Clustering of mRNA-Seq data based on alternative splicing patterns

SUMMARY

Sequencing of messenger RNA (mRNA) can provide estimates of the levels of individual isoforms within the cell. It remains to adapt many standard statistical methods commonly used for analyzing gene expression levels to take advantage of this additional information. One novel question is whether we can find clusters of samples that are distinguished not by their gene expression but by their isoform usage. We propose a novel approach for clustering mRNA-Seq data that identifies such clusters. We show via simulation that our methods are more sensitive to finding clusters based on isoform usage than standard clustering techniques. We demonstrate its performance by finding a technical artifact that resulted in different batches having different isoform usage patterns, and illustrate its usage on several The Cancer Genome Atlas datasets.

1. INTRODUCTION

Clustering techniques are widely used in gene expression studies, from visualization of the data to more formal detection of underlying subpopulations. Cancer studies, for example, often rely on clustering to detect subtypes of tumors based on the expression patterns of genes (see e.g. Perou and others 2000; Sorlie and others 2001). Traditionally, gene expression studies were based on microarray studies, but now even large studies often measure gene expression levels by sequencing of messenger RNA (mRNA) Hammerman and others, 2012; The Cancer Genome Atlas Research Network, 2013. A novel aspect of using mRNA-sequencing for measuring expression levels is that sequencing provides a wealth of information about alternative splicing within the cell. Alternative splicing is the process by which a single gene codes for multiple mRNA products (or isoforms) by the process of including or excluding portions of the DNA of a gene. Different isoforms within a gene often have different functions which are location and development specific. Some proteins even have isoforms that have antagonistic functions; for example, the gene VEGF has one isoform that is used by cancer cells to encourage new vasculature near tumors and also an anti-angiogenic form that inhibits tumor growth (Qiu and others, 2009).

Despite the possible importance of individual isoforms, clustering on mRNA-Seq data often still relies on gene estimates—i.e. the total amount of mRNA, summed over all isoforms of the gene—rather than individual isoform-level expression data. If there are not many genes with isoform differences in the samples under consideration, then a clustering based upon thousands of genes is unlikely to change regardless of whether clustering is based on isoform or gene expression levels. However, in some settings, there might be large scale changes in splicing. For example, in the setting of cancer studies, there is evidence of abnormalities in tumors that might have a wide spread effect on the splicing across many genes. Dysregulation in the machinery of the cell that controls splicing (the spliceosome) could have splicing impacts on many isoforms; significantly mutated genes that are members of the spliceosome have been found in several tumors (Yoshida and others, 2011; Je and others, 2013; Makishima and others, 2012; Furney and others, 2013; Gentien and others, 2014; Quesada and others, 2012). However, mutation is just one way in which the function of a gene can be disregulated in tumors; it is well known that similar phenotypes in tumors can be the result of abnormalities other than mutations. This suggests that unsupervised clustering techniques, which do not rely on identifying the source of the abnormality, could provide greater ability to detect dysregulated splicing on tumors. This is particularly true given that significant mutations in the spliceosome have been found at much lower prevalence for other tumors, such as gene U2AF1 which is found mutated at a prevalence of only around 5% in acute myeloid lymphoma or lung adenocarcinoma (The Cancer Genome Atlas Research Network, 2013; Cancer Genome Atlas Research Network, 2014).

There are multiple ways to incorporate the information provided by individual isoform estimates into clustering. The most obvious is to cluster based on isoform estimates, rather than gene estimates. One drawback in clustering with isoforms is that many genes may have little difference in the expression pattern between isoforms, yet contribute many isoforms, with the result that the pattern of such genes can be amplified. Clustering of expression data is always a trade off between different features, and the number of features that support different patterns play a substantial role in the clusters that are found. As a result, interesting differences in isoform expression could be easily masked by the cumulative effect of the many genes without such differences. More generally, large gene effects could mask signals of different isoform usage within a gene, which are likely to be more subtle.

