Constructing higher-order miRNA-mRNA interaction networks in prostate cancer via hypergraph-based learning
© Kim et al.; licensee BioMed Central Ltd. 2013
Received: 1 November 2012
Accepted: 15 June 2013
Published: 19 June 2013
Dysregulation of genetic factors such as microRNAs (miRNAs) and mRNAs has been widely shown to be associated with cancer progression and development. In particular, miRNAs and mRNAs cooperate to affect biological processes, including tumorigenesis. The complexity of miRNA-mRNA interactions presents a major barrier to identifying their co-regulatory roles and functional effects. Thus, by computationally modeling these complex relationships, it may be possible to infer the gene interaction networks underlying complicated biological processes.
We propose a data-driven, hypergraph structural method for constructing higher-order miRNA-mRNA interaction networks from cancer genomic profiles. The proposed model explicitly characterizes higher-order relationships among genetic factors, from which cooperative gene activities in biological processes may be identified. The proposed model is learned by iteration of structure and parameter learning. The structure learning efficiently constructs a hypergraph structure by generating putative hyperedges representing complex miRNA-mRNA modules. It adopts an evolutionary method based on information-theoretic criteria. In the parameter learning phase, the constructed hypergraph is refined by updating the hyperedge weights using the gradient descent method. From the model, we produce biologically relevant higher-order interaction networks showing the properties of primary and metastatic prostate cancer, as candidates of potential miRNA-mRNA regulatory circuits.
Our approach focuses on potential cancer-specific interactions reflecting higher-order relationships between miRNAs and mRNAs from expression profiles. The constructed miRNA-mRNA interaction networks show oncogenic or tumor suppression characteristics, which are known to be directly associated with prostate cancer progression. Therefore, the hypergraph-based model can assist hypothesis formulation for the molecular pathogenesis of cancer.
Prostate cancer is a common disease in the male population, induced by complex interactions among various genetic factors . As such, the pathological causes of this disease are not easily identified. Recent human cancer studies have demonstrated that most cancer regulations are related to modular construction and combinatorial control by multiple genetic factors. This module-based view of higher-order relationships can provide new insights into the behavior of complex biological systems [2, 3].
Recently, miRNAs have caused great excitement as diagnostic and therapeutic signatures of prostate cancer [4–8]. They play important roles in cancer pathogenesis, including disease onset, progression, and metastasis, by regulating the stability and translation efficiency of their target mRNAs. Thus, the functional relationships between miRNAs and mRNAs should be elucidated to identify key transcriptional circuits involved in cancer regulation. However, analyzing higher-order miRNA-mRNA relationships is rendered as a challenging problem due to the complexity of their interactions.
Modern cancer research has progressed from identifying biomarkers to systemically exploring gene interactions [9–11]. Many studies have focused on the interaction of genetic components at the systems level. Computational methods, which analyze gene regulatory interactions on a genome-wide scale from high-throughput biological data, have flourished in recent decades [12–14]. In addition, systems biology has proposed to build miRNA regulation networks underlying the development of many human diseases [15–17]. Moreover, miRNA regulatory mechanisms are now thought to be inferable from miRNA-mRNA interactions [18–20]. Several studies have attempted to identify groups of coherent miRNAs and mRNAs that cooperate in biological processes from heterogeneous data sources via various computational approaches, including probabilistic methods [21–28], rule-based learning [29, 30], matrix factorization , and statistical methods [32–35]. These approaches have simplified complex biological mechanisms by systematically analyzing the relationships between genetic elements at the genome level. Typically, however, bi-relationships between only two factors are assumed in many previous studies [21, 30–35]. Such restrictions are unsuitable for complex genetic interactions because information is lost under the assumption, and biological regulation is controlled by the interaction of multiple genetic components. Many studies have also investigated miRNA-mRNA regulatory interactions using biological information, especially miRNA-target information [21–25, 29–33]. Biological information reduces the number of false positives, since it provides the predictive model with prior knowledge. In contrast, unknown or hidden interactions not involved in the prior knowledge may be difficult to identify from this information. To avoid this problem, some probabilistic models which infer miRNA-mRNA modules from expression profiles only, without relying on target information, have been proposed [26–28]. Bonnet’s model, called LeMoNe [26, 27], consists of two major steps; the generation of gene clusters based on a feature-sample co-clustering method, and the inference of regulatory modules from generated clusters and regulators based on probabilistically optimized trees. In the clustering approach of Bonnet’s method, gene regulatory modules underlying a specific cancer stage are not easily identified. Liu’s approach infers functional miRNA regulatory modules using Correspondence Latent Dirichlet Allocation (Corr-LDA) . The Corr-LDA based model requires discretized data. Since the Corr-LDA model infers probability distributions from latent variables, moreover, miRNAs can be annotated to any functional modules, while mRNAs are restricted to the miRNA-inferred modules.
