Persistent homology methods have found applications in the analysis of multiple types of biological data, particularly imaging data or data with a spatial and/or temporal component. However, few studies have assessed the use of persistent homology for the analysis of gene expression data. Here we apply persistent homology methods to investigate the global properties of gene expression in post-mortem brain tissue  of individuals with autism spectrum disorders (ASD) and matched controls. We observe a significant difference in the geometry of inter-sample relationships between autism and healthy controls as measured by the sum of the death times of zero-dimensional components and the Euler characteristic. This observation is replicated across two distinct datasets, and we interpret it as evidence for an increased heterogeneity of gene expression in autism. We also assessed the topology of gene-level point clouds and did not observe significant differences between ASD and control transcriptomes, suggesting that the overall transcriptome organization is similar in ASD and healthy cerebral cortex. Overall, our study provides a novel framework for persistent homology analyses of gene expression data for genetically complex disorders. ASDs maTo investigate whether genetic variants converge onto a common set of molecular pathways at the level of gene expression, we and others have carried out gene expression studies of post-mortem brain tissue from ASD individuals –7. Theseet al. [Genome-wide expression data are characterized by complex interdependencies and nonlinearities that are often missed by standard statistical methods. Topology has emerged as a powerful tool to analyse and interpret high-dimensional data, due to its ability to study properties that are robust against choice of coordinates, choice of metric and more generally continuous deformations, motivating its use in the analysis of transcriptome data . Persistet al.  aims to et al. , includiet al. . Howeveret al.  and asseet al. . The latN genes measured in M samples was conceptualized as either of the following.(a)M points in N-dimensional space, where each point designates a sample, and the distance between points represents inter-sample dissimilarity. Studying the topological properties of such a sample-level point cloud allows the identification of nonlinear relationships between samples. We compared the topological properties of the ASD and control sample point clouds in the two distinct gene expression datasets and found significant differences between ASD and controls, suggestive of increased heterogeneity among the ASD samples. This observation was replicated across both datasets.A cloud of (b)N points in M-dimensional space, where each point designates a gene, and the distance between points represents the dissimilarity between genes. Persistent homology analysis of gene-level point clouds is conceptually a version of co-expression networks. Unlike standard co-expression networks, however, here we assessed the dissimilarity matrix using topological descriptors rather than hierarchical clustering. The use of topological descriptors such as the Euler characteristic  allowed us to globally assess the geometry of a gene expression dataset and to compare the topological properties between ASD and control transcriptomes. Interestingly, we did not observe a significant difference in the topological descriptors of ASD and control transcriptomes in either of the two datasets investigated, suggesting that the global transcriptome organization is not altered in ASD brain.A cloud of Here we assess for the first time the application of persistent homology to gene expression data from individuals with a genetically complex disorder of unknown cause . We apply this approach to two gene expression datasets from brain samples of individuals with idiopathic autism and matched controls ,7. The o2.2.1.Classical homology investigates the topological properties of objects in a manner independent of scale, while persistent homology is a more recent topological data analysis method that examines changes in topological features in an object which evolves with respect to a scale parameter . The2.1.1.In classical algebraic topology, objects are represented through simplicial complexes, which in turn are a collection of building blocks called simplices: a 0-simplex represents a point, a 1-simplex represents a segment, a 2-simplex represents a triangle, a 3-simplex represents a tetrahedron, etc. A simplicial complex consists of a finite set of simplices ‘glued’ together .n (vertex set) and a distance metric d on Rn, the Vietoris–Rips simplicial complex VR is defined as the simplicial complex where {v0, … ,kv} spans a k-simplex if d ≤ ε for all 0 ≤ i, j, ≤ k.Vietoris–Rips simplicial complexes, which are used in the present study, are defined as follows. Given a set of points V ⊂ R2.1.2.ε varies, which allows the assessment of topological invariants of an object at different scales. By choosing a sequence of epsilons that increase 0 < ε0 < ε1 < ε2 < … < nε < … εmax (where εmax is the maximum distance between two points), we form an increasing sequence of simplicial complexes: VR ⊂ VR ⊂ VR ⊂ … ⊂ VR ⊂ … ⊂ VR. Considering the kth singular homology of these simplicial complexes, we form a sequence of maps between kH homology groups: kH , Z) → kH , Z) → kH, Z) → … → kH, Z) → … kH, Z).In persistent homology, Z denotes integer numbers and here it represents the coefficients of the homology groups.kH) are composed of topological cycles; for example, connected components for k = 0 and k-dimensional holes for k > 0. The fact that homology groups have Z coefficients means that the operations applied to topological cycles are addition, subtraction and multiplication with integer numbers.Roughly speaking, homology groups , Z), goes to zero in kH , Z), its image is non-zero in all the intermediary homologies (i.e. the cycle exists from the moment it is born to the moment it dies) and the cycle does not belong to the image of the map kH , Z) → kH, Z). A simple example for a cloud of four points is shown in figure 2a.The aim of persistent homology is to identify features of an object that are ‘persistent’ with respect to scale. We say that a topological cycle (i.e. a connected component or a hole of the space) is ‘born’ at k = 0), all the connected components are born in the beginning at ε = 0. They die after several steps when two connected components merge forming a big connected component. In the end of the process, we are left with only one connected component that will survive to infinity. We can view Vietoris–Rips simplicial complexes indexed by ε as a collection of complexes {VR}k with inclusion x : VR → VR between two consecutive steps.In the case of connected components }I is defined to be the set of Abelian groups {kH , Z/2)}i with inclusions kH, Z/2) → kH, Z/2) → … → kH , Z/2) → … → kH , Z/2).The Z/2 denotes the set of remainders to the division of integer numbers by 2, i.e. {0,1}. In the context of kH groups, the fact that their coefficients are limited to {0,1} means that the only operation applied to topological cycles is addition. The choice of Z/2 coefficients for kH groups is frequently used [tly used  as it gib), in which for each topological cycle c, the ‘birth’ εb(c) is plotted on the x-axis and the ‘death’ εd(c) value is plotted on the y-axis. Topological cycles of different dimensions are plotted in distinct colours. Persistent features are topological cycles located away from the diagonal.A way to represent the topological cycles that appear in persistent homology is through persistence diagrams b, in whik-dimensional cycles (SLk) and the Euler characteristic. For a k-dimensional cycle c in a persistence diagram, we define the length of cycle c to be l(c) = εd(c) − εb(c) [l(c) of all k-dimensional cycles appearing in the persistence diagram by SLk, the sum of their birth times by SBTk and the sum of their death times by SDTk. Since all connected components (i.e. cycles of dimension 0) are born at bε = 0, SL0 equals SDT0.Some useful summaries of a persistence diagram are the sum of the lengths of  − εb(c) . We deno0 can be interpreted as a measure of the heterogeneity of the initial vertex set V, which in our case is the point cloud associated with a dataset. Since a more heterogeneous group of points would have more connected components that survive longer, a priori it is expected that higher heterogeneity of a point cloud would result in larger SDT0 numbers. An exemplification of this concept is shown in figure 2c.Note that the topological invariant SDTEuler characteristic [n is defined as: χ = SL0 − SL1 + … +(−1)nSLn.The teristic  of a perχ = SL0 − SL1 + SL2. Thus, the Euler characteristic of a persistent diagram is an invariant that depends on zero cycles, but also on higher dimensional cycles.Because cycles of dimension more than 2 are very rare in our persistent homology diagrams, the Euler characteristic was computed using dimension 0, 1 and 2 cycles, i.e. 2.2.Gene expression data were obtained from two published studies: a microarray study which quantified the expression of 9934 genes, and an RNA-seq study which quantified the expression of 22 399 genes in cerebral cortex samples from ASD cases and controls ,7. SinceThe microarray data have been quantile normalized and log2 transformed, and the RNA-seq data have been RPKM-normalized and log2 transformed.2.3.r (r: Pearson correlation coefficient) as a dissimilarity measure. For sample point clouds, we constructed Vietoris–Rips complexes, based on the vertex set given by the points in each dataset. Persistent homology was computed using the pHom function in the pHom R package [https://github.com/cran/phom/blob/master/man/pHom.Rd), and persistence diagrams were plotted using the plotPersistenceDiagram. For gene-point clouds, which included thousands of points, the Vietoris–Rips complexes are extremely large, and therefore we used an alternative implemented in the pHom function, the lazy-witness construction, with landmark_set_size = 20. The pHom function [Z/2-coefficients.For each gene expression dataset, we calculated (a) an inter-sample distance matrix and (b) an inter-gene distance matrix for ASD and control data separately, using 1 −  package   R package (https://cran.r-project.org/web/packages/pracma/).Mahalanobis distance (MD) was calculated as previously described :MD was calculated for ASD samples and compared with values obtained by 1000 random permutations of group labels. False discovery rate (FDR) was defined as the ratio of random permutation values that were more extreme than the observed SSMD value. When attempting to carry out the same analysis using the larger RNA-seq dataset on a powerful computer , the MD analysis of the RNA-seq data took over 13 h per computation, and thus a permutation-based analysis was not possible.For the MD analysis of KEGG gene sets, SSMD was calculated as above for ASD samples, using the genes within each set, rather than the entire transcriptome. For each gene set, the observed SSMD value was compared with 100 randomly sampled gene sets of the same size.https://github.com/Voineagulab/Persistent_Homology_ASD_Brain/.All data analysis codes are available as a Github repository: 3.We investigated the topological properties of gene expression data in the cerebral cortex in autism using two published datasets, generated with two distinct methods: microarays  and RNA-There is generally good agreement between gene expression measurements by microarrays and RNA-seq , with RNa,b). This observation held true regardless of whether the data were from ASD or controls, or whether they were generated by microarrays or RNA-seq . Higher-dimension topological cycles were also identified, with the maximum dimension being 2 similarity among ASD and control cerebral cortex samples, we constructed persistent homologies based on Vietoris–Rips simplicial complexes  for ASD and control data separately. The sample-level point clouds consisted of 29 ASD and 29 control samples for the microarray data and of 82 ASD and 82 control samples for the RNA-seq data. We observed that the most persistent features of these point clouds were connected components  and the Euler characteristic , which also takes into account one-dimensional and two-dimensional topological cycles. We found that STD0_ASD was higher than SDT0_Control, and χ_ASD was higher than χ_Control, an observation replicated across the microarray and RNA-seq datasets.Since connected components were persistent features, we next compared their properties between ASD and control data. To