- Research Article
- Open Access
Random walks on mutual microRNA-target gene interaction network improve the prediction of disease-associated microRNAs
© The Author(s). 2017
Received: 13 March 2017
Accepted: 6 November 2017
Published: 14 November 2017
MicroRNAs (miRNAs) have been shown to play an important role in pathological initiation, progression and maintenance. Because identification in the laboratory of disease-related miRNAs is not straightforward, numerous network-based methods have been developed to predict novel miRNAs in silico. Homogeneous networks (in which every node is a miRNA) based on the targets shared between miRNAs have been widely used to predict their role in disease phenotypes. Although such homogeneous networks can predict potential disease-associated miRNAs, they do not consider the roles of the target genes of the miRNAs. Here, we introduce a novel method based on a heterogeneous network that not only considers miRNAs but also the corresponding target genes in the network model.
Instead of constructing homogeneous miRNA networks, we built heterogeneous miRNA networks consisting of both miRNAs and their target genes, using databases of known miRNA-target gene interactions. In addition, as recent studies demonstrated reciprocal regulatory relations between miRNAs and their target genes, we considered these heterogeneous miRNA networks to be undirected, assuming mutual miRNA-target interactions. Next, we introduced a novel method (RWRMTN) operating on these mutual heterogeneous miRNA networks to rank candidate disease-related miRNAs using a random walk with restart (RWR) based algorithm. Using both known disease-associated miRNAs and their target genes as seed nodes, the method can identify additional miRNAs involved in the disease phenotype. Experiments indicated that RWRMTN outperformed two existing state-of-the-art methods: RWRMDA, a network-based method that also uses a RWR on homogeneous (rather than heterogeneous) miRNA networks, and RLSMDA, a machine learning-based method. Interestingly, we could relate this performance gain to the emergence of “disease modules” in the heterogeneous miRNA networks used as input for the algorithm. Moreover, we could demonstrate that RWRMTN is stable, performing well when using both experimentally validated and predicted miRNA-target gene interaction data for network construction. Finally, using RWRMTN, we identified 76 novel miRNAs associated with 23 disease phenotypes which were present in a recent database of known disease-miRNA associations.
Summarizing, using random walks on mutual miRNA-target networks improves the prediction of novel disease-associated miRNAs because of the existence of “disease modules” in these networks.
MiRNAs are a class of small non-coding regulatory RNAs that play an important role in the regulation of gene expression [1, 2]. Misregulation of miRNAs has been shown to contribute to both common [3–7] and rare diseases . Because the identification in the laboratory of miRNAs related to a particular disease is non-trivial, computational methods for the in silico identification of potential disease-miRNAs associations have great potential for speeding up this process.
A number of computational methods, mostly network-based or machine learning approaches, have been proposed for the prediction of disease-associated miRNAs . The network-based methods mainly rely on the construction of similarity networks expressing functional similarities between miRNAs, after which specific algorithms are used to detect novel disease-miRNA associations [10–20]. Recently, disease similarity matrices have been additionally integrated with the miRNA functional similarity network to construct heterogeneous networks of diseases and miRNAs, using known disease-miRNA associations [21–25].
Most often, the similarity networks used are functional miRNA similarity networks, containing only miRNAs as nodes (hereafter referred to as homogeneous miRNA networks). In these networks, nodes represent miRNAs and edges represent the degree of functional relatedness between the miRNAs. This functional relatedness can be derived from miRNA-target gene interactions in different ways. For example, miRNA functional similarity interactions were constructed based on the degree to which miRNAs share the same targets  or by calculating the similarity of target gene regulation patterns for each pair of miRNAs . Additionally, Wang et al.  assessed the functional similarity between two miRNAs by comparing the gene functions (using gene ontologies) of their respective sets of target genes. Similarly, Xu et al.  constructed functional synergistic regulatory interactions between miRNAs by considering common target genes in the context of gene ontology and proximity in a protein interaction network. All these methods capture a different aspect of functional similarity, and we demonstrated previously that there can be added value in constructing a functional similarity network by integrating functional similarity interactions obtained using several of the aforementioned methods .