The learning process involves the iteration of two learning phases; structure and parameter. The structure learning phase constructs a hypergraph of putative hyperedges for discovering potential gene interactions, from a huge feature space represented by the combinations of many miRNAs and mRNAs. Because the miRNA-mRNA interactions are intractably complex, we adopt an evolutionary strategy based on an information theoretic co-regulatory measure, called mutual information. This strategy is used to select genetic variables for generating hyperedges. During the parameter learning phase, the hypergraph is refined by updating the weights of the hyperedges (representing higher-order miRNA-mRNA modules). To this end, we employ a gradient descent method similar to the back-propagation algorithm for learning artificial neural networks. The learned model is then converted into a network structure reflecting the cooperative higher-order gene activities by connecting the extracted hyperedges. Data-driven learning allows the model to build new miRNA-mRNA interaction networks which display the hidden properties of primary and metastatic prostate cancers from a given dataset, which are not known a priori.
We construct cancer stage-specific miRNA-mRNA interaction networks reflecting their higher-order relationships using the MSKCC Prostate Oncogenome Project dataset  from the model. We demonstrate that the proposed model can build several biologically significant miRNA-mRNA interaction networks, including potential modules associated with primary and metastatic prostate cancer. Moreover, cancer-related miRNAs and genes dominate the identified interactions. Some of these interactions, such as hsa-miR-1, hsa-miR-133a, hsa-miR-143, hsa-miR-145, hsa-miR-221, hsa-miR-222, act as hubs in the constructed networks. We also confirm the biological relevance of the constructed networks through literature review and functional analysis.
Data and experimental settings
Parameter settings for experiments
# of miRNA
# of mRNA
# of modules
β in (5)
Epochs of structure learning
Epochs of parameter learning
η in (10)
κ in (11)
γ in (13)
Rmax , Rmin
Verification result on the simulation dataset
Frequently and rarely appearing miRNAs and mRNAs in the 100 learned models
Constructed higher-order miRNA-mRNA interaction networks in prostate cancer
Interestingly, the enriched hyperedges, and the expression levels of the miRNAs and mRNAs, differ considerably between the primary and metastatic networks. Up- and down-expressed miRNAs and genes are determined by their means at each stage. The red boxed miRNAs and genes are known to be associated with the various stages of prostate cancer [4–8, 42, 43]. The triangles rectangles, diamonds and circles denote miRNAs, oncogenes/ tumor suppressor genes, transcription factors, and other genes in the network, respectively.
Functional analysis of the constructed interaction networks
The constructed miRNA-mRNA interaction networks were validated by functional analyses based on a literature review and gene set analysis. As mentioned above, many of the miRNAs and mRNAs involved in the identified interactions are known indicators of prostate cancer [4–8]. In addition, the mRNAs comprise a portion of their predicted target genes , some of which have been experimentally validated. In particular, several miRNAs are known as ‘oncomiRs’ which function as oncogenes or tumor suppressors, including has-miR-1, -133a, -143, -145, -221, and −222 [45–48]. Many hyperedges in the constructed networks contain the above miRNAs as their components; these particular miRNAs also act as hubs in the networks.
Especially, hsa-miR-143 and hsa-miR-145 play a crucial role in metastatic prostate cancer, and are recognized as a clinicopathological signature of prostate cancer . Interaction modules involving hsa-miR-143 and −145 occupy a large portion of the networks constructed by our model. In addtion, the identified interactions in metastatic prostate cancer contain several experimentally confirmed targets of hsa-miR-143 and −145, including CLINT1, CDKN1A, IRS1, MAPK7, PPM1D and SOD2. Furthermore, hsa-miR-143 and −145 are expressed at low levels in the metastatic network, as has been experimentally validated .
