NSMAP: A method for spliced isoforms identification and quantification from RNASeq
 Zheng Xia^{1, 3},
 Jianguo Wen^{2, 3},
 ChungChe Chang^{2, 3} and
 Xiaobo Zhou^{1, 3}Email author
DOI: 10.1186/1471210512162
© Xia et al; licensee BioMed Central Ltd. 2011
Received: 12 October 2010
Accepted: 16 May 2011
Published: 16 May 2011
Abstract
Background
The development of techniques for sequencing the messenger RNA (RNASeq) enables it to study the biological mechanisms such as alternative splicing and gene expression regulation more deeply and accurately. Most existing methods employ RNASeq to quantify the expression levels of already annotated isoforms from the reference genome. However, the current reference genome is very incomplete due to the complexity of the transcriptome which hiders the comprehensive investigation of transcriptome using RNASeq. Novel study on isoform inference and estimation purely from RNASeq without annotation information is desirable.
Results
A N onnegativity and S parsity constrained M aximum A P osteriori (NSMAP) model has been proposed to estimate the expression levels of isoforms from RNASeq data without the annotation information. In contrast to previous methods, NSMAP performs identification of the structures of expressed isoforms and estimation of the expression levels of those expressed isoforms simultaneously, which enables better identification of isoforms. In the simulations parameterized by two real RNASeq data sets, more than 77% expressed isoforms are correctly identified and quantified. Then, we apply NSMAP on two RNASeq data sets of myelodysplastic syndromes (MDS) samples and one normal sample in order to identify differentially expressed known and novel isoforms in MDS disease.
Conclusions
NSMAP provides a good strategy to identify and quantify novel isoforms without the knowledge of annotated reference genome which can further realize the potential of RNASeq technique in transcriptome analysis. NSMAP package is freely available at https://sites.google.com/site/nsmapforrnaseq.
Background
More than 90% of human genes [1, 2] are estimated to be alternatively spliced which leads a single gene to produce multiple proteins with distinct functions and is implicated in many diseases including cancer [3]. In recent years, there is an increasing interest in the use of alternative splicing in developing diagnostic tools and in identifying new therapeutic targets [4]. Microarrays have been widely used to analyze alternative isoforms by combining exon arrays and exon junction arrays to quantify isoform level expression indexes [5, 6]. However, array based techniques are encountering several fundamental problems such as cross hybridization and weak signals in junction probes which are difficult to overcome [7]. Ultra highthroughput sequencing of RNA has been developed as an approach for transcriptome analysis in several different species and has offered an attractive approach to measure transcription in a comprehensive manner. RNASeq allows the direct detection of alternative splicing using the reads mapped at splice junctions including the novel splicing without the annotation information. Genomewide measurements of transcriptomes are increasingly done by RNASeq which provides a far more precise measurement of expression levels of isoforms than other methods [8].
The rapidlydeveloping RNASeq techniques require substantial algorithmic advances. Several tools and strategies have been proposed to deal with the complex bioinformatics analysis of RNASeq [9–12]. Pepke et al.[13] provided a comprehensive and uptodata review of multilayered analyses of RNASeq data. Mortazavi et al.[10] proposed to quantify the gene level expression of a transcript as Reads Per Kilobase per Million mapped reads (RPKM). Further, Jiang and Wong [14] presented a statistical model to describe how the isoform expression levels were calculated from the number of reads mapped to the annotated exons of a gene. Meanwhile, Bohnert et al.[15] also proposed rQuant to determine the abundances for each annotated isoforms by minimizing the deviation of the observation from the expected positionwide read coverage. All these methods assumed that the number and structures of isoforms of each gene are known from the reference genome. However, as Jiang and Wong [14] pointed out, the isoform level annotation is very incomplete due to the complexity of the transcriptome and the limitations of previous experimental approaches. To address this issue, Trapnell et al. proposed Cufflinks [16] to identify transcripts as well as to estimate the expression levels of identified transcripts from mapped reads without annotation information. In essence, Cufflinks constructs a covering relation on the read alignments from TopHat [12], and find a minimum path cover on the directed acyclic graph for the relation based on Dilworth's Theorem [17] to construct a parsimonious set of transcripts. After that, the expression levels of those constructed transcripts are estimated using established known isoform expression estimation methods [9, 14]. Therefore, the construction of transcripts in Cufflinks is independent of the expression level estimation. However, the construction of expressed transcripts and expression level estimation are highly associated. We argue that the determination of parsimonious set of expressed transcripts and expression level estimation should be implemented jointly. Though Scripture [18] can also detect the novel isoforms, the issue of parsimonious expressed isoforms is not addressed. We also notice that Feng et al. proposed IsoInfer [19] to identify isoforms using the detected junctions. The candidate isoforms were constructed by combining the putative exons followed by selecting a minimum best subset from all the enumerated subsets of the candidate isoforms which can explain the observation best. However, enumerating all possible subsets of the candidate isoform set with a given size is often infeasible. IsoInfer decomposes the large putative exon set into subsets to address this issue which introduces more parameters.