We offer a clustering strategy, complementary to the standard strategy of clustering on expression level, that specifically tries to detect such differences. It is based on evaluating the relative isoform usage within a gene: a measure of the tendency of a gene to prefer one isoform over another. This leads to a data structure where the isoforms are grouped by gene—a different data structure than the traditional data matrix, so that many standard clustering methods are not appropriate.

While the focus of this article is entirely on the biological application of clustering isoform usage, it can be helpful to posit this problem into a more general framework as the problem of clustering data when the features are known to have a predefined grouping assignment. Using this terminology, gene estimates are then a summary statistic (the sum) of the features in the group. Gene expression clustering is clustering of a summary statistic of the group members, while isoform clustering is clustering of the individual features ignoring the group membership.

We propose a clustering strategy that uses the group structure in a flexible manner. We assume that within each group there is a natural notion of distance between samples based on the features in that group. We then create distance metrics separately for each group (or gene), and then aggregate the distances across groups and apply standard clustering techniques on the aggregate distance. This creates a flexible clustering strategy that allows the feature information to contribute to the clustering only in the context of its relationship to other features in the group. Our focus in what follows will be entirely on the specific example of clustering of isoform usage, but it is useful to note that other choices of distances with a group could capture different kinds of relationships for clustering.

We evaluate this clustering strategy on simulated isoform expression data and show that it has improved performance in detecting isoform usage changes, as compared to clustering on the individual features (isoform clustering) or clustering on the summary statistic (gene clustering). We also demonstrate our clustering technique on a mRNA-Seq dataset that has a clear technical artifact which appears to have affected the isoform usage; using this as a gold-standard, we show that our clustering strategy detects the underlying clustering more accurately than the other two strategies. We also demonstrate that it finds different clusterings on many The Cancer Genome Atlas (TCGA) datasets, and examine Acute Myeloid Leukemia (AML) in some detail.

Before continuing, we provide a short background on some of the biological terms we use in this paper.

Alternative splicing

The DNA that contains the genetic code for a protein must be first transcribed into mRNA. In eukaryotic cells, a copy of the DNA is first made (called pre-mRNA) which is then changed into the final mRNA. In many eukaryotes, the pre-mRNA is changed by selectively cutting out portions of the pre-mRNA so that the final mRNA transcript is no longer an exact copy of the code found in the DNA of the cell. The process of cutting out portions of the pre-mRNA is called splicing. In many complex organisms, including human and many common model organisms like fruit flies and mice, there are multiple ways in which the same pre-mRNA can be spliced; in addition, there are also multiple pre-mRNA that can be made from the same gene, depending on which of several starting points and ending points are used in copying DNA into pre-mRNA. The end result is that a single gene representing a stretch of code on the DNA can result in many different transcripts, or isoforms of the gene.

Sequencing of mRNA

Previously, large-scale quantification of the amount of mRNA in a cell (also called mRNA expression) was via microarray technology; expression measurements from microarrays quantified all mRNA from a gene without distinguishing between different isoforms of the gene. The rapid expanse in sequencing technologies has allowed for direct sequencing of mRNA and therefore opens up the ability to quantify not just the cumulative amount of expression from a gene region, but also that of individual isoforms within a gene. It is important to note that current commonly used sequencing technologies still do not allow for the entire mRNA to be sequenced. This means that estimates of the amount of individual isoforms are not the simple result of counting how many sequences came from particular isoform, but must be indirectly estimated via deconvolution methods (Denoeud and others, 2008; Jiang and Wong, 2009; Trapnell and others, 2010; Richard and others, 2010; Salzman and others, 2010; Katz and others, 2010). Such methods provide an estimate of the underlying rate of transcription of each isoform, which can then be translated into “estimated counts” so that they are on the same scale as if one could have uniquely identified the sequences to isoforms and simply counted them.

2. METHODS

We are interested in the effect of clustering based on isoform usage, by which we mean the relative percentage within each gene that an isoform is used. More formally, for each sample and gene we observe not a single value, but a vector of values , where is the number of features or isoforms in gene . We note that varies across genes, and we only consider genes with multiple isoforms so that . In the data we considered, ranged from 2 isoforms up to instances of more than 30 expressed isoforms.