summarize all the connected components within a dataset, we computed two topological invariants: the sum of the death times of connected components . We should mention that in this particular case, where most one-dimensional and two-dimensional components are very transient, the Euler characteristic value is very close to the SDT0.To test the statistical significance of this observation, we carried out random permutations of sample labels . We recovariants c,f. We s0 was higher for ASD data compared to controls [What is the interpretation of a higher sum of the death time number observed for ASD data compared to control gene expression data? We propose that the higher sum of the death time number reflects higher heterogeneity within the ASD group . Remarkably, a similar observation has been made on FDG-PET brain imaging data from 26 ASD and 11 control individuals, where SDTDSDT or χD was significantly different from 100 randomly selected sets of genes of the same size. This analysis identified one gene set as significant: the MAPK signalling pathway (FDR less than 0.01). The result was replicated in the RNA-seq dataset (FDR less than 0.01).We also assessed whether the increased heterogeneity of gene expression data in ASD samples was contributed by specific subsets of genes or whether it was a property of the entire transcriptome. To this end, we used functional gene sets curated in the KEGG database (Kyoto Encyclopedia of Genes and Genomes ). Of theWe next investigated the topological properties of expression (dis)similarities between genes, within the ASD and control groups, using the same microarray and RNA-seq datasets. Here we assessed the topological invariants of point clouds consisting of 9934 genes for the microarray dataset and 22 399 genes for the RNA-seq data. Similarly to the sample-level analysis, the ASD and control data were assessed separately. Owing to the large number of points in the gene-level point clouds, we used an approximation of Vietoris–Rips complexes  and assessed statistical significance using 1000 random permutations of sample labels.The gene-level point clouds showed somewhat more complex topological features than the sample-level point clouds: in addition to persistent zero-dimensional connected components, we also observed a few persistent one-, two- and three-dimensional components . However, we did not observe any significant difference in the sum of the death times or Euler characteristic between ASD and controls, suggesting that globally, there are no significant differences in transcriptome organization between ASD and controls . This result is consistent with our earlier observations based on co-expression network analyses .To compare our results with previously reported methods of assessing the dispersion of gene expression data in ASD brain, we employed an MD-based approach . MD has We also applied the MD-based approach to functional gene sets from the KEGG database. Using the microarray data, we identified 3 gene sets showing significantly higher SSMD for ASD samples than 100 randomly sampled sets of genes of the same size: ‘MAPK signalling pathway’, ‘pathways in cancer’ and ‘cell cycle’ (FDR less than 0.01). The result for the first two gene sets, but not for ‘cell cycle’, was replicated in the RNA-seq dataset.Overall, we found that the differences between ASD and control gene expression data detected by persistent homology analysis were confirmed by the MD-based analysis, but persistent homology handled better the large datasets.4.Here we applied persistent homology methods to investigate the global properties of gene expression data from autistic individuals and matched controls in two distinct datasets (a microarray and an RNA-seq dataset). Unlike previous persistent homology studies of gene expression data , our pur0 and the Euler characteristic were significantly higher for the ASD group, in both datasets studied. This observation demonstrates that gene expression data from ASD individuals are more heterogeneous than gene expression from controls, based on inter-sample relationships. Quantifying heterogeneity is an important question for autism genetics. In addition to its clinical heterogeneity, ASD is also heterogeneous at the level of DNA sequence variation, with most ASD patients carrying a unique combination of DNA sequence changes [By assessing topological invariants of the inter-sample distance matrices, we found that both the SDT changes . Our res changes .The MAPK signalling pathway has been previously implicated in ASD . PatientFurthermore, our study provides a framework based on persistent homology that allows the quantification of heterogeneity of high-dimensional data that can be further applied for comparisons of multiple types of genomic data . Such comparisons could address an outstanding question: which molecular layers contribute to the clinical heterogeneity of ASD and will be the focus of our future work.0 or the Euler characteristic of the gene-level point clouds, we did not observe any significant difference between ASD and control groups, showing that the ASD and control networks have similar topological properties. This result is consistent with our initial observations based on co-expression networks, where we observed significant overlap in the modules detected in the ASD and control networks [Arabidopsis after exposure to multiple types of stressors [We also assessed the gene pairwise distance matrices using persistent homology, which can be thought of as a topology-based co-expression network approach. Since we are computing topological invariants, we used 1-Pearson correlation coefficient as the distance matrix, rather than the topological overlap measure which is implemented in weighted gene co-expression network analyses ,25. Co-enetworks . A recentressors .Persistent homology analyses of gene expression data are still in their infancy, and to our knowledge, our study is the first to apply persistent homology for brain co-expression networks. Further methodological developments are required in order to harness the full power of topological analyses for co-expression networks. In particular, the development of methods for assigning genes to higher dimensional components would facilitate extracting co-expression modules from topology-based networks.