Here, we put forward NSMAP to infer the structures of isoforms as well as to estimate the expression levels simultaneously. First, the exons are constructed based on the detected splicing junctions from RNASeq data using TopHat. All the possible isoforms are enumerated by combination of those detected exons. Then NSMAP is applied to identify the true expressed isoforms from the large candidate isoform set as well as to estimate the expression levels with a sparsity control term to restrict the number of expressed isoforms. The assumption behind this sparsity term is that only as few isoforms as possible should be selected to best explain the observed number of reads falling on each exon of a gene. Finally, a model selection step is conducted to select the solution which compromises the fitting of the observation and the number of expressed isoforms best. In summary, our algorithm allows for discovering the structures of the expressed isoforms of a given gene and for estimating the concentration of each spliced isoform simultaneously without the annotated isoform information, which makes the identification of new, previously unknown, alternatively spliced isoforms possible. This study will help RNASeq, a next generation sequencing technology, advance to its full potential in comprehensive transcriptome analysis.
Results
Data set
We test NSMAP on two simulations with simulated expression levels derived from two publicly available mouse RNASeq as described in [10]. We also apply NSMAP on three real inhouse RNASeq data sets of myelodysplastic syndromes (MDS) transcriptome analysis to identify isoforms including novel ones featured in MDS disease. MDS are a diverse collection of hematological conditions united by ineffective production of myeloid blood cells and risk of transformation to acute myelogenous leukemia whose frequency and incidence are increasing in the US population [20]. In our application, cryopreserved marrow cells and paraffin embedded marrow clot sections and marrow core biopsies from 2 MDS patients as well as 1 agematched control sample are being studied by Dr. Jeff Chang's lab at the Methodist Hospital. These MDS patients have been thoroughly evaluated for clinical/morphologic/immunophenotypic data and characterized clinically by transfusion dependency and pathologically by significant dysplasia, increased blasts, and immunophenotypic aberrancy. The control sample are obtained from patients without cytopenias (> 60 years old). We specifically selected these controls to be agematched for the MDSs population to control for the possibility of agingrelated changes in the expression profile mRNA of hematopoietic cells. Then we apply the RNASeq protocol to sequence our samples. We sequenced the two MDS clinical samples and one normal sample using Illumina Genome Analyzer II. There are around 40 million singleend reads with read length 76 bp for each sample.
Algorithm Summary
NSMAP comprise four consecutive steps, starting with junction detection and reads mapping using TopHat [12] and followed by the candidate isoforms construction, expressed isoform identification and expression level estimation along whole regularization path and model selection to select the best solution from the whole solution path. Short reads alignment is the first step in understanding nextgeneration sequencing data and many free alignment software packages are available [21, 22]. Here we use TopHat to perform the alignment task which can detect the junctions and map a massive amount of reads to the whole genome flexibly and efficiently. The reference genome sequences are downloaded from UCSC genome database [23]. After read alignment, the next step is to generate the candidate isoforms according to the alignment and splice junctions obtained from TopHat.
