer.

3.4. Breast cancer-related coding gene-miRNA interactions

Among 529 breast cancer-specific biclusters, 79 biclusters have p – value < 0.05. If miRNAs and coding genes were in the same bicluster with some gene-miRNA interactions recorded in the miRTarBase database [47], we selected these interactions as potential breast cancer-related gene-miRNA interactions. To show most important breast cancer related gene-miRNA interactions, coding genes and miRNAs most frequently appeared in the top 3 most significant biclusters (bicluster numbers 27, 61 and 81) were selected for gene-miRNA interaction analysis, as shown in Fig. 4. Genes BRIP1, FGFR2, PTEN and TP53 are all well-known breast cancer-related genes, and miRNAs has-mir-19b-1, has-mir-138 and hsa-mir-378 have direct literature support in their relationships with breast cancer [52–54]. Given that all interactions in Fig. 4 are known gene-miRNA interactions in miRTarBase, these interactions most likely play important roles in breast cancer.

Fig. 4.

Gene-miRNA interactions between common genes and miRNAs in top 3 significant breast cancer-related biclusters.

3.5. Comparison with other methods

To the best of our knowledge, no biclustering method was directly used for detecting cancer-related coding genes and miRNAs, and their interactions. The commonly used methods can be divided into three categories, single gene, gene module and network based methods. For comparison, we selected one representative method from each of the three categories, i.e., Endeavour [2] for single gene based method, ToppNet [55] for network based method, and MGOGP [18] for gene module based method. These three methods have a similar data source input requirement as our method; for example they all need training and testing gene sets. In order to make these methods more comparable, for Endeavour we chose HPRD and Bio-molecular pathways as the data sources; for MGOGP we used gene sets from the GSEA website and the same expression datasets as input. We fine-tuned parameters of each method and made sure the results were obtained under their best performance. For comparison, all four methods used the same datasets, and compared to the same 115 known breast cancer-related genes. More specifically, for all the four methods, we used all the 604 known cancer-related genes as the known cancer genes, and all genes in preprocessed TCGA RNA-Seq expression datasets as the candidate genes. We counted the number of genes in the 115 known breast cancer genes among the top 50 and top 100 genes selected by each method. As shown in Fig. 5, our method detected more known breast cancer genes than other three methods. Furthermore, our method detects not only cancer-related genes but also cancer-related miRNAs, as well as their interactions. In the top ranked 100 genes, there are also 12 miRNAs, of which 10 miRNAs are known breast cancer-related miRNAs. In addition, our method was much faster than any of the other methods.

Fig. 5.

Performance comparison between our method and Endeavour, ToppNet and MGOGP in terms of number of identified genes among the 115 known breast cancer genes.

4. Discussion

Detection and prioritization of cancer-related coding genes, miRNAs and their interactions play crucial role in the understanding of the genetic architecture of cancer and improve the accuracy of diagnosis. Different from other methods, we applied an unsupervised learning based biclustering method (RFN) on the analysis of the combined expression profiles under the same set of samples for both coding genes and miRNAs. With the increasing availability of biological datasets for the same samples (e.g., gene expression, miRNAs, and copy numbers), more and more studies have been conducted using multiple omics data on the same set of samples [20, 21]. Such analyses can help discover a set of co-expressed genes and miRNAs representing a functional gene module. Results show that miRNAs and coding genes fall in the same bicluster have more known interactions, and the dysregulation of their interactions may be cancer-related. Given the enrichment of known interactions, other unknown miRNAs-gene interactions predicted by computational tools based on miRNA/gene sequences in the same bicluster would have a higher confidence to be true interactions. To get more robust biomarker prioritization, we proposed a rank fusion process to obtain the final comprehensive rank by combining multiple sources of information, which makes our method more robust.

To demonstrate the effectiveness of our method, we applied our method on breast cancer datasets analysis and detected many breast cancer-specific biclusters. We used TopGO to annotate the enriched biological processes of these biclusters. Many of these b iclusters are enriched in some well-known cancer-related processes, which indicates that coding genes included in these biclusters are more likely cancer related. Based on these breast cancer-specific biclusters, we prioritized all the coding genes and miRNAs. As shown in Table 2, genes MYEOV, OLFML3, MRPL21, TPCN2 and CDCA7, miRNAs hsa-mir-155, hsa-mir-455, hsa-mir-144 and hsa-mir-106b are all known breast cancer-related coding genes and miRNAs. James et al. [56] found PIWIL2 was uniquely expressed in various stages of breast cancers, suggesting that PIWIL2 plays an important role in breast cancer development. Jiang et al. [57] showed that TEKT4 could act as biomarkers for predicting treatment response and prognosis. Most recently, Sui et al. [58] observed that the expression of miR-133a was significantly downregulated in breast cancer tissues and cell lines. Reduced miR-133a levels were significantly associated with shorter survival time of patients with breast cancer. All these results suggest that our method is effective in identifying cancer-related biomarkers.

Our method is the first attempt to prioritize cancer-related coding genes and miRNAs, and their interactions based on the cancer-specific biclusters generated by rectified factor networks. To get the robust ranking of final cancer-related biomarkers, we rank coding genes and miRNAs based on both their own importance and the importance of biclusters that they belonged to. Our method can be applied to other combined multi-omics data analysis [including data such as DNA methylation, Copy Number Variation (CNV), and protein expression datasets] and prioritize key cancer-related biomarkers.

Highlights:

• Biclustering analysis of integrated expression data of coding genes and microRNAs from the same set of samples.

• Identify breast cancer-specific biclusters with an efficient unsupervised learning based method named Rectified Factor Networks.

• Identify breast cancer-related coding genes, microRNAs and their interactions based on breast cancer-specific biclusters.

• Prioritize biomarkers by integrating multiple data sources and a rank fusion process.