Let the estimates of isoform expression for individual in gene be denoted as and let be the total expression in gene , i.e. the estimate of gene expression. Then our estimate of isoform usage within gene for sample is given by the relative proportion of each isoform within the gene, We note that for our clustering method we could consider any vector that is a function of our isoform information, including for example the original, untransformed vector of isoform expression values, but our focus is on the relative expression within the gene so we focus on the proportion. Gonzàlez-Porta and others (2012) similarly convert isoform estimates to proportions per gene to quantify variability in splicing and identify those genes with varying splicing ratios.

Our data of isoform usage is not a simple matrix expected by many clustering routines. Many clustering techniques need simply a distance matrix between the samples for clustering, but it is also not obvious how to create a distance matrix between the samples when each of the vectors lies in an entirely different dimensional space. However, for a single gene (or group), there are numerous distances defined between vectors that lie on the simplex (see Deza and Deza, 2013, for a review); Gonzàlez-Porta and others (2012) use Hellinger’s distance in their analysis of isoform proportions. We consider some of the most popular: distance, Euclidean distance, Jeffrey’s divergence, and Hellinger’s distance; we also consider a distance based on the log-likelihood (Berninger and others, 2008; Witten, 2011) to account for the difference in variability due to different counts (see Supplemental Text, Section 1 for more details).

Therefore, we take the strategy of calculating—per gene—distances and aggregating the different across genes. By adopting this framework, we now only need to define a distance for relative isoform usage per feature. There are obviously also many choices for aggregating the distance matrices, and a straightforward strategy is to define a aggregate distance based on a (weighted) average of the different distance matrices, In the results that follow, we ultimately weighted each feature equally so that was a simple average of the distances calculated per gene—that is, . As only a small fraction of features differ between clusters, identifying and weighting these genes based on the data may lead to improved clustering and interpretable weights. For example, Witten and Tibshirani (2010) propose a penalty for automatically finding a sparse set of such weights (though when we generalized the sparse methods of (Witten and Tibshirani, 2010) to find weights automatically in our clustering, this added an enormous amount of variability in our clustering results and therefore did not perform well even in simple situations).

Our strategy is also related to kernel strategies. Specifically, because of the relationship between distances and kernels, we can see this approach as defining a separate kernel for each gene, and then combining the kernels via (weighted) averaging. Methods for combining multiple kernels have been proposed and how to choose functionals that combine multiple kernels is termed the multiple kernel learning problem (see Gönen and Alpaydin, 2011, for a review), and weighted combinations like we describe are common, Many of these methods are computationally difficult for the large numbers of features we have here. Zeng and Cheung (2010) propose creating a sparse multiple kernel for each feature for unsupervised clustering, with the similar goal as Witten and Tibshirani (2010) of finding sparse weights for the linear combinations of the kernels for each feature.

3. RESULTS

3.1. Simulation study

We evaluate via simulation the performance of clustering on gene expression, isoform expression, or proportion levels. To test the ability of the gene, isoform, and proportion clustering algorithms, we simulated gene counts and corresponding isoform proportions under different cases for how a gene could show clustering: (i) gene expression differs between groups, while the proportion levels are constant across groups; (ii) gene expression is constant across samples, while the proportion levels vary between groups; or (iii) both the gene expression and proportion levels vary across groups, which may not be the same.

We set up simulations of 5000 genes across 135 samples. For each simulation, a percentage of the genes were given a clustering pattern for their gene expression and/or for their isoform proportions depending on which of the above scenarios was being considered. We also consider a more complicated scenario where some genes fall into one of the above categories, and others fall into a different one. For example, some genes follow Case 1 above, with only gene expression differences, and other genes show both gene and alternative splicing differences, as in Case 3 from above. For simulating from this combination scenario, we chose 25% of the genes to have differential gene expression, while a varying number of genes (0.5%, 1%, 2%, 4%, 8%, and 10%) showed both differential gene expression and differential alternative splicing in their clustering. In both the simple and complex scenarios described, the remaining genes had both constant gene and isoform expression (no clustering). For specific details regarding the simulations of the isoform counts, see the Supplemental Text available at Biostatistics online, Section 2. In all of these settings, we ran gene, isoform, and proportion clustering. We also compared choices in distances and clustering methods for the proportion clustering, see Supplementary Text available at Biostatistics online, Section 2.5.