Candidate isoforms construction
Isoform Expression level estimation
Given the candidate isoforms constructed from last step, we need to select the expressed isoforms from this candidate set as well as to estimate the express level of selected isoforms. We adapted the expression level estimation framework of Jiang and Wong [14] by incorporating a sparsity regularization term. For a gene g, suppose it has m exons with lengths [L = l_{1},...,l_{ m }] and n isoforms with expression Φ = [ϕ_{1},...,ϕ_{ n }]. Assuming each exon can be either included in an isoform or not, we have a set of observations , where is an index set of events which we are interested in. Each observation X_{ s }∈ X is a random variable representing the number of reads falling into a certain region of interest in gene g. For example, reads falling into certain exon or exonexon junction.
The natural statistical model of count data is the Poisson distribution. Each X_{ s }∈ X follows Poisson distribution with a parameter λ which is the expected count or the mean parameter of the Poisson distribution. For instance, the λ for the number of reads falling into exon j is , where N is the total number of mapped reads and c_{ ij }is 1 if isoform i contained exon j and 0 otherwise. For a exonexon junction event, the λ is , where l is the length of the junction region, j and k are indexes of the two exons involved in the junction being investigated.
where and .
Then the expression levels of all the candidate isoforms can be obtained by optimizing Equation (1) with a given t. When t → +∞, the solution equals zero without expressed isoforms. With the decreasing of t, some elements of will be nonzero to become expressed isoform. So we have to select an optimal t. Before doing this, we will calculate the solution path which consists of solutions corresponding to different values of t. BLasso [27] is adapted to approximate this solution path efficiently (see Methods).
Model selection from solution path
After getting the solution path which consists of solutions corresponding to different values of t, we have to select the best solution (model) from this solution path which makes a good balance between the number of expressed isoforms and the fitting function in equation (2). The solution path will first be grouped into subsets with increasing model size according to the number of expressed isoforms of each solution (the number of positive components of ). Here the model size means the number of expressed isoforms. Then the solution with minimal in each group is selected as the best solution for each model size. Starting from model size 1, we compare the of current model size with the next model size which have one more expressed isoforms. If is significantly improved by the larger model size, the model with larger model size will be updated to the current model and compared with the remaining models with larger model size than the updated model. Otherwise the solution corresponding to the current model size is selected as the final solution. In this way, the solution with smaller number of expressed isoforms will be selected preferably. See the Methods for more detail.
Simulation on the whole genome with different L_{ p }norm in equation (2)
In the absence of RNASeq data from samples for which we have ground truth isoform quantities, we conduct simulations to validate our method and evaluate its performance in terms of isoform identification and expression levels estimation with p = 1 and p = 0.5.
We first derive expression level of each isoform from the mouse brain and liver RNASeq data sets described in [10] using the Poisson model of [14] with the mouse UCSC Genes as the annotated reference genome database. Those derived expression levels are employed as the ground truth to perform the following simulations. Which exon or splice region the read will fall on is determined by uniformly sampling proportional to the simulated ground truth RPKM and the same mapped reads number of each gene in the real data. After uniformly sampling and counting reads number, we can identify isoform structures and their concentrations from the simulated RNASeq reads data and evaluate the performance of NSMAP with the simulated ground truth.
The percentage of expressed isoforms with RPKM ≥1 included in the candidate isoform set.
Tissue  Total number of expressed isoforms  Percentage of expressed isoforms included in candidate isoforms 

Brain  14,154  96.5% 
Liver  10,583  96.1% 
We further compute the fraction of isoforms for which the estimates are significantly consistent with the simulated ground truth (percent error = ). We refer to this statistic as the positive fraction[9]. Given the positive isoforms which are within the 5% deviation from the ground truths, overall specificities of the two simulations are also calculated by setting the truly expressed isoforms with RPKM no less than 1 as positive isoforms and the false reported isoforms by NSMAP and truly expressed isoforms with RPKM < 1 as negative isoforms.
Positive fraction and specificity of the estimation results of NSMAP on the two simulated data sets.