We present Telescope, a computational software tool that provides accurate estimation of transposable element expression (retrotranscriptome) resolved to specific genomic locations. Telescope directly addresses uncertainty in fragment assignment by reassigning ambiguously mapped fragments to the most probable source transcript as determined within a Bayesian statistical model. We demonstrate the utility of our approach through single locus analysis of HERV expression in 13 ENCODE cell types. When examined at this resolution, we find that the magnitude and breadth of the retrotranscriptome can be vastly different among cell types. Furthermore, our approach is robust to differences in sequencing technology and demonstrates that the retrotranscriptome has potential to be used for cell type identification. We compared our tool with other approaches for quantifying transposable element (TE) expression, and found that Telescope has the greatest resolution, as it estimates expression at specific TE insertions rather than at the TE subfamily level. Telescope performs highly accurate quantification of the retrotranscriptomic landscape in RNA-seq experiments, revealing a differential complexity in the transposable element biology of complex systems not previously observed. Telescope is available at  Almost half of the human genome is composed of transposable elements (TEs), but their contribution to the transcriptome, their cell-type specific expression patterns, and their role in disease remains poorly understood. Recent studies have found many elements to be actively expressed and involved in key cellular processes. For example, human endogenous retroviruses (HERVs) are reported to be involved in human embryonic stem cell differentiation. Discovering which exact HERVs are differentially expressed in RNA-seq data would be a major advance in understanding such processes. However, because HERVs have a high level of sequence similarity it is hard to identify which exact HERV is differentially expressed. To solve this problem, we developed a computer program which addressed uncertainty in fragment assignment by reassigning ambiguously mapped fragments to the most probable source transcript as determined within a Bayesian statistical model. We call this program, “Telescope”. We then used Telescope to identify HERV expression in 13 well-studied cell types from the ENCODE consortium and found that different cell types could be characterized by enrichment for different HERV families, and for locus specific expression. We also showed that Telescope performed better than other methods currently used to determine TE expression. The use of this computational tool to examine new and existing RNA-seq data sets may lead to new understanding of the roles of TEs in health and disease. PLOS Computational Biology Methods paper.This is a Transposable elements (TEs) represent the largest class of biochemically functional DNA elements in mammalian genomes,2 compriThe ability to observe and quantify TE expression, especially the specific genomic locations of active elements, is crucial for understanding the molecular basis underlying a wide range of conditions and diseases. TraditiA growing field of study is now interested in using high-throughput sequencing to characterize the retrotranscriptome,9,39–41.Several existing software packages have implemented these approaches specifically for TE quantification. RepEnrich,43 maps Here, we introduce Telescope, a tool which provides accurate estimation of TE expression resolved to specific genomic locations. Our approach directly addresses uncertainty in fragment assignment by reassigning ambiguously mapped fragments to the most probable source transcript as determined within a Bayesian statistical model. We implement our approach using a descriptive statistical model of the RNA-seq process and use an iterative algorithm to optimize model parameters. We use Telescope to investigate the expression of HERVs in cell types from the ENCODE consortium.Resolution of transposable element  expression from RNA-seq data sets has been complicated by the many similarities of these repetitive elements. Telescope is a computational pipeline program that solves the problem of ambiguously aligned fragments by assigning each sequenced fragment to its most likely transcript of origin. We assume that the number of fragments generated by a transcript is proportional to the amount of transcript present in the sample; thus, the most likely source template for a randomly selected fragment is a function of its alignment uncertainty and the relative transcript abundances. Telescope describes this relationship using a Bayesian mixture model where the estimated parameters include the relative transcript abundances and the latent variables define the possible source templates for each fragment.The first step in this approach is to independently align each fragment to the reference genome; the alignment method should search for multiple valid alignments for each fragment and report all alignments that meet or exceed a minimum score threshold . Next, aa posteriori estimates of the transcript abundance dependent on the expected values from the E-step , the expected value of the source template for each fragment is calculated under current estimates of transcript abundance . The maxe E-step . These se E-step . Telescoe E-step . The finThe core statistical model implemented in Telescope is based on the read reassignment model described by Francis et al. and is sTo demonstrate that our algorithm can truly resolve repetitive element expression to precise genomic locations, we generated sequencing fragments from a single genomic locus in silico and used Telescope to resolve alignment ambiguity and quantify expression. The locus selected was HML2_1q22 (HERV-K102), an HML-2 provirus that is highly similar to several other HML-2 loci and shouTo investigate HERV expression in a robust way across a diverse platform of cell types we relied on publicly available RNA-seq data. The ENCODE data project is an invaluable source of genomic data from disparate sources and provides the opportunity to mine the transposable element expression in a setting of maximum genomic information. We profiled 13 human cell types, including common lines designated by the ENCODE consortium, as well as primary cell types, and applied our approach to determine HERV expression across the spectrum of human cell types, including normal or transformed, and contrasting cell lines with primary cells .Over 2.7 billion sequenced fragments aligned to human reference hg38 with between 23.6% and 46.1% of the fragments in each sample aligning ambiguously to multiple genomic locations. Telescope intersected the aligned fragments with a set of 14,968 manually curated HERV loci belonging to 60 families see  and idenWe developed genome-wide maps of HERV expression for 8 of the analyzed cell types that had replicates , and useWe found 1365 HERV loci that were expressed in at least one of the cell types (CPM > 0.5). Not all HERVs were expressed in all cell types, some were widely expressed in all cells, whereas others were only expressed in one or more cell type . There iTo ascertain global, subfamily and locus level specific HERV expression, we assessed the