Once a homogeneous miRNA networks is available, associations between miRNAs and diseases are subsequently predicted by assuming that functionally related miRNAs associate with phenotypically similar diseases, which is referred to as the “disease module” principle [26, 27]. Specific methods that exploit this principle have been proposed. Local similarity measures only assess direct neighbours of known disease-associated miRNAs [10, 11] or neighbours of candidate miRNAs (as used e.g. by HDMP ) in homogeneous miRNA networks. Another state-of-the-art method for disease miRNA prediction, RWRMDA [14, 15], obtains a global network similarity metric by running a random walk with restart (RWR) algorithm (a network propagation technique) on homogeneous miRNA networks. RWR-based techniques were also applied on different network types where either a phenotype similarity network  or a protein interaction network  was used as input for the analysis. In addition, we recently demonstrated that network-based ranking algorithms, which were successfully applied for either disease gene prediction or for studying social networks and networks of interlinking web pages, could also be used effectively for disease microRNA prediction on homogeneous miRNA networks, achieving comparable performance with the RWR-based method . For heterogeneous networks of diseases and miRNAs, pathfinding-based methods were used [21, 22] that rely on the assumption that the more paths exist between a miRNA and a disease, the more likely it is that there exists an association between them. In addition, based on the assumption that functionally similar miRNAs tend to be associated with similar diseases, other methods were proposed relying on the identification of clusters of similar diseases and similar miRNAs [23–25].
Next to network-based methods, machine learning-based methods that do not use miRNA-target interactions have also been proposed. For example, a Naïve Bayes model was used to integrate genomic data for prioritizing disease-related miRNAs . Qinghua et al.  applied support vector machines for identifying disease-associated miRNAs. In addition, Qabaja et al.  used a Lasso regression model to infer disease-miRNA associations. The common limitation of these machine learning methods is the necessity to compile a set of negative training samples consisting of non-disease-related miRNAs. As the absence of an observed association does not imply the non-existence of an association (there are no proven negatives), obtaining such a negative training set is not straightforward . More recently, RLSMDA , a semi-supervised classifier-based method, was proposed to overcome this limitation, prioritizing candidate miRNAs for all considered diseases without the need for negative samples. Importantly, RLSMDA was reported to outperform the aforementioned state-of-the-art methods RWRMDA  and HDMP .
A common limitation of the homogeneous miRNA network-based methods is that the knowledge of biological relationship between miRNAs and their target genes might be used ineffectively because this relationship is only partially integrated in the metric used to capture degree of similarity between two miRNAs. Also, the application of the RWR algorithm, underpinning several state-of-the-art network-based algorithms, is not limited to homogeneous networks containing only miRNA nodes. It can be applied to heterogeneous networks where both miRNAs and their gene targets are present in the network as nodes, and edges represent miRNA-target interactions. With the human genome containing thousands of miRNAs [34, 35], regulating the expression of thousands of genes [36, 37] and with these miRNA-target interactions (predicted or experimentally validated) now being largely available in a number of miRNA-target databases (as comprehensively reviewed in ), here we propose to use heterogeneous networks as input for the identification of disease-related miRNAs, in order to make optimal use of this increased level of detail.
MiRNAs have emerged as key regulators of gene expression in diverse biological pathways; the relationship of a miRNA and its target genes are usually considered as direct interactions between the miRNA and the target genes (i.e., a miRNA regulates target genes by binding to target sequences in mRNAs). Consequently, miRNA-target gene regulatory interactions were used as directed interactions in a number of studies [32, 39, 40]. However, recent developments introduced a new twist to this: targets can reciprocally control the level and function of miRNAs . This mutual regulation of miRNAs and target genes in combination with the large coverage of miRNA-target interactions available in publicly available miRNA-target databases  has inspired us to propose a novel network-based method for disease miRNA prediction. In this study, instead of constructing homogeneous miRNA networks from target genes or using directed miRNA-target gene interactions, we exploit the mutual regulatory relations between miRNAs and their target genes to construct mutual heterogeneous miRNA-target gene networks (hereafter, referred to as mutual heterogeneous miRNA networks). Next, we propose a novel framework, RWRMTN, in which we apply the RWR algorithm on these heterogeneous miRNA networks to prioritize candidate disease miRNAs. In particular, based on a previous study indicating that miRNAs regulate diseases through their target genes , we hypothesize that the mutual regulation between a miRNA and their targets leads to a transfer of disease information between them. Therefore, in the proposed method, we force the RWR algorithm to start from a set of seed nodes, consisting not only of known disease miRNAs but also of their target genes. To assess and evaluate the predictive performance of RWRMTN, we use a leave-one-out cross-validation scheme on a set of experimentally verified disease phenotype-miRNA associations. Experimental results indicate that RWRMTN outperforms RWRMDA , a state-of-the-art network-based method using RWR operating on homogeneous miRNA networks. Additionally, we demonstrate that this superior performance of our proposed method is because of the existence of “disease modules” in the heterogeneous miRNA networks used as input for our algorithm. Indeed, we observe that (1) a large amount of known disease genes are present in the heterogeneous miRNA networks and (2) most known disease miRNAs in the network regulate at least one known disease gene. Moreover, we showed that our method also outperformed RLSMDA , a state-of-the-art machine learning-based method that uses a semi-supervised learning method. Furthermore, we demonstrated that our method is stable and can achieve relative high performance for both experimentally validated and predicted miRNA-target gene interaction data. Finally, using RWRMTN, we identified 76 novel miRNAs associated with 23 disease phenotypes which were present in an recent database of known disease-miRNA associations HMDD .