The results of the simulations show that the proportion clustering reliably finds the clusters that vary by proportional isoform usage even when the pattern represents a low percentage of genes in the data (around 2% of genes, Figure 1(a)). Moreover, the proportion clustering finds the pattern even in the presence of complicated backgrounds of other clustering signals based on gene expression differences (Figure 1(b)). These are both important characteristics, since we expect that differences in alternative splicing will affect a comparatively small numbers of genes and differences in overall gene expression will dominate.

Fig. 1.

Jaccard scores from simulation study. Plotted are the mean Jaccard scores over 1000 simulations (-axis) against the percent of genes in which the clustering pattern varies (-axis). The Jaccard score is the proportion of pairs of samples correctly co-clustered, with one indicating perfect detection of the clusters. Different lines correspond to different clustering methods, indicated by the legend. “Hellinger”, “Jeffrey’s” and “Loglikelihood” refer to different choices for the distance taken in clustering on the proportions; “Isoform” and “Gene” refer to standard clustering on the isoform or gene expression estimates directly. Vertical bars stretch to 2 standard errors. (a) Shows the results of the clustering when the only clustering signal comes from changes in proportional isoform usage within the gene (as expected, there is no signal from gene clustering). (b) Shows the results of clustering when there are a complicated mix of clustering signals; specifically 25% of the genes show different gene expressions according to three gene expression clusters, and a varying percentage of different genes (as indicated in the -axis) show both the different gene expression patterns according to the three gene expression clusters as well as different proportional isoform usage according to six non-nested proportional usage clusters (see Supplemental Text, Section 2 available at Biostatistics online for a more complete description). The dotted lines show the Jaccard scores when trying to find the gene clusters, while solid lines show those from trying to find the proportional usage clusters. Shown here are the results from K-medoids as the clustering method; results from other scenarios and from hierarchical clustering are shown in, Supplemental Figures S2–S5 available at Biostatistics online.

If we examine clustering isoform expressions directly, clustering on the isoform levels quite readily captures groups differences when they are due to overall gene expression differences (See Supplemental Figure S2 available at Biostatistics online). Even when there are competing signals due to differences in relative proportional isoform, the isoform generally finds the differential gene clusters (Figure 1(b) and Supplemental Figures S4 and S5 available at Biostatistics online).

In contrast, clustering on isoform expression does not perform as well at finding clusters that differ in relative isoform usage, as compared to clustering directly on proportional isoform usage. Even in scenarios where there is no competing gene signal and all clustering is due to relative isoform usage, clustering on the isoforms does not find the clusters until the percentage of genes with the signal is relatively larger than that of proportion clustering (Figure 1(a)). In the more complicated settings we examine, where gene expression and proportional usage clusters co-exist and have related, though not identical, clustering information, the isoform clustering performance improves slightly because the gene expression provides information about the clustering as well. However, it is still not as good as clustering on the proportional isoform usage. Clustering on the isoform expression only starts to have high concordance with the true proportional usage clusters when about 7–10% of the genes show that pattern—a much higher required percentage than that of the proportion clustering, which finds the same pattern reliably even when only 2% of the genes show the pattern.

These results indicate that proportion clustering has the potential to be more sensitive to finding clustering based on this type of alternative splicing, and particularly when there are a mix of gene and alternative splicing signals as would be expected in true biological data.

3.2. Detection of batch effect in AML data

In general, it is difficult to compare clustering methods on real data absent knowledge of true groupings in the sample. Finding data with such groupings is quite difficult for our method, since it is difficult to know a priori that there are differences in relative isoform usage. However, in analyzing mRNA-Seq data of AML tumors, sequenced as part of the TCGA project (The Cancer Genome Atlas Research Network, 2013), our method of clustering discovered an unreported batch effect in the data. Further exploration of this batch effect suggests that its effect on the data plausibly resulted in different relative levels of isoform abundance within genes, as we explain below. This gives us a gold-standard to which we can compare the efficiency of our clustering methods. We find that clustering on the relative isoform usage (i.e. proportions) in this dataset gives a practically exact correspondence to this batch effect and performs much better in finding this batch effect than clustering based on isoform levels.