number of HERVs expressed in each cell type. All cell types expressed HERVs; the number of expressed loci ranged from 216 (in MCF-7), to 533 (H1-hESC) . The numPrevious work has suggested that estimates of HERV expression are highly sensitive to sequencing technology used, and differences due to sequencing technology can obscure biological differences due to cell type. Since aWe further explored differences among cell types using differential expression (DE) analysis. Pairwise contrasts between cell types were performed to determine the number of significant DE loci  > 1.0) . As founFinally, we asked whether other existing approaches for TE quantification would be sufficient to identify cell type specific signal in the data or whether these approaches would be sensitive to other variables. We analyzed the ENCODE datasets using default parameters for five other approaches, including best counts, unique counts, TEtranscripts, RepEnrich, and SalmonTE. Hierarchical clustering of the resulting expression profiles reveal that cell types clusters are only recovered using unique counts and Telescope , though In order to examine the sensitivity and biases of computational approaches for quantifying TE expression, we designed simulation experiments with known expression values. Earlier studies have suggested that the HERV-K(HML-2) subfamily (hereafter referred to as HML-2) is expressed in human tissue and may be relevant to human health,10,50,51For all simulations, we plotted the final counts estimated by each approach compared to the expected read count . We calcPerformance of the other five approaches differed primarily in the type and magnitude of misclassification errors. False positives occur when reads are incorrectly assigned to annotated loci that are not expressed, resulting in incorrect detection of unexpressed HERV loci. Best counts had a high false positive rate; on average, 12.1% of fragments were incorrectly assigned to unexpressed loci resulting in false detection of unexpressed loci in all simulations “Other”, . SimilarOf all methods considered here, Telescope had the highest rate of precision and recall from all other counting methods tested . In contTransposable elements represent a major biochemically active group of transcripts that are increasingly recognized as important regulators in complex biological systems and disease. However, difficulties in identifying and quantifying these elements has led to TEs being largely ignored in the literature. Here we present Telescope, a novel software package that can be used to mine new or existing RNA-seq datasets to accurately quantify the expression of TEs. The key advantage of our approach is the capability to localize TE expression to an exact chromosomal location.Based on our analysis of 13 ENCODE cell types, we have identified 1365 individual HERV loci that are expressed in one or more cell types and generated genomic maps that showing cell type specific HERV expression profiles. The ability to quantify expression at specific loci demonstrates that regulation of HERV expression occurs at the locus level (in addition to subfamily-level regulation), as different expression patterns are observed for loci within the same subfamily. For example, our results confirm previous studies identifying HERVH upregulation in embryonic stem cells ,39,52 anAn earlier study investigating HERV expression using the same datasets found strong differences in estimated HERV expression profiles depending on the sequencing technology used (paired or single end). Using TOur simulations show that Telescope is highly sensitive and has low type I and II error rates. Unique counts, a heuristic that is commonly chosen for its unambiguous assignments, was shown to discard much of the data and underestimate true TE expression. Best counts, which is commonly used for convenience, also performed poorly and spuriously identified transcripts that were not expressed. Several software packages, including RepEnrich, TEtranscripts, and SalmonTE, also aim to quantify TE expression, but use a family-level approach that quantifies TE subfamilies instead of individual loci. Our simulations used modified inputs for these approaches that allowed us to compare them to Telescope. Based on our simulation results, we find that our approach achieves high sensitivity while minimizing spurious detections, while all other approaches tend to identify TEs that are not expressed. We conclude that Telescope offers superior accuracy for TE quantification and is the only available software package that quantifies TE expression at single-locus resolution.Telescope will have widespread utility in other settings. Studies on TE expression have become prominent in studies of embryonic stem cell development9], neur, neur9],F =  be the set of N observed sequencing fragments. We assume these fragments originate from K annotated transcripts in the transcriptome T = . In practice, annotations fail to identify all possible transcripts that generate fragments, thus we include an additional category, t0, for fragments that cannot be assigned to annotated transcripts. Let G =  represent the true generating transcripts for F, where Gi∈T and Gi = tj if fi originates from tj. Since the process of generating F from T cannot be directly observed, the true generating transcripts G are considered to be “missing” data. The objective of our model is to estimate the proportions of T by learning the generating transcripts of F.Telescope implements a generative model of RNA-seq relating the probability of observing a sequenced fragment to the proportions of fragments originating from each transcript. Formally, let qi =  be the set of mapping qualities for fragment fi, where qij = Pr(fi|Gi = tj) represents the conditional probability of observing fi assuming it was generated from tj; we calculate this by scaling the raw alignment score by the maximum alignment score observed for the data. We write the likelihood of observing uniquely aligned fragment fu as a function of the conditional probabilities qu and the relative expression of each transcript for all possible generating transcripts Guπ =  represents the fraction of observed fragments originating from each transcript. Note that qju = 0 for all transcripts that are not aligned by fu. For non-unique fragments, we introduce an additional parameter in the above likelihood to reweight each ambiguous alignment among the set of possible alignments. The probability of observing ambiguous fragment fa is given byθ =  is a reassignment parameter representing the fraction of non-unique reads generated by each transcript.The alignment stage identifies one or more possible alignments for each fragment, along with corresponding alignment scores. Telescope uses the alignment score generated by the aligner and reported in the AS tag. This isπ and θ. The K mixture weights in the model are given by π, the proportion of all fragments originating from each transcript. To account for uncertainty in the initial fragment assignments, let xi =  be a set of partial assignment (or membership) weights for fragment fi, where xij = 0 if fi does not align to tj. We assume that xi is distributed according to a multinomial distribution with success probability π. Intuitively, xij represents our