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Alternative splicing significantly contributes to proteomic diversity and mis-regulation of splicing can cause diseases in human. Although both genomic and chromatin features have been shown to associate with splicing, the mechanisms by which various chromatin marks influence splicing is not clear for the most part. Moreover, it is not known whether the influence of specific genomic features on splicing is potentially modulated by the chromatin context. Here we report a deep neural network (DNN) model for predicting exon inclusion based on comprehensive genomic and chromatin features. Our analysis in three cell lines shows that, while both genomic and chromatin features can predict splicing to varying degrees, genomic features are the primary drivers of splicing, and the predictive power of chromatin features can largely be explained by their correlation with genomic features; chromatin features do not yield substantial independent contribution to splicing predictability. However, our model identified specific interactions between chromatin and genomic features suggesting that the effect of genomic elements may be modulated by chromatin context.
Almost all genes in human have multiple isoforms. Thus, alternative splicing (AS) is a major contributor to proteomic diversity [1,2]. Further, alternative splicing is much more prevalent in human and mouse compared to invertebrates , andhas direct role in normal development and disease . Aberrant splicing is known to have major phenotypic consequence e.g. Hutchinson-Gilford Progeria Syndrome (HGPS), a rare and devastating disease manifesting early ageing symptoms, is caused by splicing aberrations in Lamin A gene . In cancer, a wide array of splicing aberrations due to somatic mutations have been previously noted [6,7].
Splicing is catalyzed by the spliceosome complex, containing five ribonucleo-proteins U1, U2, U4, U5, U6 and many associated auxiliary proteins . Splice site recognition and “exon definition” are critical steps in splicing regulation [9,10]. Specific genomic and chromatin context as well as availability of various proteins can result in alternative usage of splice sites resulting in alternative isoforms [9–12]. While “AG” at acceptor site and “GT” at donor site are hallmarks of exon definition during splicing, the choice of specific sites is influenced by auxiliary proteins (SR protein or hnRNPs) that bind to the splicing enhancer or silencer elements. The splicing enhancer and silencer are divided into four categories based on their locations and function: ESE (exonic splicing enhancer), ESS (exonic splicing silencer), ISE (intronic splicing enhancer), ISS (intronic splicing silencer). In addition, due to its coupling with transcription, splicing can also be influenced by chromatin state via multiple mechanisms [11,12]. For instance, Pol II elongation rate is known to influence the usage of specific splice site; slow elongation rate, influenced by nucleosome density, allows more time for splice machinery to recognize weak splicing sites, thus changing the relative proportion of alternative isoform . Certain chromatin marks are associated with specific chromatin remodeling proteins that can recruit splicing factors thereby regulating splicing. Interestingly, the same chromatin mark can have opposing effect on splicing depending on the mediating partner. For instance, H3K36me3 can recruit SRSF1 via Psip1 to enhance exon inclusion . However if H3K36me3 recruits PTB via MRG15, it represses inclusion .
Recent availability of RNA-seq data has spurred several computational investigations into the determinants of alternative splicing [15–19]. While several different types of alternative splicing events have been documented, due to ease and robustness of inference, most investigations have focused on alternative exon inclusion/exclusion events, specifically cassette exons, where an alternative internal exon is immediately flanked by two ubiquitously included exons. A previous work has suggested existence of a ‘splicing code’ composed of numerous genomics features including splice sites signals, conservation score, ESE, ESS, ISE, ISS, etc, that can accurately predict exon inclusion in a cell type relative to other cell types [17,18]. On the other hand, Shindo et al have shown correlation between several chromatin marks and splicing ; they found H3K36me3 and H3K79me1 around the exon-intron boundaries and within exons to be strongly correlated with splicing. Zhou et al have shown a correlation between H3K36me3 and splicing . Another report suggested that DNA methylation within exon body may have a positive effect on exon inclusion . Finally, a linear regression model to predict exon inclusion based on multiple chromatin features showed several chromatin features, especially H3K36me3 and H4K20me1 to be correlated with exon expression . However, this previous approach suffers from a technical limitation in that it does not distinguish exon expression and gene expression, and an alternative measure – percentage-spliced-in (PSI), better quantifies alternative exon inclusion. Moreover, the ability of chromatin marks to affect splicing can be overestimated without using genomics features as control since genomics features can, presumably causally, predict chromatin features very accurately . Overall, the relative contributions of genomic and chromatin contributions to alternative splicing, specifically, alternative exon inclusion event, is not clear. Here, based on deep neural network model, we carefully analyzed the relative contributions of genomic and chromatin features on exon inclusion levels, in multiple cell lines. To contrast our work with previous similar works, our focus is comparative assessment of genomic and chromatin features in terms of their effectiveness in predicting splicing, and not to develop a tool to predict splicing.