Isoform expressions in RPKM  

Tissue  RPKM  [1,10)  [10,10 ^{ 2 } )  [10 ^{ 2 } ,10 ^{ 3 } )  [10 ^{ 3 } ,10 ^{ 4 } )  Total 
Brain p = 1/2  Number of isoforms  7,730  5,630  767  27  14,151 
Positive fraction  67.9%  88.2%  95.4%  100.0%  77.5%  
Specificity  83.6%  
p = 1  Positive fraction  67.8%  87.9%  95.3%  100.0%  77.3% 
Specificity  83.3%  
Liver p = 1/2  Number of isoforms  6,470  3,390  661  62  10,583 
Positive fraction  70.0%  89.8%  97.1%  100.0%  78.2%  
Specificity  90.3%  
p = 1  Positive fraction  69.5%  89.7%  97.1%  100.0%  77.9% 
Specificity  89.8% 
Comparing the performances of NSMAP with p = 0.5 and p = 1, we notice that L_{ p }norm with p = 0.5 provides better results than p = 1 in the simulations. To explain this observation, we conduct the following experiment and give a mathematical interpretation of the two L_{ p }norms.
Demonstrations of features of L_{ p }norm with p= 0.5 and p= 1
Then, the lower row of Figure 2 shows the mathematical properties of the two norms. L_{1/2} norm regularization has more similar sparsity property with L_{0} norm than L_{1} norm because the points with high probabilities in the Laplacelike distribution with L_{1/2} norm are more focusing around the axes than those in the Laplace distribution. This means L_{1/2} norm regularization imposed stronger sparsity than L_{1} norm. The simulation depicts the stronger sparsity constraint by setting p = 1/2 is superior to Laplace priori distribution with p = 1 in our application. In the following experiments, we select the L_{ p }norm with p = 1/2.
Comparison with IsoInfer on two RNASeq data sets of MDS samples
Here we compare NSMAP with IsoInfer which have similar ideas in isoform construction from putative exons and minimum expressed isoform set selection. However, IsoInfer selects a subset as expressed isoforms from candidate isoform set by enumerating all the possible subsets of the candidate isoform set. In NSMAP, the selection of expressed isoforms is embedded into the isoform expression level estimation framework by incorporating a sparsity control term.
A transcript can be constructed from all the exonintron boundaries as well as the transcription start site (TSS) and polyA site (PAS) of an isoform. The exonintron boundaries can be inferred from RNASeq using alternative splicing detection tool, such as TopHat and SpliceMap [29]. The TSS and PAS represent the start and end expressed segments of a transcript, respectively. Theoretically, any expressed segments can be the TSS or PAS which will introduce many false short isoforms to make isoform inference difficult. We prefer to retrieve the TSSPAS from the UCSC known isoform table as the starts and ends of predicted transcripts and to identify isoforms within the regions of known genes whose functions and pathways are intensively studied. IsoInfer (version 0.9.1) and NSMAP will use those TSSPAS and the detected junctions using TopHat to infer the expressed isoforms from RNASeq. Because it is infeasible to validate all the predicted isoforms, we evaluate the two methods by comparing their predictions with UCSC known isoform data set. The performance of the method is measured by sensitivity and precision. Here we use hg19 known human isoforms data set downloaded from UCSC which contains 77,614 transcripts. A known isoform is identified if it is in the prediction result of a method. Sensitivity is defined as the number of identified isoforms divided by the number of all known isoforms from UCSC data base. Precision is defined as the number of identified known isoforms divided by the number of predicted isoforms by the method.
The performance of IsoInfer and NSMAP on two RNASeq data of MDS samples by comparing the results with the UCSC known isoforms.
Samples  MDS 1  MDS 2  

#Mapped reads  18,729,721  22,436,651  
Methods  IsoInfer  NSMAP  IsoInfer  NSMAP 
#Predicted isoforms  10,695  9,772  12,466  10,185 
#Identified known isoforms  1,128  1,078  1,632  1,469 
#Common known isoforms predicted by both methods  857  1103  
Sensitivity  1.5%  1.5%  2.1%  2.0% 
Precision  10.5%  11.0%  13.1%  14.4% 
However, IsoInfer selects a subset as expressed isoforms from candidate isoform set by evaluating all the possible subsets of the candidate isoforms. In NSMAP, the selection of expressed isoforms is embedded into the isoform expression level estimation framework by incorporating a sparsity control term. In this way, the selection of expressed isoforms is automatic and more efficient than testing all the possible sub sets of the candidate isoforms.