Construction of heterogeneous miRNA networks
Construction of homogeneous miRNA networks
To compare the prediction performance of RWRMTN with that of RWRMDA  on homogeneous miRNA networks, we constructed two homogeneous miRNA networks based on miRNA-target gene interactions (Fig. 1b). More specifically, based on an identical procedure of construction of homogeneous miRNA network as in our previous study , we defined a functional relation between two miRNAs as follows: two miRNAs are considered to be functionally interacting if they share at least one target gene, with the degree of similarity defined as the number of shared target genes normalized by the minimum number of target genes of the two miRNAs under consideration. As a result, two networks respectively containing 730 miRNAs with 29,089 interactions (HomomiRWalkNet) and 1428 miRNAs with 46,118 interactions (HomoTargetScanNet) are constructed from the miRNA-target gene interactions in HetermiRWalkNet and HeterTargetScanNet.
Database of known disease phenotype-miRNA associations
In order to be able to evaluate the performance of the propose method, and to put the new method in perspective, a database of known disease-miRNA associations is required. Here we will use miR2Disease , a comprehensive resource of miRNA - human disease associations that is manually curated and maintained. We used 270 manually curated disease phenotype–miRNAs associations between 53 disease phenotypes and 118 miRNAs from that database (See in Additional file 1: Table S3).
Construction of a disease phenotype similarity matrix
To compare the performance of RWRMTN and RLSMDA, we additionally collected a disease phenotype similarity matrix of 5080 phenotypes from , where an element of the matrix represents degree of similarity between two disease phenotypes. The similarities in this matrix were obtained by applying various text mining algorithms to OMIM records .
RWRMTN: A random walk with restart algorithm applied to heterogeneous miRNA networks
RWR is a variant of the random walk algorithm, simulating a walker that either moves from a current node in a network to a randomly selected adjacent node or alternatively returns to the source node (also called the seed node) where the random walk was started, with a fixed probability of returning (restart probability) γ. This algorithm has been used successfully in a number of related studies such as prediction of disease-associated lncRNA , disease-associated gene , drug target  and disease-related microRNA-environmental factor interactions .
(V out ) i is a set of outgoing nodes of v i . If an unweighted graph (e.g., a heterogeneous miRNA network) is used, all interactions are assigned a unity weight.
p t is a N×1 probability vector of |V| nodes at a time step t of which the i th element represents the probability of the walker being at node v i ∈V.
p 0 is the N×1 initial probability vector.
For both methods, all miRNAs/genes in the network are eventually ranked according to the steady-state probability vector p ∞ , which is obtained by repeating the iterations until convergence is reached (in this study, ||p t + 1-p t|| <10−6).
Note that, for directed heterogeneous miRNA networks such as HetermiRWalkNet-directed and HeterTargetScanNet-directed, the random walker is trapped at seed target genes because there is no outgoing link at these nodes. Therefore, non-seed nodes (including previously unidentified disease miRNAs and other target genes) cannot be ranked as they are all assigned a zero probability (Fig. 1d). Therefore, RWRMTN can only be applied to mutual heterogeneous miRNA networks such as HetermiRWalkNet-mutual and HeterTargetScanNet-mutual. Figure 1 illustrates these two methods.
RLSMDA: Regularized least squares for MiRNA-disease association
w is the weight between these two spaces. η M and η D are trade-off parameters in the miRNA and disease phenotype spaces, respectively.