3.2.1. Implementation of the clustering

To cluster the AML data, we normalize the AML samples by TMM normalization (Robinson and Oshlack, 2010), and perform an initial filtering of the data to remove extremely lowly expressed isoforms. Using the isoform counts as our initial input, we create the three different types of features: gene counts, isoform counts, and isoform proportions. The number of isoforms and genes provided is still quite large—28 014 expressed isoforms and 12 218 expressed genes. We then apply filters to each dataset to reduce to the 5000 top genes or isoforms based on variability, or in the case of proportion clustering, the 5000 genes with the largest summed distance matrix. For comparison, we also ran the proportion clustering based on the same set of isoforms found with the top 5000 most variable isoforms (excluding genes that then have only a single isoform). To provide greater stability in our clustering and to not be influenced by outlying samples, we performed consensus clustering (Monti and others, 2003) with each of our clustering routines. Briefly, this involves repeated subsampling of the entire dataset and enumeration of how frequently samples were clustered together in a consensus matrix. After performing 1000 subsamples, the consensus matrix is clustered to achieve our final clustering. See Supplementary Text available at Biostatistics online, Section 3 for further details regarding the implementation of the clustering methods on the AML data.

3.2.2. Results

In Figure 2 we compare the clustering assignments from clustering on the three different features (gene, isoform, and proportion) in order to demonstrate the differences in how the samples are clustered. In this figure, we have also superimposed the “plate” from which the sample originated, which signifies the batch in which the samples were sent to be sequenced. We can see that in the cluster assignments of all of the methods, plate 734 clusters together. Given that this is public data from the TCGA project, it is difficult to know exactly what differences occur between plates, but they usually indicate batches of samples for which the mRNA extraction and other library preparation steps are done jointly. Therefore, observing such an effect is not terribly surprising, since effects due to different batches are quite common in large projects such as these and many other TCGA datasets have reported plate effects (Leek and others, 2010) [though we note that the accompanying AML paper from which this data is drawn explicitly states that this data did not show a batch effect due to plate (The Cancer Genome Atlas Research Network, 2013)]. Removal of the plate effect with the batch correction tool ComBat (Johnson and others, 2007), results in quite different clusterings, and the resulting clusterings have a much closer relationship with the other clinical data on the samples (the correlation between clinical variables and the clustering results shown in the accompanying AML paper closely match our results after we removed the plate effect, perhaps suggesting that they did perform some batch removal with their data, contrary to their statement). This suggests that this clustering is a technical artifact.

Fig. 2.

Comparison of clustering assignment. Each column corresponds to a sample and each row to a clustering method. The cluster assignments of the three different clusterings (isoform, gene, and proportion) are shown for groups by coloring the sample according to its clustering in the above plot. We also show for gene clustering, since this is the point at which the gene clustering starts to have clusterings corresponding to the plate. The samples have been ordered to highlight the similarity between the clusterings. The top row shows the plate assignment of each sample, showing an almost perfect correspondence with proportion clustering. This clustering is based on consensus clustering of hierarchical clustering.

In comparing the performance of the methods in detecting the plate artifact, it is clear that proportion clustering is almost perfectly detecting the plate effect, which is clearly its primary signal. The other two methods do not have as clear a correspondence with plate, regardless of what is used or the method of clustering (k-medoids or hierarchical). The performance of proportion clustering in detecting the plate remains the same when the proportions for the proportion clustering are based on the same set of isoforms as isoform clustering, as well as when the clustering is via K-mediods (Supplemental Figure S6 available at Biostatistics online).