We also notice that more known isoforms are predicted in MDS sample 2 than MDS sample 1, because there are more reads are mapped in MDS sample 2. This observation tells us that deeper sequencing will improve the performances of IsoInfer and NSMAP.
Here, the sensitivities of the two methods are very low. The reason is that we compare the predicted isoforms with the large UCSC known isoform set. Some of the UCSC known isoforms may not express in the sample. So the effective sensitivities will be larger than those numbers. This comparison against UCSC known isoform data set does not mean all the predicted isoforms without annotation are false. Especially those predicted novel isoforms with high RPKM are promising to be true novel isoforms. For example, if we select the predicted isoforms with expression level larger than 100 RPKM, in MDS sample 1 and 2, 37 out of 67 and 53 out of 105 predicted isoforms by NSMAP will be annotated in the UCSC known isoforms table. And the lowly expressed isoforms have higher probability to be false positive or artifacts due to the insufficient reads for capturing the true structure of an isoform. So we need to set an expression level threshold to refine the predicted isoforms. This issue is addressed in the following section.
Example of identified isoforms using NSMAP and Expression Level Threshold Selection
In the predicted isoforms of gene TCF20 in Figure 4, the two annotated isoforms have expression levels 3.0 and 3.5, respectively, which are above the selected threshold T = 1.216. While the expression level of the unannotated isoform is 0.1 which is obviously under this threshold. In this way, we perform a further refinement of the prediction result. In the following real data analysis, we only consider NSMAP predicted isoforms which are larger than the optimal expression level threshold in each sample.
Clinical MDS sequencing data analysis
The goal is to use our NSMAP to identify known and novel isoforms which may be related with MDS. We apply NSMAP on the alignment results of the three data sets from TopHat to identify the expressed isoforms and their expression levels. The predicted isoforms are compared with the UCSC annotated reference genes to distinguish the known and novel isoforms.
The top 4 enriched canonical pathways from Ingenuity Pathways Analysis of the differentially expressed known isoforms and novel isoforms.
Differentially Expressed known isoforms  Differentially expressed novel isoforms 

Granzyme A signalling  Mitochondrial dysfunction 
Oxidative phosphorylation  Oxidative phosphorylation 
Mitochondrial dysfunction  Methane metabolism 
cAMPmediated signaling  Protein ubiquitination pathway 
Discussion
Through simulations that closely modelled real data, we confirm our method's effectiveness for experiments in both mouse brain and liver RNASeq data. We also compare NSMAP with IsoInfer to show that NSMAP has comparable performance in identifying known isoforms from RNASeq reads. Finally, we apply NSMAP on our MDS RNASeq data analysis and find some differentially expressed known isoforms and novel isoform candidates which involve in some MDS related pathways.
Recently, Lacroix et al.[32] showed that unique solution cannot be guaranteed theoretically in isoform identification from short sequence reads. For example, in our case, all possible transcript isoforms are enumerated according to the detected junction reads. Among these isoforms, one truly expressed isoform may be linear combinations of the other isoforms in terms of exon arrangements. Then the solution of this case is not unique. The assumption of NSMAP to address this issue is that the solution which employs as few expressed isoforms as possible to explain the most observation is preferred. Though this assumption is identical to the assumption made by Cufflinks, the implementation of this assumption in NSMAP is totally different from Cufflinks. Cufflinks constructed a parsimonious set of transcripts followed by the expression level estimations of those constructed transcripts using established expression level estimation model. However, NSMAP enumerates all the possible isoforms formed by the combinations of identified putative exons from TopHat and incorporates a prior distribution into the expression level estimation model to control the number of expressed isoforms. That means the identification of expressed isoforms and the expression level estimations of those identified isoforms are done jointly in NSMAP.
Pairedend sequencing can dramatically improve the accuracy of isoform level expression estimation which is becoming ubiquitous. Recently, Salzman et al.[33] proposed "insert length model" to extend Jiang and Wong's singleend sequencing work [14] to pairedend sequencing analysis by modeling the insert length distribution. So we can use this idea to handle pairedend sequencing data in our current framework.