S D (m × m) is the disease phenotype similarity matrix containing m diseases. S M (n × n) is the corresponding similarity matrix of the homogeneous miRNA network containing n miRNAs, where S M (i, j) is the degree of similarity between two miRNAs.
I M and I D are identity matrices with the same size as matrices S M and S D , respectively.
A(m × n) is an association matrix, where A (i,j) = 1 if disease phenotype i is known to be associated with miRNA j, otherwise A (i,j) = 0.
To compare the potential of RWRMTN for associating novel miRNAs with disease phenotypes with that of RWRMDA and RLSMDA, we applied a leave-one-out cross-validation (LOOCV) scheme on the set of disease phenotypes with known miRNA associations in miR2Disease . For each disease phenotype d, in each round of LOOCV, we held out one known miRNA associated with d. The rest of the known miRNAs associated with disease d are used as seed nodes (S m ) in the RWRMDA method. For the RWRMTN method, this set was enlarged by adding the target genes S g of the miRNAs in S m . The held-out miRNA and the remaining miRNAs in the miRNA networks which were not known to be associated with d, were ranked by both RWRMTN and RWRMDA. For RLSMDA, A (i,j) is set to 0 corresponding to d and the held-out miRNA. Then, receiver operating characteristic (ROC) curves are constructed and the area under the curve (AUC) is used to compare the performance of both methods. The ROC curve represents the relationship between sensitivity and (1-specificity), where sensitivity refers to the percentage of miRNAs known to be associated with d that were ranked above a particular threshold and specificity refers to the percentage of miRNAs that were not known to be associated with d and ranked below this threshold. Finally, the performance of each method was summarized as the average of AUC values over the entire set of disease phenotypes in the validation set.
Results and discussion
In this section, we compare the performance of RWRMTN with two state-of-the-art methods. We selected RWRMDA  as a representative network-based method, as we intended to demonstrate the added value of using heterogeneous miRNA networks over using homogeneous miRNA networks. Additionally we compared with RLSMDA , a state-of-the-art machine learning-based method, that does not use a network as a basis for its analysis.
Comparison between RWRMTN and RWRMDA
In contrast to the homogeneous miRNA networks, miRNAs connect to each other via target genes in the heterogeneous miRNA networks. In other words, disease miRNAs are less modularized in these networks. Indeed, Fig. 3 show that the performance of RWRMTN slightly increased when the restart probability increased in both networks (the slopes of regression lines are 0.029 and 0.004 with p = 0.004 and p = 0.011, respectively for HetermiRWalkNet-mutual and HeterTargetScanNet-mutual). It is also slightly more positive on HetermiRWalkNet-mutual indicating that disease miRNAs/genes in that network is less modularized than those in HeterTargetScanNet-mutual.
Comparison between RWRMTN and RLSMDA
Comparison between RWRMTN and RWRMDA, RLSMDA using 10-fold cross-validation
In previous section, we compare the performance of RWRMTN with that of RWRMDA and RLSMDA using leave-one-out cross validation (LOOCV). Considering that LOOCV is equivalent to n-fold cross validation (where n is number of known miRNAs of a given disease), this evaluation method is flexible and can be used to assess the prediction performance for any disease, even for those with only two known associated miRNAs. To show the robustness and stability of our method, we further test it with 10-fold cross validation on the TargetScan database. Due to this re-sampling method, only diseases known to be associated with at least 10 miRNAs can be taken into account. Using this criterion, only eight diseases in miR2Disease  were found to be eligible for validation. Additional file 2: Figure S1 shows the performance of the three methods using their respective optimal parameter settings (i.e., α = 0.9 and γ = 0.7 for RWRMTN, γ = 0.7 for RWRMDA, and η M = η D = 1, w = 0.9 for RLSMDA). It is obvious that RWRMTN (AUC = 0.840) outperforms both RWRMDA (AUC = 0.792) and RLSMDA (AUC = 0.753). We additionally used a larger disease-miRNA association database HMDD (version 2.0 ), containing 57 diseases eligible for performance assessment using 10-fold cross validation. Additional file 2: Figure S2 indicates that, again with optimal parameter settings for each method, the performance of RWRMTN (AUC = 0.896) is better than that observed for both RWRMDA (AUC = 0.875) and RLSMDA (AUC = 0.749).