confidence that fi was generated by transcript tj. In order to simplify our notation, we introduce an indicator variable y =  where yi = 1 if fi is ambiguously aligned and yi = 0 otherwise. The complete data likelihood isUsing these probabilities of observing ambiguous and unique fragments, we formulate a mixture model describing the likelihood of the data given parameters π and θ are initialized by assigning equal weight to all transcripts. In the expectation step, we compute the expected values of xi under current estimates of the model parameters. The expectation is given by the posterior probability of xi:π and θaj and bj are prior information for transcript tj. Intuitively, these priors are equivalent to adding unique or ambiguous fragments to tj. As currently implemented, the user may provide a prior value for either parameter that is distributed equally among all transcripts. We have found that providing an informative prior for the bj (--theta_prior) is recommended given the repeat content of the human genome, since large values for this parameter prevents convergence to boundary values. Convergence of EM algorithms to local maxima has been shown by Wu[ϵ<0.001.Telescope iteratively optimizes the likelihood function using an expectation-maximization algorithm. First, own by Wu, and is A Telescope analysis requires an annotation that defines the transcriptional unit of each TE to be quantified. For HERV proviruses, the prototypical transcriptional unit contains an internal protein-coding region flanked by LTR regulatory regions. Existing annotations, such as those identified by RepeatMasker  were identified using the RepBase database. RepeatMhttps://github.com/rvalieris/parallel-fastq-dump). Adapter trimming, quality trimming, and filtering were performed using Flexbar[--very-sensitive-local) with up to 100 alignments reported for each fragment pair (-k 100). The minimum alignment score threshold was chosen so that fragments with approximately 95% or greater sequence identity would be reported . Sequence alignment map (SAM/BAM) files from different runs corresponding to the same sample were concatenated to obtain sample-level BAM files. An annotation of HERV locations in hg38 (--max_iter 200) and an informative prior on theta (--theta_prior 200000). The “final counts” column in the Telescope report are used as HERV expression data in subsequent analysis.We identified 30 ENCODE datasets with available whole-cell bulk RNA-seq data from tier 1 and 2 common cell types . Sequencg Flexbar  were calculated by dividing the raw count by the library size and multiplying by 1 million. A CPM cutoff of 0.5 was used to identify expressed loci; since the smallest sample considered has more than 20 million fragments, expressed loci are represented by at least 10 observations. Raw counts output by Telescope were used for differential expression analysis. Size factors for normalization were calculated by dividing the library sizes by their geometric mean. Normalization, dispersion estimation, and generalized linear model fitting was performed using DESeq2; the modRead counts for clustering were transformed using a variance stabilizing transformation in DESeq2. HierarcFor the simulation study, we simulated 25 independent RNA-seq datasets with 2100 paired-end fragments each. For each dataset, we randomly selected 13 loci to be expressed, including 10 HML-2 proviruses and three “non-TE” loci. HML-2 proviruses were selected from 92 HML-2 loci present in our annotation; non-TE loci were selected from a set of 968 unannotated genomic regions that share sequence similarity with the HML-2 subfamily . Non-TE -k 100 --very-sensitive-local --score-min L,0,1.6) and filtering reads with multiple alignments. The same bowtie2 parameters were used for best counts without specifying -k .Each simulation dataset was analyzed using 7 TE quantification approaches: 1) unique counts, 2) best counts, 3) RepEnrich, 4) TEtranscripts, 5) RSEM, 6) SalmonTE, and 7) Telescope. To ensure a fair comparison among approaches, the same annotation  was usedThe five software packages include final read counts as part of the output. Read counts for the unique counts and best counts approaches were obtained using htseq-count. After mhttps://github.com/mlbendall/telescope. We recommend installing Telescope and its dependencies using the bioconda package manager[Telescope is implemented in Python, is available as an open-source program under the MIT license, and has been developed and tested on Linux and MacOS. The software package and test data can be found at e manager.https://github.com/mlbendall/TelescopeEncode. Scripts for reproducing the simulations are available from https://github.com/LIniguez/Telescope_simulations. A tutorial for running the single-locus analysis is available from https://github.com/mlbendall/telescope_demo.A complete snakemake pipelineS1 Fig-k 100); bottom track shows the alignments after being reassigned using Telescope. Fragments shown in gold represent unique mapping locations, dark blue fragments represent a best alignment out of several possible alignments, and light blue fragments represent alignments with suboptimal alignment scores. Alignments shown in white (bottom track only) are included to indicate alignments that were present in the initial alignment but were reassigned to HML2_1q22 by Telescope.Visualization of simulated fragment alignments to three selected HML-2 loci. Simulated fragments were generated from HML2_1q22. Proviruses HML2_5q33.3 and HML2_11q22.1 were chosen as examples because they are closely related to HML2_1q22 and have high numbers of initially ambiguous mappings. The top track shows alignments found using bowtie2 while allowing for multimapping ((PDF)Click here for additional data file.S2 FigOuter track is a plot of RefSeq gene locations, with genes containing zinc-finger domains in green.(EPS)Click here for additional data file.S3 FigOuter track is a plot of RefSeq gene locations, with genes containing zinc-finger domains in green, human leukocyte antigen (HLA) genes in blue, and histone genes in purple.(EPS)Click here for additional data file.S4 FigExpression values were estimated using each approach using author provided annotations and default arguments. Resulting counts were normalized by library size, transformed, and clustered using pvclust. Support(EPS)Click here for additional data file.S1 TableInformation about each sample analyzed, including ENCODE experiment ID, GEO sample accession, and SRA run accessions. The first column contains the display name of each sample used in (XLSX)Click here for additional data file.S1 FileAnnotation contains 14,968 HERV loci in GTF format. The “locus” attribute is used to identify features belonging to the same locus. “Exon” features are regions matching to transposable element models, while “gene” features span the full locus, including insertions.(GTF)Click here for additional data file.S2 FileAnnotation contains a set of 968 unannotated genomic regions that share sequence similarity with the HML-2 subfamily.(BED)Click here for additional data file.S3 FileThe HERV annotation created for this study was compared to previously described HML-2 proviruses. Tables 1 and 2 from Subramanian et al. were lif(PDF)Click here for additional data file.


