Bioinformatics Advance Access originally published online on March 9, 2007
Bioinformatics 2007 23(9):1141-1147; doi:10.1093/bioinformatics/btm045
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Discovery of microRNA–mRNA modules via population-based probabilistic learning
1Center for Bioinformation Technology, Seoul National University, Seoul 151-742, School of Computing, Soongsil University, Seoul 156-743 and 3School of Computer Science and Engineering, Seoul National University, Seoul 151-742, Korea
*To whom correspondence should be addressed.
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ABSTRACT |
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 TOP ABSTRACT 1 INTRODUCTION2 METHODS3 RESULTS4 DISCUSSION AND CONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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Motivation: MicroRNAs (miRNAs) and mRNAs constitute an important part of gene regulatory networks, influencing diverse biological phenomena. Elucidating closely related miRNAs and mRNAs can be an essential first step towards the discovery of their combinatorial effects on different cellular states. Here, we propose a probabilistic learning method to identify synergistic miRNAs involving regulation of their condition-specific target genes (mRNAs) from multiple information sources, i.e. computationally predicted target genes of miRNAs and their respective expression profiles.
Results: We used data sets consisting of miRNA–target gene binding information and expression profiles of miRNAs and mRNAs on human cancer samples. Our method allowed us to detect functionally correlated miRNA–mRNA modules involved in specific biological processes from multiple data sources by using a balanced fitness function and efficient searching over multiple populations. The proposed algorithm found two miRNA–mRNA modules, highly correlated with respect to their expression and biological function. Moreover, the mRNAs included in the same module showed much higher correlations when the related miRNAs were highly expressed, demonstrating our method's ability for finding coherent miRNA–mRNA modules. Most members of these modules have been reported to be closely related with cancer. Consequently, our method can provide a primary source of miRNA and target sets presumed to constitute closely related parts of gene regulatory pathways.
Contact: btzhang{at}bi.snu.ac.kr
Supplementary information: Supplementary data are available at Bioinformatics online.
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1 INTRODUCTION |
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TOPABSTRACT1 INTRODUCTION2 METHODS3 RESULTS4 DISCUSSION AND CONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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MicroRNAs (miRNAs) are a class of small endogenous RNA molecules (
22 nt), which are presumed to participate in the developmental control of gene expression (Bartel et al., 2004). They can suppress their target genes (mRNAs) posttranscriptionally by complementary base pairing. Hence, miRNAs are related to diverse cellular processes and regarded as important components of the gene regulatory network. Researchers have tried to elucidate the function of miRNAs in cellular processes using experimental and computational approaches (Denli et al., 2004; Han et al., 2006; Thomson et al., 2004). Early efforts in this area mainly focused on the identification of miRNAs and their targets (Lewis et al., 2005; Nam et al., 2006). Expression profiling techniques were also deployed for characterizing differentially expressed miRNAs according to cellular states and environmental conditions (Liu et al., 2004, 2005; Thomson et al., 2004). Correspondingly, significant amounts of data on miRNAs have now accumulated (Griffiths-Jones et al., 2006).
To understand the regulatory mechanism of miRNAs in complex cellular systems, it is important to identify the functional modules involved in complex interactions between miRNAs and their targets. Previously, the concept of miRNA regulatory modules (MRMs) was introduced by Yoon and De Micheli (2005). Their modules are related to only miRNA–mRNA duplexes in the sequence level without considering their expression profiles. Additional information on the expression profiles of miRNAs and mRNAs could be useful to detect the actual MRMs in specific biological processes. Recently, integrated analysis of targeting information and expression profiles was trialed to discover functional miRNA targets (Huang et al., 2006; Zilberstein et al., 2006). They reported that the utilization of expression profiles could help identify targets with high confidence.
Here we propose a population-based probabilistic method to identify coherent miRNA–mRNA modules by integrating heterogeneous information, i.e. computationally predicted target genes of miRNAs and two respective expression profiles of mRNAs and miRNAs. Here, miRNA–mRNA modules are defined as groups of miRNAs and their target mRNAs involved in similar biological processes. In our approach, a module consists of highly related miRNAs and their targets, which can be thought to have similar biological functions. Our main idea is to combine multiple information sources to extract common patterns among them, and to minimize noise and errors in each information source. Figure 1 illustrates our method of extracting coherent miRNA–mRNA modules from heterogeneous information sources.