Moreover, hsa-miR-200c emerges as a distinct miRNA in the network of primary prostate cancer. According to several studies, hsa-miR-200c overexpression inhibits metastasis prostate cancer, while aberrant regulation triggers the invasion and migration of prostate cancer at the post-transcriptional level .
Our model identified several transcription factors associated with prostate cancer metastasis, such as ETS2, HOXC4, STAT3, STAT5B, SOX4 and ZEB2. Among these, SOX4, STAT3 and STAT5B are known regulators of metastatic prostate cancer through the regulation of genes involved in miRNA processing, transcriptional regulation, and developmental pathways [50–52]. Indeed, SOX4 is directly regulated by hsa-miR-335 in cancer progression , while hsa-miR-125b coordinates STAT3 regulation in the proliferation of tumor cells [51, 53].
Examples of modules (hyperedges) in primary and metastatic prostate cancer
miRNAs [exp. levels: up (+), down (−)]
mRNAs [exp. levels: up (+), down (−)]
Primary prostate cancer
Metastatic prostate cancer
Canonical pathway analysis of the constructed interaction networks in primary and metastatic prostate cancer
Canonical pathway analysis
Primary prostate cancer
Pathways in cancer
Retinoic acid pathway
Aurora A pathway
Beta-catenin degradation pathway
Wnt canonical signaling pathway
Met pathway (signaling of HGF receptor)
P38-alpha/beta downstream pathway
Beta-catenin nuclear pathway
Aurora B pathway
EPHB forward pathway
P53 hypoxia pathway
MYC repress pathway
Progesterone mediated oocyte maturation
Rac CycD pathway (Ras and Rho protein on G1/S transition)
IL-6 (interleukin-6) pathway
FGFR2C ligand binding and activation
PDGFR-beta signaling pathway
Metastatic prostate cancer
MYC activate pathway
ErbB network pathway
KIT receptor signaling pathway
Pathways in cancer
Her2 pathway (ErbB2 in signal transduction and oncology)
Yap1 and Wwtr1/Taz stimulated gene expression
Smooth Muscle Contraction
IL-6 signaling pathway
ErbB2/ErbB3 signaling pathway
Integrin signaling pathway
HDAC class I pathway
The proposed hypergraph-based model characterizes higher-order interactions among heterogeneous genetic factors from archived data. Human cancers are typically caused by the modular control of multiple genetic factors. By analyzing gene relationships at higher-order levels, thus, we can better understand the behavior of complex cancer mechanisms. Moreover, the cooperative activities and the combinatorial regulations governed by miRNAs and mRNAs are largely unknown. We have demonstrated that higher-order relationships discriminate between specific cancer stages more precisely than pair-wise analyzes of single miRNA and mRNA interactions. From this viewpoint, we can construct a more complete interaction network consisting of putative biologically significant miRNA-mRNA modules.
In addition, our method focuses on discovering potential interactions in unknown miRNA-mRNA regulatory circuits related to specific cancer stages without the known biological information [60, 61]. The proposed model finds statistically significant gene modules from given expression profiles using a data-driven approach with co-regulatory measure (mutual information). However, a similar hypergraph structure could be readily constructed from other types of quantitative biological information, such as miRNA-target information and gene sequence similarity values. Furthermore, the hypergraph-based model more flexibly represents miRNA-RNA interactions than other methods (which assume that the expression states of miRNAs and mRNAs are linearly proportional to each other), because it isolates significant modules from the statistical co-expressed pattern among genes at a higher-order level.
The proposed hypergraph-based model is similar to Bonnet’s et al.[26, 27] and Li et al., where higher-order relationships governed by miRNA-mRNA interactions are inferred solely from expression profiles. Bonnet’s method is based on a clustering approach, it cannot readily infer gene regulatory modules at a specific cancer stage. In contrast to Bonnet’s method, our method explicitly considers the sample status, (the primary or metastatic state of prostate cancer), from which it constructs cancer stage-specific networks. Liu’s approach is based on Corr-LDA, which requires that data are discretized. By contrast, our method uses intact real-valued data, thus preventing the information loss caused by the discretization.