Background: Chromosome 1p/19q codeletion is increasingly being recognized as the crucial genetic marker for glioma patients and have been included in WHO classification of glioma in 2016. Fluorescent in situ hybridization, a widely used method in detecting 1p/19q status, has some methodological limitations which might influence the clinical management for doctors. Here, we attempted to explore an RNA sequencing computational method to detect 1p/19q status.Methods: We included 692 samples with 1p/19q status information from TCGA cohort as training set and 222 samples with 1p/19q status information from REMBRANDT cohort as validation set. We reviewed and compared five tools: TSPairs, GSVA, PAM, Caret, smoother, with respect to their accuracy, sensitivity and specificity.Results: In TCGA cohort, the GSVA method showed the highest accuracy (98.4%) in predicting 1p/19q status  and smoother method showed the second-highest accuracy . While in REMBRANDT cohort, smoother method exhibited the highest accuracy (98.6%)  in 1p/19q status prediction.Conclusions: Our independent assessment of five tools revealed that smoother method was selected as the most stable and accurate method in predicting 1p/19q status. This method could be regarded as a potential alternative method for clinical practice in future. Glioma is the most common and deadliest malignant primary brain tumor in adults . OligodeNowadays, 1p/19q codeletion is increasingly recognized as a crucial genetic aberration in glioma patients and was first time included in the WHO classification of brain tumor in 2016 . This paFluorescent in situ hybridization (FISH), targeting 1p36/1p21 and 19q13/19p13 regions via fluorophore-labelled DNA probes , was useNowadays, next generation RNA sequencing (RNA-seq) technologies greatly promote the exploration of the complex and dynamic nature of cancer  and coulHowever, the comprehensive study that integrated RNA-seq data analysis methods to predict 1p/19q status has not been conducted yet. Therefore, in this study, we reviewed and assessed five methods which were designed to detect gene expression variations with RNA-seq data, and attempted to find out a precise, objective and cost-effective method to replace FISH for identifying 1p/19q status in clinical practice in the future.In order to assess the feasibility of predicting 1p/19q status with RNA expression data, we used whole genome expression profiling (20501 genes) from TCGA dataset to explore the relationship between 1p/19q status and gene expression profiles. As shown in Based on this finding, we selected five methods which have been used to process RNA sequencing data to identify 1p/19q status.tspcalc function, HDAC1(Histone deacetylase 1) and DRG2  gene pair which had the highest TSP score (0.962) was selected as the most consistent switch  1p/19q co-deleted samples were clustered into the first branch while 99.6% (513/515) 1p/19q intact samples were clustered into the second branch  array were used as golden standard in our study. As shown in the Meanwhile, when integrated samples in TCGA and Rembrandt dataset, the smoother (96.5%) and PAM (82.3%) exhibited the highest sensitivity and lowest level of sensitivity among five methods, respectively . And TSPAfter synthetical comparing the differences of sensitivity, specificity and accuracy among five methods in two individual datasets, we found that smoother method clearly outperformed the other methods in predicting 1p/19q status with little room for improvement.With the rapid expansion of multi-platform integrated analysis of glioma, molecular markers have greatly facilitated the understanding of the genetic progress underlying the progress of cancer and provided key insights on precision medicine. The status of chromosome 1p/19q is one of the most crucial molecular markers in glioma, which has shown well-established association with the diagnosis and prognosis of patients .DNA sequencing, processing the order of nucleotides in DNA, is considered as the most accurate method in detecting large regions chromosome variation . HoweverThe main purpose of this study was to explore an appropriate RNA sequencing computational method to detect 1p/19q status. In this study, several analysis pipelines have been applied to analyze gene expression data for predicting 1p/19q status. TSPairs method, which identifies an alteration by comparing ratio of two genes expression, has been used in breast cancer and lung adenocarcinoma for molecular classification and predicting prognosis , 25. GSVThere were some advantages in inferring 1p/19q status with gene expression data. Firstly, the cost in RNA sequencing is much less than FISH. Prediction 1p/19q status with RNA sequencing data could reduce financial burden for patients. Secondly, identifying 1p/19q status by gene expression data could eliminate the limitation of FISH probes of testing only two regions. Thirdly, the RNA sequencing data could also be applied to call or predict IDH mutation, ATRX mutation, TERT mutation, EGFRvIII deletion, fusion genes and so on. The integrated analysis of DNA sequencing technology, RNA sequencing technology and FISH were shown in However, several limitations should be considered in this research. Firstly, the prediction models based on five RNA sequencing data processing methods were established retrospectively. The prospective longitudinal study was need to estimate this research in future. Second, the consistency between FISH and prediction models in predicting 1p/19q status could not be evaluated due to the limitation of FISH information of glioma patients in TCGA database and REMBRANDT database.In summary, along with the application of next-generation sequencing in clinical practice, we believed that RNA sequencing processing method will show great potential as the standard detection method to detect various genetic and molecular alterations. For detecting 1p/19q, we would recommend smoother method using RNA sequencing data, which was more cost-effective and convenient in clinical practice.http://cancergenome.nih.gov/), containing 172 1p/19q co-deleted and 520 1p/19q intact patients. TCGA RNA-seq expression data was log2 transformed before using. Validation set: RNA microarray expression data of 222 glioma samples from Repository for Molecular Brain Neoplasia Data , containing 33 1p/19q co-deleted and 189 1p/19q intact patients. The characteristics of glioma patients were described in Training set: RNA-sequencing data of 692 glioma samples downloaded from The Cancer Genome Atlas  contains functions for selecting top scoring pairs whose relative rankings can be used to accurately classify individuals into one of two classes (20501*20500 =420500270 gene pairs) [e pairs) .Gene Set Variation Analysis (GSVA) is a non-parametric, unsupervised method for estimating variation of gene set