Our analyses showed that genomics features could predict exon inclusion much more accurately than chromatin features, and an integration of the two types of features does not improve the prediction accuracy. We specifically assessed the contributions made by either genomic or chromatin feature in addition to the other type of feature using multiple approaches, and found that, while genomic features make a significant additional contributions to predictability of exon inclusion, the converse is not true, suggesting that genomic features encode most of the information relevant to exon inclusion. Besides the assessment of predictability, we specifically model the position-specific contribution of each feature. Finally, even though chromatin features do not make a substantial contribution independent of the genomic features, our model detected specific interactions between genomic and chromatin features, suggesting that the effect of specific genomic features may be sensitive to the chromatin context.
Overall, we provide a first direct comparative assessment of genomic and chromatin features, and interaction thereof, in predicting cell type specific alternative splicing.
We obtained a list of 16,000 cassette exons based on prior annotations by MISO, which is based on integration of transcript data from a wide variety of cell types and conditions . Given the annotation, for a given RNA-seq sample, we estimated the inclusion rate for each annotated cassette exon using MISO package and classified them as either skipped or included based on specific thresholds (M&M). For each annotated exon, we obtained 1,366 genomic and cell type-specific chromatin features, including the feature-location combinations, from ENCODE database (M&M). Broadly, our features, both genomic and chromatin, were quantified in 7 distinct genomic loci relative to the cassette exon (M&M and Fig. 9). We formulated the exon inclusion prediction problem as a 2-class supervised classification problem and, using deep neural network model (M&M), performed several analyses: (i) estimating splicing predictive power of genomic and chromatin feature independently in three tissues (GM12878, h1-hESC, K562), (ii) cross-tissue predictability of a model trained in one of the cell lines, (iii) prioritization and interpretation of most relevant features in splicing, (iv) estimating relative contributions made by chromatin features in addition to those made by the genomic features alone, and (v) characterization of interactions between genomic and chromatin features.
Previous studies have reported correlations between various types of splicing events and proximal chromatin features [15, 16, 19, 20]. We directly assessed the cross-validation predictability of exon inclusion using chromatin features alone. Fig. 1A shows the 8-fold cross-validation classification accuracy in three different cell lines. The prediction accuracies in all cell types are significantly higher than the random expectation of 50%, albeit, modest. Notably, prediction accuracy is much higher in h1-ESC relative to the other two cell lines. This may be either because the chromatin state is indeed more closely associated with splicing in pluripotent cells or alternatively, because of better quality of chromatin modification data in h1-ESC cell line; these need to be explored in future.
Previous studies have shown that genomic features can accurately predict change in exon inclusion propensity in a cell line relative to other cell lines [17, 18]. We emphasize that our goal here is not necessarily to improve exon inclusion predictability, but rather to contrast the independent and synergistic contributions of chromatin and genomic features and also to assess location specificity of various features relative to splice sites. Nevertheless, we first establish a baseline for predictability of exon inclusion using genomic features in our datasets and using tissue-specific performance metric. Also, in contrast to previous genomic element-based relative exon inclusion prediction approach [17,18], here we only employ genomic features with a potential mechanistic link to splicing machinery and excluded features such as ‘exon translatability’ that was shown to be the single-most powerful predictor but is not linked to the splicing mechanisms per se. We used only the cis-elements discussed above to predict splicing. However, we note that by excluding translatability as a feature, our approach does not account for nonsense mediated decay of the mRNA caused by pre-mature stop codon [23,24].
Similar to chromatin features, we employed 8-fold cross validation to estimate prediction accuracy. As shown in Fig. 1B, genomic features can predict exon inclusion very accurately, consistent with previous studies [17,18], and importantly, much more accurately than chromatin features. This suggests that exon inclusion, even in a specific context, is largely determined by genomic sequences.
