MiRTif: a support vector machine-based microRNA target interaction filter

Overall prediction accuracy

Current miRNA target prediction methods are mostly based on similar characteristics of base pairing derived from lin-4 and let-7, and their genetically validated mRNA targets in C. elegans [28–32]. Despite the fundamental similarities of those methods, many of their predictions are not in common. In addition, the prediction methods usually produce hundreds of targets for a given miRNA, meaning a large number of them could be false positives. Using the known miRNA:target interaction pairs, our trained SVM classifiers successfully predict most of the false positives: 28 out of the 38 (73.68%) negative samples are correctly predicted to be false interactions. Although this is at the expense of 32 incorrectly predicted positive samples, most of the positive samples (163 out of 195) are correctly predicted.

Informative features

It is worth noting that almost all the 25 most informative features in Table 2 come from either the non-seed region or the entire duplex (the only exception is feature "2-gram, seed, GU/GC"). For example, two of the interesting features, the gap frequencies in the non-seed region and the entire region ("1-gram, non-seed, gap" and "1-gram, entire, gap" in Table 2), differ considerably between the positive and the negative samples. We suspect that a highly discriminative k-gram code in the non-seed region makes some contribution to the discriminating ability of the same k-gram code in the entire region; otherwise we would have observed a high F score for this k-gram code in the seed region. This observation hints the potential importance of the k-gram frequencies in the non-seed region in discriminating positive and negative miRNA:target interaction pairs. In fact, among the 100 most informative features, non-seed region features account for 43, entire region features account for 44, whereas seed region features only account for 13. It again shows that many of the highly informative features lie within the non-seed region.

Dataset

Known miRNA:target interactions were downloaded from the TarBase version 3.0 [13]. Translationally repressed targets are not separated from cleaved ones. This is because the experimental techniques used to validate targets usually only prove one case but do not disprove others. For example, luciferase reporter assay and immunoblotting assay are widely used to validate translationally repressed targets, but these experiments cannot substantiate whether the given target mRNA is also cleaved by miRNA. Similarly, microarray and real-time RT-PCR assay are often used to validate cleaved targets, but they cannot distinguish translationally repressed targets. Only miRNA:target interactions with reported binding duplexes from drosophila, C. elegans, human, mouse, rat and zebrafish were extracted. Duplicated entries and entries with incomplete binding diagrams were removed, resulting in 195 positive and 21 negative miRNA:target duplexes. As the number of negative samples is small, we went on predicting the binding patterns of those known negative interactions without duplexes being reported in the original papers. There are 15 negative miRNA:target interactions from two papers [10, 36] that do not have reported binding duplexes. The six experimentally validated negative interactions from Krek's paper [10] have their binding diagrams available from the PicTar website http://pictar.mdc-berlin.de. For the nine negative interactions from the work of Robins [36], we used RNAhybrid [16] to predict the binding duplexes. Two of the 15 negative interactions contain two target sites, as a result, 17 new negative miRNA:target duplexes were added, resulting in a total of 38 negative samples. Both the positive and the negative training sets can be found on the MiRTif website http://bsal.ym.edu.tw/mirtif.

Data representation

For a given miRNA:target duplex, the gaps at both ends are firstly removed, if any. The duplex is then partitioned into two parts, with the first part covers nucleotides 1–9 from the 5' end of the miRNA, and the second part covers the rest of the duplex. These two parts are named "seed" and "non-seed" regions, respectively (see Figure 1). We define five types of pairing in a duplex: AU (AU or UA pair), GC (GC or CG pair), GU (GU or UG pair), gap and mismatch. A k- gram is known as a subsequence of length k. For the case of miRNA:target duplex, we define a k- gram as a duplex fragment of length k. Therefore, a 1-gram contains 5 different pairing types, which we call them "1-gram codes". Similarly, 2-gram and 3-gram contains 5² and 5³ codes, respectively. For each miRNA:target interaction, we compute the 1-gram, 2-gram and 3-gram frequencies in the seed, non-seed and entire duplex, giving 3 × 5 + 3 × 5² + 3 × 5³ = 15 + 75 + 375 = 465 features. The 2-gram and 3-gram codes are counted from the 5' end of the miRNAs. For example, in Figure 1, there are two but not one occurrences of AU/GC (AU pair followed by GC pair) in the seed region, because the 2-gram code is counted from 5' of the miRNA.

Feature selection

Although state-of-the-art classifiers such as neural networks and support vector machines can accommodate redundant and noisy features, removing non-informative features may still improve the performance of these classifiers [37]. Therefore, a feature selection procedure adopted from Golub et al. [38] was performed. For each feature x _j , j = 1,..., 465, the mean ${\mu }_j^{+}$(${\mu }_j^{-}$) and the standard deviation ${\sigma }_j^{+}$(${\sigma }_j^{-}$) for both the positive and the negative sets are calculated. The F score is defined as $F(x_j)=\left|\frac{{\mu }_j^{+}-{\mu }_j^{-}}{{\sigma }_j^{+}+{\sigma }_j^{-}}\right|$, which can be used to rank the features according to how well they discriminate the positive and negative samples. In this work, we used a threshold of 0.1 for feature selection, that is, if a feature has an F score greater than 0.1, it is retained; otherwise it is removed from the feature vector.

The F-value threshold was chosen based on a survey of the number of retained features using various F-value cut-off values. Using a cut-off value of 0.05, 0.06, 0.07, 0.08, 0.09, 0.10, 0.20, 0.30, 0.40 and 0.50, the numbers of retained features are 327, 312, 290, 255, 242, 227, 82, 19, 2, and 1, respectively. Although we would like to remove the redundant and irrelevant features, using an F-score cut-off greater than 0.20 would reduce the number of features drastically, down to 82 features from 227. Hence we decided to use 0.1 as the F-value threshold.

The final feature vector contains 229 features with F scores greater than 0.1. These 229 informative feature can be obtained from the MiRTif website http://bsal.ym.edu.tw/mirtif.

Support vector machines

Support Vector Machine (SVM) was first introduced by Vapnik [23, 24]. It has been used extensively in a wide range of areas of classification and regression and has shown excellent empirical performance. In bioinformatics investigation, SVM has been utilized to study problems such as microarray gene expression data analysis [39], protein secondary structure prediction [40], prediction of protein-protein interaction [41] and RNA-protein interaction [42], prediction of protein subcellular localization [43–45], protein remote homology detection [46–49], and classification of real and pseudo miRNAs [50, 51]. SVM is a learning algorithm that, upon training with a set of positively and negatively labeled samples, produces a classifier that can then be used to identify the correct label of unlabeled samples. Each sample is described by a feature vector, which is often not linearly separable. SVM thus maps the input vectors into a high dimensional space H and construct an optimal hyperplane that divides the positive and the negative samples with the maximum margin of separation between the hyperplane and the closest points from both classes.

The SVM algorithm requires the solving of a quadratic optimization problem. To simplify the problem, SVM does not explicitly map the feature vectors of all the samples to the space H. Instead, mapping is done implicitly by defining a kernel function $K(\overrightarrow{x},\overrightarrow{y})$ between two samples with feature vectors $\overrightarrow{x}$ and $\overrightarrow{y}$ as $K(\overrightarrow{x},\overrightarrow{y})=\phi (\overrightarrow{x})\cdot \phi (\overrightarrow{y})$, where ϕ is the mapping to the space H. A detailed description of the mathematics behind SVM can be found in an article by Burges [52]. In the present study, we used soft-margin SVM implementation in SVM^light (version 6.01) created by Joachims [53]. The package can be downloaded from http://svmlight.joachims.org/ and is free for academic use.

Hyper-parameter selection