It is encouraging to find strong concordence with an known grouping of the observations. Yet, it is unclear whether this demonstrates that the clustering of proportions is finding clusters of differential isoform usage—it is not clear why a batch effect would have anything to do with isoform usage within the gene. However, when we examine the plate effect more closely, we see that plate 734 appears to have a different level of 5/ bias. A 5/3 bias refers to the fact that different positions along a gene are more likely to be sequenced than others. In Figure 3 we show a plot of the relative proportion of the mRNA-Seq sequences that came from the beginning of the transcript (5 end) versus the end of the transcript (3 end), as calculated by RSeQC (Wang and others, 2012). It is clear from this plot, that plate 734 has greater relative coverage of the beginning of the gene compared to the other plates; Figure 3 shows short genes (0–1000 base pairs) but the effect can be seen in a range of gene lengths (Supplemental Figure S7 available at Biostatistics online).

Fig. 3.

5 to 3 bias differs by plate. Here we show the results of RSeQC (Wang and others, 2012) calculation of the average coverage of the mRNA-Seq data; shown here are the results of the calculation for 318 housekeeping genes that have only a single isoform and have total length in the range of 0–1000 bp. This calculation divides the gene into equally spaced bins and calculates the number of sequences falling in the bin, relative to the overall number sequences assigned to the gene region. The -axis shows the percentile of the gene body that the bin falls in (referenced from the beginning, or 5 end, of the gene). This plot shows a closeup of the results at the 5 start of the gene; the plot showing the rest of the gene as well as plots showing genes of longer lengths are shown in Supplemental Figure S7 available at Biostatistics online.

The 5/3 bias is a well-documented bias of mRNA-Seq data (Sigurgeirsson and others, 2014; Wu and others, 2011; Mortazavi and others, 2008) where the 3 end of a transcript is more likely to be captured and sequenced than the 5 end of a transcript. Various steps in the library preparation can cause such an effect (see discussion in Wu and others, 2011), so it is plausible that small variation in library preparation between the plates could cause the differences seen here. With respect to relative isoform usage, isoforms often differ in their starting and ending exons, and therefore different relative coverage of the beginning or end of a gene due to technical artifacts can mean that isoforms will get assigned different relative expression levels. Indeed many methods for estimating isoform expression have been proposed to model this bias (Roberts and others, 2011; Li and Jiang, 2012; Wu and others, 2011). Therefore, it is plausible that the 5/3 differences in the plates have created different relative expression of the isoforms, which the proportion clustering captures more accurately than the other methods.

3.3. Clustering of TCGA data

We also performed gene, isoform, and proportion clustering of nine other TCGA datasets. All of these datasets were corrected like AML via the batch correction program ComBat using the plate ID and the tissue source site ID, when relevant, as potential source of batch effects. Each was run through the clustering procedures of gene, isoform, and proportion described above for the uncorrected AML data, see Supplementary Text, Section 3 available at Biostatistics online.

In Supplementary Figure S8 available at Biostatistics online, we plot the Jaccard Similarity Score between different clusterings to give an overview of how similar the gene, isoform, and proportion clusterings were between the datasets for different . For many datasets, the similarity in clusters found between gene and isoform clustering, or isoform and proportion clustering, is not large, particularly when . The proportion clustering starts to be particularly different from isoform for several datasets with higher . Relative to the similarity seen between gene and isoform clustering, AML, OV, and HNSC, for example, show low levels of similarity between proportion and isoform clustering. Filtering the isoform differently, so that the same set of variable isoforms was used for isoform clustering as for proportion clustering, did not make much difference in the similarity of the two clustering methods for most of the datasets (Supplementary Figure S8c available at Biostatistics online).

In order to understand the performance of proportion clustering on biological data more closely, we focused more closely on a single dataset. We chose to again examine AML (only now with the batch correction based on plate), as an example of a dataset showing large differences between proportion and isoform clustering; AML notably continues to show differences even for low , where it is simpler to examine isoforms and describe their differences between the clusters.

In Figure 4 we visualize the difference in cluster assignments between the proportion clustering and the isoform clustering for ; the split seen in is echoed in the clusterings of higher numbers of clustering, representing a strong difference for each of these clusterings. The clusters in this figure are visualized in Figure 4 against a heatmap of individual isoform expression of those isoforms with strong differences between the two sets of clusterings (see Supplementary Text available at Biostatistics online for details).