In our deep learning model, we assessed the effect of each chromatin mark in 3 regions (multiple sub-regions in each broad region) relative to the cassette exon; each mark-locus combination is a distinct feature in our model. Here we report the locus-specific effect size of various chromatin marks. Fig. 2A, S1, and S2, show, respectively for h1-hESC, GM12878, and K562, the most significant chromatin features (M&M) in all locations considered – the cassette exon, the 5′ flanking intron and in the 3′ flanking intron. Interestingly, by and large, almost all features in exonic regions have negative effect on exon skipping, i.e., their presence in specific exonic regions is associated with higher inclusion levels, discussed later. Also the trends are largely consistent across cell types, particularly across h1-hESC and K562.
We further ascertained the importance of features selected above as follows. We partitioned the entire set of exons into two sets based on the feature values (top and bottom half). We then randomly sampled (100 times) 1000 exons from each of the two groups and compared their inclusion levels using Wilcoxon test. We noted the fraction of tests (out of 100 tests) that yielded significant results consistent with the directionality of the feature’s effect according to the model above. To rank the features in terms of their overall relevance, which captures both significance and effect size, we multiplied each feature’s effect size (obtained from the model) with the fraction of Wilcoxon tests that were significant (significance). This procedure yields a view of every single feature’s independent contribution (without considering interactions). Fig. 2B, S3, S4 shows the relevance for all the three tissues (Fig. S3 and S4 are in the supplementary file). We ranked the features based on their relevance as estimated above. Our results suggest that H3K36me3 is one of the most relevant features consistent with previous reports [16,19]. The analysis also reveals H3K79me2, H4K20me1, H3K27me3, H3K9ac to be highly relevant to exon inclusion. Interestingly, we found that leukemia and stem cell lines have more and stronger feature signals for enhancing inclusion, however, blood cell lines have more features associated with repression of exon inclusion.
We have shown in section 2.3 that chromatin features are modestly predictive of exon inclusion. Even though specific mechanisms linking histone modifications to splicing have been reported [11, 12, 14], it is not clear to what extent the predictive power of chromatin features are independent of genomic features. To specifically investigate this, we assessed the extent to which chromatin features can explain the variance in exon inclusion that is unexplained by genomic features. We used two approaches to assess this: (i) we trained a model using chromatin (genomics respectively) features and then assessed the prediction accuracy using genomic (chromatin respectively) features with an additional feature representing the prediction score using the chromatin-based (genomic-based respectively) model; an improvement in prediction accuracy associated with the added feature represents additional contribution of that feature. (ii) we quantified the extent to which chromatin (genomics respectively) features could explain the residuals of a linear model based on genomic-based (chromatin-based respectively) model. A high explanatory power of the residual is consistent with an independent contribution.
Fig 3A and 3B show the results for the first analysis, which suggest that while adding chromatin-based model score to genomic features does not improve prediction accuracy, adding genomic-based model score to chromatin features substantially improves the prediction accuracy. Analogously, Fig. 4A and 4B show the result of the residual analysis, consistent with the first analysis, namely, chromatin features explain very small fraction of variance of the residual from the genomics-based model, as opposed to the converse. Overall, these analyses strongly suggest that that genomics features provide robust prediction of exon inclusion, largely independent of chromatin features and that the previous observed associations between chromatin features and splicing can largely be explained by the links between genomics and chromatin features, also noted previously .
Next, to assess the extent to which similar rules govern exon inclusion in different cell lines, for each pair of tissues we trained the model on one tissue and tested on the other. First, for chromatin-based modeling, as shown in Table 1, GM12878 model cannot predict exon inclusion in the other cell types and conversely, model trained on other cell types cannot predict exon inclusion in GM12878. However, cross-tissue predictability is much higher than random expectation between h1-hESC and K562. As shown in Table 2, genomics-based model exhibits a similar trend, however the absolute prediction is much greater for the genomics-based models. These results suggest that, even though a large portion of cis elements contribute to exon inclusion across cell types, exon inclusion also depends on specific cis elements that are recognized by cell type specific splicing factors (including splice enhancers and repressors). And the cross-cell type predictability for chromatin feature follow similar trend likely because chromatin features are largely encoded in cis elements .