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It is not straightforward to combine heterogeneous information sources, because they have different characteristics, e.g. sizes, scales and dimensions. Our population-based probabilistic learning method is built on coevolutionary learning (Potter and De Jong, 2000) and estimation-of-distribution algorithms (EDAs) (Baluja, 1994, 1997; Larrañaga and Lozano, 2002; Zhang, 2003), addressing the problem of combining multiple data sets effectively. The fitness function is defined as a balanced aggregate of the degree of coherences between the possible pairs of miRNAs and their putative targets, i.e. miRNA–mRNA, miRNA–miRNA and mRNA–mRNA. It represents relatedness between miRNAs and mRNAs in terms of three kinds of different views. The coevolutionary learning algorithm guides the search for an optimal module by maintaining two populations consisting of miRNAs and mRNAs. EDAs are used for generating ‘offspring’ based on a probability model describing the current population. Our approach can identify highly correlated miRNAs and mRNAs efficiently from a high-dimensional search space through these learning strategies.
We applied our algorithm to the combined analysis of miRNA–target gene binding information and expression profiles of miRNAs and mRNAs on human cancer samples. The detected miRNA–mRNA modules were validated using correlation coefficient analysis biological functional analysis and a survey of the biomedical literature.
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2 METHODS |
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TOPABSTRACT1 INTRODUCTION2 METHODS3 RESULTS4 DISCUSSION AND CONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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2.1 Formulation of the problem
Our goal is to find optimal miRNA–mRNA modules based on computationally predicted miRNA–target gene information and their respective expression profiles. Let M = { m1, m2, ... , mNm} denote the set of miRNAs and T = { t1, t2, ; ... , tNt} the set of mRNAs, where Nm and Nt correspond to the number of miRNAs and mRNAs, respectively. From the total set of miRNAs and mRNAs, a subset B = (M', T') can be selected as a module, where |M'|
|M| and |T'| |T| . The target information can be represented as an Nm x Nt scoring matrix consisting of prediction scores of target binding. The expression profiles of miRNAs (mRNAs) can also be represented as an Nm x Nms (Nt x Nts) matrix, where Nms (Nmt) denotes the number of microarray samples.
2.2 Definition of the fitness function
The putative target information describes the similarity between miRNAs and their target mRNAs from the viewpoint of complementary base pairing. The expression profiles of miRNAs and mRNAs provide information about their coherence in transcription across various cellular states or conditions. Taking into account these factors, the fitness of a module (M', T') can be measured as follows:
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| (1) |
, ß and 
are the parameters of the fitness function, which control the balance among the three scoring terms. In addition to the above scoring terms, a volume term is added to the fitness function to prevent finding a trivial solution consisting of one or two miRNAs and mRNAs. The volume term is given as:
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| (2) |
and 
are the subset size, and w , wm and wt are control parameters similar to , ß and , respectively.
2.3. Description of the learning algorithm
Our algorithm for finding an optimal miRNA–mRNA module is based on coevolutionary learning and EDA approaches. Here, coevolutionary learning evolves cooperatively for two populations in the context of each other, and EDAs generate new solutions using the probability distribution. Figure 2 summarizes the probabilistic learning algorithm for miRNA–mRNA module identification. The function to optimize is defined over the binary space { 0, 1} Nm for the set of miRNAs, M and { 0, 1} Nt for the set of mRNAs, T . M' and T' are 1's sets in this binary space.
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During the learning process, we maintain two respective populations of miRNAs and mRNAs. First, the algorithm initializes these populations by random selection. The populations X (for miRNAs) and Y (for mRNAs) can be represented as follows: X = { x1, x2, ;... , xµ } , Y = { y1, y2, !... , y
} , where µ and denote the respective population size. The i -th individual xi (yi) corresponds to a binary string representing the inclusion (1) or exclusion (0) of the miRNAs (mRNAs).