Fig. 4.

Isoform expression for proportion and isoform clusterings. Here we show a heatmap of the isoform expression for isoforms found to be different either between the proportion clustering or the isoform clustering for . The samples are in the rows and the isoforms are in the columns. The color scale corresponds to the expression level of an isoform in a sample. To the left of the heatmap, a color scale gives the identification of the samples to the proportion and isoform clustering groups. Along the top of the heatmap are assignments of isoforms to different groups of isoforms, for referencing in the text.

We can see in this figure that proportion clustering is finding a different assignment of samples to clusterings, compared to isoform, and that those differences in cluster assignments correlate strongly with different sets of isoforms. The proportion clusters correspond strongly with the expression of two subsets of isoforms (that we label P1 and P2 groups in Figure 4), while the isoform clusters correspond strongly with the expression patterns found in a different class of isoforms (the I1 and I2 groups in Figure 4).

If we inspect these different class of isoforms, we see that for the genes whose isoforms constitute the P1 and P2 isoform groups (those whose expression patterns correspond highly with the proportion) there are a relatively high proportion of genes that contain an isoform in both P1 and P2 (Supplemental Table S1 available at Biostatistics online). The P1 and P2 groups of isoform have contrasting expression patterns, and the presence of both of such expression patters in a single gene creates the pattern in proportions that detected in the proportion clustering. The isoforms in class I1 and I2, whose expression patterns correspond highly with the isoform groups, also have contrasting expression patterns, but it was rare for them to be found together in a single gene. This suggests that the proportion clustering is detecting isoform switching patterns within a gene, and that such patterns may not as easily be detected by clustering directly on isoforms due to the presence of other expression patterns that dominate.

In examining genes that show this switching pattern, we find several genes with known relationship with AML or other cancers, including SON, RBBP6, SENP5, and CHD8. SON, in particular, is a known splicing factor involved in regulating of the machinery of splicing. Recently it has been suggested that different isoforms of SON result in different regulation of the mixed lineage leukemia gene (MLL) complex assembly that activates several leukemia-associated target genes (Kim and others, 2016; Yokoyama and others, 2005). While we cannot assume this is the cause of the phenomena we detected with only this limited knowledge, these examples at least provide some support to the idea that the clustering we find with proportion clustering is finding isoform switching behavior within genes that could give meaningful biological results. The example of the splicing factor SON also demonstrates to how widespread patterns in alternative splicing could occur, since SON itself regulates splicing.

4. DISCUSSION

We have presented a method for clustering on isoform relative proportions so as to find shared patterns in alternative splicing. We demonstrate on simulated data that clustering on the proportions can more accurately detect changes in isoform usage within a gene than just clustering on isoform expression levels, even in the absence of any conflicting signal from gene expression. We further apply the method to a mRNA-Seq dataset which we demonstrate has a clear batch effect. We see that clustering on relative proportions clusters the data by this batch effect, unlike the clustering from isoform or gene, which both imperfectly find the batch effect. Because the batch effect appears to create technical artifacts in the data that would influence isoform relative expression, this suggests that clustering on isoform relative proportions is more sensitive to correctly clustering the samples by differences in isoform usage.

We also apply proportion clustering on numerous TCGA datasets, and show that the proportion clustering gives different clustering of the samples than isoform or gene clustering. Looking at the specific example of AML, we see that the genes whose isoforms reflect the clustering found by proportion clustering do indeed appear to demonstrate different levels of isoform expression within genes, unlike those clusters found by isoform clustering which do not have this tendency.

Proportion clustering enables the user to emphasize certain types of feature patterns over others, and thus provides a complementary clustering technique to the standard clustering directly on isoforms or genes.

SUPPLEMENTARY MATERIAL

Supplementary material is available at http://biostatistics.oxfordjournals.org.

FUNDING

Helman Faculty Grant, National Institutes of Health grant U24 CA143799 and National Science Foundation grant DMS-1026441.