Our results thus far suggest that previously observed links between chromatin features and splicing may be largely explained by their correlations with genomic features, which are more directly and likely mechanistically linked with splicing. Nevertheless, it is possible that the effect of some of the location-specific genomic features may be modulated by chromatin context. In other words, there may be interactions between specific genomic and chromatin features. However, these interactions cannot be directly quantified in our DNN model. Therefore, we applied L1 norm to the first layer of the DNN model to make the connections sparse, then explicitly assessed the interactions among the selected features based on a linear regression model, using the model selection package “stepwiselm” in Matlab . We investigated both chromatin-genomic and chromatin-chromatin interactions. The results are summarized in Fig. 5–7 for each cell line respectively. Our results suggest that chromatin context can potentially modulate the effect of genomic features on splicing. Moreover, both chromatin-genomic and chromatin-chromatin interactions are position specific, which is consistent with a mechanisms that relies on specific genomic and RNA conformation and binding of splicing factors. What’s more, many cis-elements within the skipped exons tend to interact with chromatin features. However, interactions between chromatin and genomic features in the context of splicing has not been studied before making it difficult to directly assess the observed interactions based on existing literature and more experimental work is needed to further investigate our findings.
We downloaded MISO skipped exon splicing events annotations . Based on the MISO skipped exon splicing events annotations and the RNA-seq data in three cell lines, we used MISO package  to estimate the sample-specific exon inclusion fractions for all annotated cassette exons. We excluded the genes which are not expressed in any given cell type based on expression data from Gene Expression Omnibus as an independently ascertained expression data. Figure 8 shows the distributions of exon inclusion levels in the three cell lines. Since the distributions are bimodal, suggesting that most exons tend to be either included or excluded in a given context. Moreover, these extreme cases are more likely to be robust. We therefore considered 40% of events from each end (total of 80% of data) of the distributions for three tissues for the investigation of determinants of exon inclusion. Exons whose inclusion levels are closer to 0 represent excluded exons, whereas the exons to the right of the spectrum are considered included exons. We thus formalize the problem as a two-class classification problem.
We obtained processed Histone modification (Chip-seq), CTCF (ChIP-seq), RNA-seq, DNA Methylation (Methyl RRBA), Dnase-seq data for each other for Blood tissue (GM12878), Embryonic Stem cell tissue (H1-hESC), Leukemia tissue (K562) respectively from ENCODE project (www.encode.org). The chromatin features include histone modifications (H2AFZ, H3K36me3, H3K27ac, h3K27me3, H3K4me1, H3K4me2, H3K4me3, H3K79me2, H3K9me3, H3K9ac, H4K20me1), DNA methylations, DNAse hypersensitivity (DHS), and CTCF binding. The genomics features include a total of 560 motifs (which include validated known splicing motifs [18,26] and new potential splicing motifs [27,28], splice sites scores, exon length, intron length and conservation scores for the 7 regions.
For each cassette exon, given the flanking exons and the introns, we selected seven regions for feature extraction as shown in Fig. 9. Regions 1, 4, 7 are exons whose length varied. Regions 2, 3, 5, 6 are 450 bps intron regions proximal to the 3 exons. A previous work used the regions 1–7 for genomics features . For chromatin features we only used regions 3, 4, and 5 because we found signals from region 1, 2, 6, 7 not to be effective by comparing the prediction accuracies before and after we include these regions (results not shown). For each region, we divided it into 9 windows and used as the chromatin feature value, the fraction of the windows overlapping a broad peak for each feature.
As mentioned earlier we treat the exon inclusion prediction problem as a two-class classification problem. We applied the deep neural network model, which has been widely used in computer vison and nature language processing field. DNNs are probabilistic generative network models with multiple hidden layers . All nodes at a layer have complete directed connections to the nodes in the next layer. Each layer includes multiple neural units, which contain a transfer function. Transfer function can be customized based on the application.
The activation ac of each node depends on the input features f, connection weights w, the bias b and transfer function T:
We used logistic function as the transfer function:
The DNN architecture is shown in Fig. 10. There is a one-to-one mapping between features and the nodes in the input layer. The number of nodes for the output layer is two since this is a two-class classification problem; one of the nodes outputs the probability pe for an exon to be excluded, and the other node outputs the probability of being included pi. The predicted class c is based on maximum of the two probabilities:
We utilized previously developed convenient deep neural network toolbox .
A Restricted Boltzmann Machine (RBM) is an undirected stochastic neural network model , composed of a visible layer and a hidden layer. In neural network architecture this model could efficiently provide better initialization compared to random initialization based on maximum likelihood approach . We treat each pair of adjacent layers as RBMs to perform supervised learning pre-training greedily. Hinton et al.  have shown that RBM pre-training substantially improves the training with a backward fine-tuning phase.