The quality of each individual xi (yi) in X (Y) is evaluated using Equation (1). To evaluate the fitness of an individual in a population, a corresponding individual in another population must be determined. In our approach, the individual producing the best score (Equation (1)) with any given individual is chosen. This strategy induces a coevolutionary learning effect that finds complete solutions cooperatively. Then, the best R and V (R!<!µ , ! V!<!) individuals from X and Y are selected for updating the probability distribution for each population. Specifically, the probability distribution over miRNAs (mRNAs) is revised according to the number of times each miRNA (mRNA) is included in the selected set of individuals, as follows.
For the probabilistic learning, vectors of probabilities 
and 
are maintained. Here, 
denotes the probability of choosing the j th element as a member of the individual set. The probability distribution of the (q+1) st generation is updated from the q th generation as
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| (3) |
(
) represents the j th value in the k th selected individual. The update rate is controlled by the two parameters, 
m 
(0, 1] and t (0, 1] . When these parameter values are near zero, current probability vectors depend highly on the previous probabilities. Finally, new populations are generated based on these current probability distributions of miRNAs and mRNAs. The above procedure is iterated until the maximum number of generations is reached. Our probabilistic model for generating the next population is relatively simple. More complicated probabilistic models, considering the dependencies between miRNAs (or mRNAs), were not employed because of their extremely high computational burden. Figure 3 depicts the search procedure of this probabilistic learning algorithm for miRNA–mRNA module identification.
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In the presented algorithm, two insulated populations of miRNAs and mRNAs evolve cooperatively. The performance of this type of optimization technique depends on interdependencies among the subcomponents, i.e. miRNAs and mRNAs. Each population is adapted dynamically in accordance with another population. This strategy can achieve good results via the decomposition of complex problems (Potter and De Jong, 2000; Zaritsky and Sipper, 2004). Co-adaptive changes of the two populations towards the optimum in our experiments are shown in Supplementary material.
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3 RESULTS |
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TOPABSTRACT1 INTRODUCTION2 METHODS3 RESULTS4 DISCUSSION AND CONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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3.1 Preparation of the data sets
Expression profiles of mRNAs and miRNAs were extracted from the experimental data set of (Lu et al., 2005). We used expression profiles of 217 miRNAs and about 16 063 mRNAs on 89 multiple human cancer samples. From these, we analyzed the relationships among 99 human miRNAs and 2012 mRNAs, which are linked together in miRBase Targets Version 3.0 (http://microrna.sanger.ac.uk/targets/v3/, (Griffiths-Jones et al., 2006)). Of these 2012 mRNA x 99 miRNA possible binding pairs, 3982 pairs with significant binding scores (P -value < ! 5 x 10–3) were used in our experiments.
Some characteristics of the putative target-binding association between miRNAs and mRNAs were investigated. Figure 4a shows the distribution of the numbers of putative binding sites for miRNAs in the 3 ' UTR of each mRNA. In our data set, one mRNA contains on average 1.97 binding sites. Figure 4b depicts the distribution of the numbers of target mRNAs of each miRNA. Here, one miRNA binds putatively to the 3 ' UTR of 40.22 mRNAs on average.
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3.2 Discovery of miRNA–mRNA modules
3.2.1 Parameter setting
The parameters of the population-based probabilistic learning algorithm were set as follows. The population sizes, µ (for mRNAs) and
(for miRNAs), were set to 4000 and 500, respectively. Parameters for controlling the update rate in Equation (3), m and t values were set as 0.8. The maximum number of iterations was set to 100. The balancing parameters in the fitness function (Equation (1)), , ß and were 0.6, 0.3 and 0.1, respectively. Parameters of the VOL term in the fitness functions w, wm and wt were set to 0.1, 0.5 and 0.5, respectively. In addition, the minimum subset size was two for miRNAs and five for mRNAs. Details of the parameter settings are given in Supplementary material. Figure 5 shows the two best miRNA–mRNA modules found by the algorithm. The score of module I was 0.66 and that of module II was 0.78. To evaluate the significance of these scores, we estimated the distribution of scores of randomly chosen miRNA–mRNA modules. Figure 6 shows the estimated distribution. Here, the scores of the two best modules are extremely high, meaning that the probability of finding these modules by chance is close to zero. Details of the predicted miRNA modules are described in Supplementary material.