Identification of novel disease-associated miRNAs
MiRNAs present in the top-100 ranked candidate miRNAs that are known to be associated with diseases, as reported in the HMDD database. P-value is the result of the hypergeometric enrichment test
Total in HMDD
Known disease miRNAs
hsa-miR-17, hsa-miR-182, hsa-miR-200b, hsa-miR-200c, hsa-miR-20a, hsa-miR-27a
hsa-let-7e, hsa-miR-17, hsa-miR-20a
hsa-let-7a, hsa-let-7b, hsa-let-7c, hsa-miR-19a, hsa-miR-200c, hsa-miR-203, hsa-miR-29c, hsa-miR-98
hsa-miR-106b, hsa-miR-137, hsa-miR-15a, hsa-miR-15b, hsa-miR-17, hsa-miR-181b, hsa-miR-195, hsa-miR-20b, hsa-miR-26b, hsa-miR-29a, hsa-miR-29b, hsa-miR-29c, hsa-miR-30a, hsa-miR-30b, hsa-miR-30d, hsa-miR-30e, hsa-miR-9
hsa-let-7c, hsa-let-7d, hsa-let-7e, hsa-let-7f, hsa-let-7 g, hsa-let-7i, hsa-miR-106a, hsa-miR-106b, hsa-miR-137, hsa-miR-15a, hsa-miR-15b, hsa-miR-16, hsa-miR-17, hsa-miR-181a, hsa-miR-182, hsa-miR-195, hsa-miR-196a, hsa-miR-19a, hsa-miR-19b, hsa-miR-200b, hsa-miR-200c, hsa-miR-20a, hsa-miR-20b, hsa-miR-218, hsa-miR-23b, hsa-miR-27b, hsa-miR-30a, hsa-miR-30b, hsa-miR-30d, hsa-miR-30e, hsa-miR-429, hsa-miR-506, hsa-miR-9, hsa-miR-93
hsa-miR-17, hsa-miR-181a, hsa-miR-19a, hsa-miR-19b, hsa-miR-20a, hsa-miR-27a
hsa-miR-106b, hsa-miR-124, hsa-miR-125b, hsa-miR-128, hsa-miR-137, hsa-miR-17, hsa-miR-181c, hsa-miR-195, hsa-miR-20a, hsa-miR-9
hsa-miR-106b, hsa-miR-124, hsa-miR-128, hsa-miR-19a, hsa-miR-19b, hsa-miR-20a, hsa-miR-27b, hsa-miR-340, hsa-miR-9, hsa-miR-93
hsa-miR-17, hsa-miR-19a, hsa-miR-19b, hsa-miR-20a, hsa-miR-93
hsa-let-7b, hsa-let-7c, hsa-let-7e, hsa-miR-106a, hsa-miR-137, hsa-miR-17, hsa-miR-181a, hsa-miR-181b, hsa-miR-182, hsa-miR-195, hsa-miR-19a, hsa-miR-19b, hsa-miR-200b, hsa-miR-200c, hsa-miR-20a, hsa-miR-218, hsa-miR-23a, hsa-miR-26a, hsa-miR-26b, hsa-miR-27b, hsa-miR-29a, hsa-miR-340, hsa-miR-497, hsa-miR-9, hsa-miR-93, hsa-miR-96
hsa-let-7b, hsa-let-7c, hsa-let-7d, hsa-let-7e, hsa-let-7f, hsa-let-7 g, hsa-let-7i, hsa-miR-106a, hsa-miR-128, hsa-miR-15a, hsa-miR-15b, hsa-miR-17, hsa-miR-181b, hsa-miR-182, hsa-miR-200a, hsa-miR-200c, hsa-miR-20a, hsa-miR-23a, hsa-miR-26a, hsa-miR-27a, hsa-miR-30c, hsa-miR-429, hsa-miR-96
hsa-let-7i, hsa-miR-106a, hsa-miR-181a, hsa-miR-181b, hsa-miR-181c, hsa-miR-182, hsa-miR-19b, hsa-miR-200b, hsa-miR-200c, hsa-miR-206, hsa-miR-23a, hsa-miR-25, hsa-miR-27b, hsa-miR-301a, hsa-miR-30a, hsa-miR-30b, hsa-miR-30c, hsa-miR-30d, hsa-miR-30e, hsa-miR-32, hsa-miR-497, hsa-miR-9, hsa-miR-92a, hsa-miR-93, hsa-miR-96, hsa-miR-98
hsa-miR-19b, hsa-miR-29a, hsa-miR-29b, hsa-miR-29c, hsa-miR-30a, hsa-miR-30b, hsa-miR-30c
hsa-let-7b, hsa-let-7c, hsa-let-7d, hsa-let-7e, hsa-let-7f, hsa-let-7 g, hsa-let-7i, hsa-miR-1, hsa-miR-106b, hsa-miR-137, hsa-miR-15a, hsa-miR-16, hsa-miR-181a, hsa-miR-181b, hsa-miR-182, hsa-miR-195, hsa-miR-19a, hsa-miR-19b, hsa-miR-202, hsa-miR-20b, hsa-miR-23a, hsa-miR-23b, hsa-miR-27b, hsa-miR-29a, hsa-miR-29b, hsa-miR-29c, hsa-miR-302a, hsa-miR-302b, hsa-miR-302c, hsa-miR-302d, hsa-miR-30a, hsa-miR-30b, hsa-miR-30c, hsa-miR-30d, hsa-miR-340, hsa-miR-497, hsa-miR-519d, hsa-miR-520b, hsa-miR-9, hsa-miR-93, hsa-miR-96