Overfitting is a potential concern in supervised learning, especially for complex model with numerous parameters. Dropout technique introduced by Hinton et al.  could be used to significantly reduce overfitting. Essentially, it tries to randomly drop some nodes along with all their connections in every round, followed by a fine-tuning phase. In this way, dropout can randomly sample diverse network structures and combine them in prediction step.
We counted the occurrences of motifs within the regions of interest as motif features. For both chromatin states and sequence conservation, we determined the average signal within our regions of interest as feature values. We performed greedy feature selection based on the feature contributions derived from the first model. We used all the features to build the model and then employed Milne’s method  to calculate all the features’ contributions by making use of the connection weights from the model as follows:
Where 1h is the number of units in the first hidden layer, 2h indicates the number of units in the second hidden layer, rc(i) is the raw contribution of the ith feature, nc(i) is the normalized contribution of the ith feature, w is the connection weight, fea is the number of input features.
Then we ranked all features based on their contributions, and greedily added features to the feature set till convergence of prediction accuracy.
In this study, we formalized the exon inclusion prediction problem as a 2-class supervised learning problem. Our primary goals here were to assess the relative contributions of chromatin and genomic features and specifically test the possibility that the previous reported associations between chromatin features and exon skipping might be largely due to their correlations with genomic features . Our additional goal was to test whether the effect of specific cis elements may be modulated by the chromatin context. Based on a comprehensive set of genomic and chromatin features in 7 and 3 regions respectively, and using deep learning model, we first verified that the genomics features are robust predictors of exon inclusion consistent with previous studies , . At the same time we found that, not only chromatin features can only modestly predict exon inclusion, they do not lend substantial information beyond what is captured by genomic features. However, our analysis reveals specific significant interactions between chromatin and genomic features suggesting that the effect of latter on exon inclusion may depend on the context provided by the former.
We employed DNN with pre-training and dropout methods, which have been widely used and proved effective in computer vision and natural language processing domains, relative to other machine learning approaches , . Essentially, DNN, as a model with greater number of hidden layers, can represent higher level of abstract features, which should contribute to modeling of the association between splicing inclusion and features, in a situation such as splicing where the precise mechanisms are not known and there are likely to be several interactions among features and stepwise decision being made,. However, complex model are more vulnerable to overfitting. Pre-training and dropout algorithms are meant to reduce overfitting. Finally, it is not easy to quantify interactions within this complicated network model. While we rely on DNN to rank features by significance, to assess interaction we employed a simpler model. In our study we used standard linear regression to model interactions because of their high interpretability.
Previous works relying entirely on genomic features have proposed a highly accurate context-specific splicing code . We rely on the dictionary of cis elements compiled in these previous works. However, there are some notable differences between our work and these previous works. Our focus is not to optimize the prediction accuracy, but rather to explore relative contributions of genomic and chromatin features. We have therefore explicitly excluded operational, but non-mechanistic, features such as ‘translatability’. Moreover, while we estimate prediction accuracy within a cell line independent of other cell lines, these previous works in fact predict increase/decrease in exon inclusion in a cell line relative to other cell lines, and as such they rely on data from all cell lines simultaneously and boost the accuracy through information shared across cell lines. Therefore the absolute prediction accuracy reported here are not directly comparable to the previous reports.
Even though, by and large, the chromatin features are not highly predictive of exon inclusion, we found specific features to be highly significant. H3k36me3 is one of the most significant features and is consistent with previous report. For each feature revealed by our model as significant, we also directly verified the association between that specific feature and splicing inclusion, and examined the joint effect-size and significance as the feature relevance (Fig 2B, S3, S4). We found that most of the detected relevant features are consistent with previous correlation study [16,19,20]. In both GM12878 and h1-hESC, H3K36me3 is one of the most significant chromatin marks contributing to splicing, consistent with previous reports [16,19,20]. While previous computational association studies suggest that H3K36me3 at exon-intron boundary and exon has a positive effect on exon inclusion, in contrast, our analyses suggest that this mark can have both positive and negative effect in GM12878, depending on its precise location, which is consistent with various potential mechanisms based on experimental studies . H4k20me1 is significant in all three tissues, consistent with . Moreover, H3K79me2, H3K9ac, H3K27me3, H3K9me3 also showed varying degrees of significance. In addition, in stem cell most chromatin features within skipped exon have strong positive correlation with exon inclusion, which may imply that they can contribute to define exon or recruit SR proteins during splicing.