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3.3 Validation of the modularity
To validate the modules found, we calculated correlation coefficients between mRNAs. Our approach considers not only the similarity between mRNA expressions but also the putative miRNA–mRNA relationships and the similarity between the related miRNAs. Thus, the mRNAs included in our modules are expected to be much more correlated when the miRNAs are actively functioning, i.e. highly expressed. Differences in the correlation coefficients between the mRNA pairs included in the same module according to the miRNA expression level are contrasted in Figure 7. The x -axis denotes the correlation coefficients calculated using the subset of samples, where the mean expression level of the miRNAs included in the same module is in the upper 25%. The y -axis corresponds to the correlation coefficient across all samples. It can be shown that the expression correlation is likely to be much higher when the related miRNAs are highly expressed. The P -values denoting the significance of these differences were estimated by random sampling and are shown in Supplementary material.
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3.4 Biological significance of the modules
In module I, three miRNAs share putative target genes. Of these, mir-212 and mir-132 are tandem-arrayed in the same chromosomal location within 300 bp and may be on a transcript (polycistronic miRNAs). They are located to a minimal loss of heterozygosity (LOH) region described in hepatocellular carcinomas (Calin et al., 2004). Also, in their upstream and downstream regions, there are tumor suppressor genes, hypermethylated in cancer 1 (HIC1) and ovarian cancer gene-2 (OVCA2), respectively. Therefore, these polycistronic miRNAs may be involved in tumor suppression. The gene mir-127, which was downregulated in 75% of the human cancer cells tested, was induced strongly after treatment with chromatin-remodeling drugs (Saito et al., 2006). Induction of mir-127 resulted in the downregulation of B-cell CLL/lymphoma 6 (BCL6), a known proto-oncogene. Therefore, mir-127 may have a role as a tumor suppressor, as with the clusters mir-212 and mir-132.
Considering the miRNAs in the module as tumor suppressors, most of their target genes should be oncogenes. Indeed, among the target genes, EIF4A2, GUSB and ACVR2B are thought to be candidate oncogenes (Myllykangas et al., 2006). EIF4A2 is known as the partner of the BCL6 translocation (Akasaka et al., 2003). Overexpressed human GUSB increases the susceptibility to tumor formation (Donsante et al., 2001). Also, the loss of activin signaling through mutation of ACVR2 may be important in the genesis of MSI-H colorectal cancer (Jung et al., 2004). Although RPL34, RPL13A and SNRPD3 are considered as genes coding for structural proteins, they can show differences in expression levels between malignant and non-malignant tumor pairs. For example, the expression of RPL13A in prostate cancer tissue differs (is upregulated) significantly from the norm (Ohl et al., 2005). All genes in module I can be assumed to be involved in common biological functions. Although the GO annotation (Table 1) of this module is related to metabolism, the assigned genes are specifically associated with cancer in the literature.
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Module II consists of two miRNAs and their five target genes. The miRNA let-7a has been reported as a tumor suppressor by negatively regulating the Ras oncogene in lung tissue (Johnson et al., 2005), and the other members of the let-7 family that have a similar mature sequence and expression pattern are suspected to code for cancer-related miRNAs. Both mir-98 and let-7f-2 are on an intron of the HUWE1 gene, which ubiquitinates the p53 tumor suppressor and core histones (Chen et al., 2005). We suspect that the mir-98 and let-7f-2, processed products of the HUWE1 transcript, may modulate or attenuate cancer development. In fact, their target genes are also involved in cancer development or the cell cycle. In terms of GO category (Table 1), they are involved in two forms of biological functions (cell cycle or metabolism).
For example, ESPL1 plays a central role in chromosome segregation by cleaving the SCC1/RAD21 subunit of the cohesin complex at anaphase (Zou et al., 2002) and CDC34 is involved in the late G1-to-S transition, a key regulator of the cell cycle (Pagano, 1997). Collectively, we can conclude that the predicted module II is an important cancer-related miRNA–mRNA module with strong correlation.