hsa-miR-124, hsa-miR-133b, hsa-miR-15a, hsa-miR-17, hsa-miR-181a, hsa-miR-19a, hsa-miR-19b, hsa-miR-200b, hsa-miR-200c, hsa-miR-20a, hsa-miR-20b, hsa-miR-218, hsa-miR-26a, hsa-miR-29c
hsa-miR-106a, hsa-miR-17, hsa-miR-181b, hsa-miR-182, hsa-miR-19a, hsa-miR-19b, hsa-miR-20a, hsa-miR-30a, hsa-miR-96
hsa-let-7f, hsa-let-7 g, hsa-miR-106a, hsa-miR-107, hsa-miR-124, hsa-miR-130a, hsa-miR-17, hsa-miR-181a, hsa-miR-181b, hsa-miR-182, hsa-miR-195, hsa-miR-200b, hsa-miR-200c, hsa-miR-20a, hsa-miR-27a, hsa-miR-27b, hsa-miR-29a, hsa-miR-30b, hsa-miR-30c, hsa-miR-340, hsa-miR-372, hsa-miR-373, hsa-miR-429, hsa-miR-497, hsa-miR-503, hsa-miR-519a, hsa-miR-9
MiRNAs are known to have a strong impact on biological processes and play a pathogenic role in human diseases . Therefore, the identification of novel disease-associated miRNAs is an essential part of biomedical research studying the underlying mechanisms of human diseases. Here we proposed a novel approach using a random walk with restart-based algorithm applied on mutual heterogeneous miRNA networks (RWRMTN), where contrary to previous efforts, miRNA-target gene relations were considered as bidirectional interactions, and the network used as input explicitly incorporates miRNA-target interactions. Experimental results demonstrate that our method achieves higher performance than a state-of-the-art network-based method (RWRMDA) that uses homogeneous miRNA networks, only containing miRNA nodes. We motivated that the superior performance of the proposed method can be partially attributed to the improved exploitation of the “disease module” principle. This concept is explicitly present in the heterogeneous miRNA networks used as input for our analysis, and we showed that a large amount of disease-associated miRNAs and disease related genes mutually interact with each other. Additionally, our method outperformed RLSMDA , a state-of-the-art machine learning-based method, confirming the added value of using network information when predicting novel disease related miRNAs. MiRNA-target interaction data predicted by in silico prediction tools typically have a high rate of false positive and false negative results. Therefore, we applied our method to two databases containing respectively predicted and experimentally validated miRNAs-target interactions. We could show that our method can achieve stable and high performance for both experimentally validated and predicted interaction data. Finally, using RWRMTN, we identified 76 miRNAs which were reported to be associated with 23 disease phenotypes in HMDD, an recent disease-miRNA association database.
Availability of data and materials
Source code and experiment data can be accessed at https://sites.google.com/site/duchaule2011/bioinformatics-tools/rwrmtn
DHL conceived of the study, DHL wrote the program code. DHL, LV, LHS, DTC and VHP wrote the manuscript. All authors read and approved the final version of the manuscript.
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