Furthermore, the proposed model finds the true solution in a small subset of the features, because the problem space is small enough to search exhaustively. Also, unlike other models, our model can efficiently handle the very high-dimensional data required for complex higher-order interactions among features. However, the limitation of the proposed hypergraph-based model emerges at small sample sizes. If the data are few, the reliability of the mean and covariance defined in a hyperedge is reduced.
We have proposed a hypergraph-based model consisting of higher-order miRNA-mRNA modules, which allows the construction of biologically meaningful interaction networks associated with specific cancer stages. For identifying potential significant interactions and refining model performance, we introduced a two-phase learning approach comprising structure and parameter learning. Finally, we constructed cancer stage-specific interaction networks reflecting higher-order miRNA and mRNA relationships by converting the hypergraph structure into an ordinary graph.
We constructed higher-order miRNA-mRNA interaction networks associated with the specific stage of prostate cancer from a matched dataset using the proposed model. The performance of the proposed model is similar to that of SVMs and superior to other classification models (outperforming them by approximately 6–10%). More importantly, our model can construct carcinogenic miRNA-hubbed networks that characterize primary and metastatic prostate cancer. Furthermore, we demonstrated that a large proportion of the miRNAs and mRNAs identified in the constructed interaction networks are indeed involved in prostate cancer progression and development. The proposed hypergraph-based model therefore presents as an alternative method for discovering potential gene regulatory circuits. Such discoveries will greatly assist our understanding of cancer pathogenesis.
A hypergraph-based model characterizes complex interactions among many genetic factors using hypergraph structures. A hypergraph generalizes the edge concept to a hyperedge by which more than two variables can be connected simultaneously [62, 63]. As such, it is suitable for representing higher-order relationships among heterogeneous features (e.g. miRNAs and mRNAs). In our model, a hyperedge contains two or more variables corresponding to miRNAs and mRNAs, weighted by the strength of the higher-order dependency among its elements for each class (where the class denotes a specific cancer stage). Thus, each hyperedge implies a set of miRNA-mRNA modules associated with a certain stage of cancer. The proposed model therefore facilitates the construction of higher-order miRNA-mRNA interaction networks among a population of candidate gene modules related to a specific cancer stage.
- 1.Calculate c y ', the sum of the expected values for each y ' in Y over all hyperedges of H:(7)
- 2.Predict the cancer stage as y*:(8)
In terms of distance-based connectionist models, our model is related to radial basis function networks (RBFNs) . Whereas RBFNs use kernelized distance for all variables, the proposed hypergraph model uses the probability derived from the subdimensional distance on the projected space corresponding to each hyperedge. Unlike RBFNs, therefore, the hypergraph-based model can detect embedded subpatterns reflecting higher-order relationships among the components. Because these embedded subpatterns influence the classification, we can intuitively analyze the complex interactions of genetic factors that contribute to classifying a specific cancer stage.
Learning hypergraph-based models
where (x(n), z(n)) denotes the n-th miRNA-mRNA expression and y(n) is the cancer stage of the example. is the label predicted by H and δ(y(n), ) is an indicator function, equal to 1 if y(n) equals , and 0 otherwise. To enhance the classification accuracy, it is essential that the population comprises hyperedges with high discriminative capability, and the hyperedge weights must be refined to minimize (9) in the generated hypergraph.
To meet these requirements, the learning iterates two phases: structure learning and parameter learning. The structure learning constructs a hypergraph from hyperedges that identify potential miRNA-mRNA modules. The weights of the hyperedges are updated to minimize the classification error of the generated gene module population during the parameter learning phase. Because the hypergraph-based model represents a huge combinatorial feature space (size 2|x|+|z|) of many miRNAs and mRNAs, exhaustively searching for the optimal population is infeasible. Instead we adopt an evolutionary learning method based on information-theoretic criteria to generate putative hyperedges for the structure learning.
where k is the number of variables of e i and κ denotes the ratio of the variance to MI.
Representing interaction networks from hypergraphs
This work was supported by the National Research Foundation (NRF) Grant funded by the Korea government (MSIP) (NRF-2010-0017734, NRF-2013M3B5A2035921, and the Bio & Medical Technology Development Program, No.2012M3A9D1054622), supported by KEIT grant funded by the Korea government (MKE) (KEIT-10035348 and KEIT- 10044009), supported by AOARD R&D grant funded by AFORS (124087).
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