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4 DISCUSSION AND CONCLUSIONS |
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TOPABSTRACT1 INTRODUCTION2 METHODS3 RESULTS4 DISCUSSION AND CONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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Critical cellular processes can be affected by miRNAs. However, their precise functional roles are still largely unknown. Many miRNAs regulate gene expression by binding to and inhibiting mRNAs. Although this phenomenon is mostly observed in plants, our results presented in Figure 7 could serve as preliminary evidence for the posttranscriptional regulation by miRNAs in animals. Some experimental results have been reported that animal miRNAs could also guide the cleavage of endogenous targets (Yekta et al., 2004). Various miRNA expression profiles have been observed in human tumors and diseases. The advantage of using expression profiles is that modular miRNAs can be detected in a broader biological context than when only using miRNA–target duplexes. Furthermore, the information on mRNA expression profiles may be used as additional evidence that they are indeed target genes of miRNAs.
In the miRNA–mRNA modules discovered using our method, expression patterns of miRNAs as well as mRNAs were highly correlated. Moreover, expressions of the mRNAs in the same module were more strongly correlated when the miRNAs in that module were highly activated (i.e. expressed) than across the whole sample. The mRNAs included in the same module also shared similar biological functions, demonstrating the ability of our method to detect functionally related genes. The relationship between cancer and our modules was also analyzed using a literature survey, confirming the effectiveness of this proposed method for finding biologically meaningful subsets of miRNAs and mRNAs.
We proposed a population-based probabilistic search method for identifying miRNA modules from their predicted miRNA targets as well as their expression data sets. The proposed discovery method facilitates the incorporation of multiple heterogeneous information sources by adopting a balanced fitness function and coevolutionary learning strategies. As the two groups of miRNAs and mRNAs are fitted cooperatively to the best solution, the algorithm found miRNA–mRNA modules with significantly high fitness scores. The search strategy is based on the use of global statistical information contained in subsets within populations. Thus, it can search efficiently in parallel for the global optimum.
Our method is related to biclustering methods that have been noted in various biological issues (Madeira and Oliveria, 2004). The biclustering approach groups rows and columns simultaneously in a two-dimensional matrix. Similarly, our method tries to cluster miRNAs and mRNAs simultaneously. Most biclustering methods have been specified in microarray data sets (Cheng and Church, 2000; Madeira and Oliveira, 2004). They identified groups of genes that show correlations between their expression patterns under given experimental conditions. Whereas they focused on single resource, our method deals with diverse resources using well-designed objective functions.
To discover more significant biological modules summarizing multiple aspects of biological system, the computational approach needs to deal with heterogeneous biological data sets. For example, regulatory modules can be revealed by clustering rows and columns simultaneously in a two-dimensional matrix composed of heterogeneous genome-wide resources of expression profiles as well as genomic sequences (Joung et al., 2006). Our method can be applied to detect miRNA modules as well as other types of biological modules from multiple resources.
In spite of the advantage obtained by utilizing diverse resources, our method needs prior setting of several parameters of the fitness function. Multi-objective optimization techniques, such as the Pareto-based ranking scheme (Deb, 2001; Fonseca and Fleming, 1993), could be exploited to reduce the number of parameters by implicit balancing between several objectives. We used expression data sets of miRNAs and mRNAs that were obtained from independent experiments. Therefore, the measurement of correlations between two expression data sets may produce additional artifacts, which can affect the analysis adversely. The regulatory effects of multiple miRNAs and mRNAs could be investigated more precisely from data sets that observe expression profiles of miRNAs and mRNAs and proteins for the same samples at the same time. Comparative analysis of homologous species (e.g. mouse) is another research direction for detecting miRNA–mRNA modules more precisely.
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ACKNOWLEDGEMENTS |
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TOPABSTRACT1 INTRODUCTION2 METHODS3 RESULTS4 DISCUSSION AND CONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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This research was supported in part by the National Research Laboratory Program of the Korea Ministry of Science and Technology (MOST) and in part by the Soongsil University Research Fund.
Conflict of Interest: none declared.
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FOOTNOTES |
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Associate Editor: Satoru Miyano
Received on October 30, 2006; revised on December 15, 2006; accepted on February 4, 2007
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