Pairedend sequencing can dramatically improve the accuracy of isoform level expression estimation which is becoming ubiquitous. In paired end sequencing, only the fragments in a specified range will be selected. Several papers have used this information by modeling the fragment length distribution to improve isoform deconvolution problem [16, 34]. Salzman et al. [33] proposed "insert length model" to extend Jiang and Wong's singleend sequencing work [14] to pairedend sequencing analysis by modeling the fragment length distribution. So we can use this idea to handle pairedend sequencing data in our current framework. In pairedend sequencing, Salzman et al. defines a_{ si }= q(f_{ si })N for an event s where the mate reads are mapped into two specified positions on genome. Here f_{ si }is the length of corresponding fragment on the ith transcript and q(f) is the probability of observing a fragment with length f. In practice, q(f) can be approximated by the empirical probability mass function computed from all the mapped pairedend reads. In order to reduce the number of events, the minimal sufficient statistics is used to group the events into minimal categories for computational purpose. In this way, we can incorporate the pairedend information into our model by redefining a_{ si }to address pairedend sequencing data.
Currently, NSMAP uses the TSS and PAS retrieved from UCSC known isoforms. We will extend it to identify TSS and PAS from RNAseq by the following scheme. If the start point of a putative exon is not a junction point, this putative exon can be regarded as TSS. And if the end point of a putative exon is not a junction point, this putative exon can be regarded as PAS. Here junction point means this point is the start or end of a splicing junction.
As our primary motivation is to design a method to identify the isoform structure without annotated reference isoform genome, the usefulness of NSMAP is largely dependent on the expression levels of true isoforms and splicing junction detection. We believe that the accuracy of this approach will increase significantly as the sequencing technology evolves such as pairedend sequencing technique and generates longer sequences with less noise and higher throughput.
Conclusions
In this paper, we propose a statistical model NSMAP for RNASeq data analysis which can be used to identify and quantify isoforms simultaneously without isoform annotations from reference genome.
Methods
Implementation
We must select a particular value of t at which the estimation is optimal. Before that, the solutions corresponding to different values of t should be calculated. Efron et al.[35] proposed an efficient algorithm LARS to determine the exact piecewise linear coefficient paths for the lasso. Unlike lasso, the path of our solution is not piecewise linear. To address this nonpiecewise solution issue, we modify the BLasso [27] to get the solutions corresponding to different t. The basic ideal of BLasso is to correct the forward stagewise boosting algorithm by allowing backward steps whenever a stop in forward stagewise boosting fitting deviates from that of the lasso.
Optimization: Generalized BLasso for NSMAP:

Step 1(Initialization) Given a small stepsize constant ε > 0 and a small tolerance parameter ξ ≥ 0, take an initial forward step on L(Φ^{(0)}) in equation (2). We define Φ^{(0)}≜m 1_{ j }.
We use I_{ A }to represent the active index set. Set the initial active set and k = 0.

Step 2 (Steepest descent step). Find the steepest coordinate descent direction on J(Φ;t) in equation (2):
Take the step if it leads to a decrease of moderate size ξ in the objective function J(Φ;t):
If
then
Update whose elements are the indexes of the positive entries of .

Step 3 (iteration). Increase k by one and repeat Step 2 until t^{(}^{ k }^{)} ≤ 0.
Computationally, BLasso takes roughly O(1/ε) steps to produce the whole path [27]. The actual computation complexity depends on the actual objective function and minimization method used in each step when calculating . In the following experiments, ∈ is set as 0.1 and ξ = 1e  10.
Model selection and expression level estimation
We first select the best solution within each group H_{ h }. Because the model size within each group is the same, the solution whose is minimal in group H_{ h }is selected as the best solution in this group.
Those best solutions in each group are put into a set ordered by the increasing number of expressed isoforms where M is the largest number of expressed isoforms in the solution path and has one expressed isoform which is the best solution among the solutions with one expressed isoform. The final best solution is selected from by likelihood ratio test (LRT) [36].
Declarations
Acknowledgements
We thank Dr. Hui Jiang from Dr. Wing Wong's Lab at Stanford for providing the code and discussion of his paper. This work is funded by NIH 1R01LM01018501 (Zhou) and The Institute for Biomedical Imaging Sciences IBIS foundation (Zhou).
Authors’ Affiliations
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