Our finding that genomic signals carry almost all of the information predictive of exon inclusion, and that predictive power of chromatin features is not independent of genomic elements should not come as a surprise. Despite previously shown associations between chromatin marks and splicing, it is likely that the chromatin signals themselves may be ultimately governed by the underlying genomic elements and the proteins binding to them. This could be true even in the rare cases where a direct mechanistic link has been inferred from a specific chromatin feature and splicing [12,14]. Recent reports showing highly accurate predictability of chromatin features by genomic sequence strongly suggests that not just for splicing, but, unsurprisingly, numerous other cellular processes, such as transcription initiation, poly-Adenylation, etc., even when there strong association and mechanistic links with chromatin features, the ultimate drivers are likely to be the underlying genomic elements.
We performed cross tissue test using genomics and chromatin model respectively. We found that the rules learnt from one cell type are reasonably applicable to a different cell type. The differences can be attributed to cell type specific splicing factors. We expect that chromatin features, after being largely determined by genomic features, should have conserved rules governing exon inclusion across cell types. We found high cross-cell type predictability for stem cell and leukemia. This specific observation is consistent with known broad similarities in active cellular processes between stem cell and cancers [34–36].
Even though our analyses suggest that chromatin features are not likely to be the primary drivers of alternative splicing, they might still be able to affect splicing at the molecular level, as suggested by our interaction study (Fig. 5, ,6,6, ,7).7). First, chromatin features may serve to provide the recognition specificity for specific factors, similar to genomics features. At the molecular level, in most of the reported potential mechanism, chromatin features interact with many other molecules to affect splicing, such as chromatin remodeling protein and SR protein. We speculate that the spatial position of those chromatin marks may influence their protein recruitment or conformational changes after recruiting other factors. Moreover, recruitment of different protein factors can have different effect on splicing. For example, H3K36me3 can both facilitate or suppress splicing by recruiting MRG15 or Psip1 respectively [12,14]. In GM12878 cell line, we observed interaction between H3K27me3 and H3K4me1, which have been suggested to together mark poised enhancer [37,38]; In h1-hESC cell line we identified interaction between CTCF and H3K9me3, which have been shown to co-localize . In K562, we observed interactions between H3K79me2 and H3K36me3, which are both markers of gene bodies [40,41], that is likely to be important for exon definition process in splicing regulation. While we do observe interactions between chromatin and genomic features, very little is known in the literature to reasonably corroborate our findings. Moreover, the mapping between specific cis element and corresponding splicing factor is not known for the most part, making it difficult to interpret the results pertaining to cis element interactions. In GM12878 sample, we detected a potential interaction between H3K9ac and motif “GGCTGC”. Even though the protein interacting with the cis elements is not known, we speculate that a splicing repressor like hnRNP binds to the motif to repress inclusion when H3K9ac is present. In h1-hESC, we identified an interaction between SRSF9 protein and H3K79me2. However, the specific locations of the two features are genomically distal from each other (Fig. 6). Such distal interactions are entirely possible due to looping at both DNA and RNA level [42–44]. In K562 sample, the interactions of H3K36me3 with different motifs have different effects on exon inclusion suggesting diverse potential mechanisms discussed earlier.
We present a first comprehensive model-based comparison of relative contributions of genomic and chromatin features in determining exon inclusion. We have shown that both genomics and chromatin features are associated with exon inclusion, however genomics features are more robust and better predictors, and incorporating chromatin features does not improve splicing prediction substantially. Genomics elements are thus likely to be the ultimate drivers of splicing event, which can affect chromatin marks. However, in some cases, the effect of genomic elements on splicing may be modulated by the chromatin context.
This work is funded by NIH R01GM100335 to S.H. and Ellison Medical Foundation New Scholar Award and NIH R21 AG043801 to K.C. In addition we would like to thank Avinash Das, Justin Malin, Seung-Gu Park, Shrutii Sarda, and Dr. Steve Mount for constructive comments on the manuscript.
Categories and Subject Descriptors
G.3 [Probability and Statistics]: correlation and regression. analysis, experimental design, nonparametric statistics.
Kun Wang, Center for Bioinformatics and Computational Biology, University of Maryland.
Kan Cao, Cell Biology Molecular Genetics, University of Maryland.
Sridhar Hannenhalli, Center for Bioinformatics and Computational Biology, University of Maryland.