enrichment through the samples of an expression data set and bypasses the conventional approach of explicitly modeling phenotypes within the enrichment scoring algorithm [lgorithm .Prediction analysis for microarrays (PAM), which can be defined as a ‘nearest shrunken centroid classifier’ is a statistical method for class prediction by adding a ‘fudge-factor’ to each statistic's denominator [ominator . TCGA anFunctions Relating to the Smoothing of Numerical Data (smoother) could smooth numerical data, blur images and remove detail and noise. The gaussian window smoothing function allows users to infer the pattern of DNA aberration from gene expression [pression .Classification and Regression Training(caret), a machine learning algorithm, could integrate with the features in training and the modeled interaction features. The model was evaluated independently through stratified (k=10)-folds cross-validation [lidation .http://www.r-project.org).Hierarchical clustering was performed using complete agglomeration algorithm and a distance metric equal correlation coefficient with data processed by PAM, smoother and GSVA methods. We obtained TSPairs method from R package “tspair”, GSVA method from R package “GSVA”, PAM method from R package “pamr”, smoother method from R package “smoother”, caret method from R package “caret”, Combat function for removing batch effects  among TCSupplementary FigureSupplementary Table


Arabidopsis RNA-Seq data set, we were able to successfully pinpoint the visualization angles where genes from two biological pathways are the most separated, as well as identify potential outliers.The accumulation of RNA sequencing (RNA-Seq) gene expression data in recent years has resulted in large and complex data sets of high dimensions. Exploratory analysis, including data mining and visualization, reveals hidden patterns and potential outliers in such data, but is often challenged by the high dimensional nature of the data. The scatterplot matrix is a commonly used tool for visualizing multivariate data, and allows us to view multiple bivariate relationships simultaneously. However, the scatterplot matrix becomes less effective for high dimensional data because the number of bivariate displays increases quadratically with data dimensionality. In this study, we introduce a selection criterion for each bivariate scatterplot and design/implement an algorithm that automatically scan and rank all possible scatterplots, with the goal of identifying the plots in which separation between two pre-defined groups is maximized. By applying our method to a multi-experiment  Arabidopsis thaliana have resulted in an ever-accumulating amount of data from multiple RNA-Seq experiments. In this article, we will develop tools for the exploration and visualization of such multi-experiment data.High throughput RNA sequencing (RNA-Seq) has been widely adopted for quantifying relative gene expression in comparative transcriptome analysis. In recent years, the increasing number of RNA-seq studies on the model plant For examining treatment effects of individual genes under multiple conditions and across multiple experiments, a vector summarizing the differential expression (DE) results under different treatment conditions seems adequate. To visualize the DE profile under different treatments, a line plot can be used. However, since genes work interactively in all biological processes, it is of interest to examine expression patterns of groups of genes, through which the genes’ biological context can be better understood. In light of this, researchers often would like to both identify the general trend and pinpoint individual aberrations in the expression profile of genes belonging to the same biological pathway, as well as compare the profiles between multiple pathways.When multiple genes are being examined together, the line plots are less effective for visualizing DE or expression profiles: The lines often cross each other, making it difficult to identify the grouping and understand the behavior of individual genes. One common alternative visualization method is the scatterplot, which shows expression level under two treatment conditions at a time. Scatterplots are effective in showing clustering patterns and outliers, greatly assisting with data exploration . For higIn this paper, we propose to automatically search for the best low dimensional visualization angles  based on a context-sensitive, numeric measure of importance, thereby reducing the amount of effort invested in scatterplot scanning. In our study, we hope to explore the patterns and differences in gene expression profile between two phytohormone signaling pathways, and therefore, we would like the top ranked scatterplots to contain as much information as possible on pathway classification. We thus define such an importance measure for the dimension subsets such that the scatterplots will show the largest separation between different pre-defined groups in the data set.For this study, we will look for feature subsets upon which the pathways ethylene (ET) and jasmonic acid (JA) are the most separated, and quantify the between-group separation by calculating the repeated cross-validation (RCV) error of misclassification using MclustDA , a modelThe rest of the paper is formatted as follows: “Data Description and Processing” outlines the collection and processing of the data and information on the experiments and biological pathways. The statistical methods are described in “Methods.” In “Results,” we list the results obtained by applying our method to the collected data. Finally, we state our conclusion and discuss limitations and possibilities for future work in “Conclusion.” Additional proofs and graphs are included in the www.ncbi.nlm.nih.gov) and processed through a customized assembly pipeline to obtain a matrix of counts for genes in samples. All datasets originate from RNA-Seq experiments on the model plant A. thaliana, with treatment conditions (including genetic variants) varying between experiments. Tissue types in the original data include leaf, seed, and multi-tissue. The number of treatments/factor levels also vary among the experiments.In this study, we use a portion of the data collected and processed by Arabidopsis, which include a total of five datasets. The Gene Expression Omnibus (GEO) accession numbers (which can be used to directly search for the experiment/dataset information) are available as part of the meta-data, and the assembly pipeline that produced the read count matrix is described in detail in  will be one between each column of normalized relative frequencies, ij/NjRjc, and a pseudo column, ic0/N0R0 . In Arabidopsis RNA-Seq experiments (including the five experiments we use in this study). In this paper, we used these 104 genes as a reference gene set to compute the normalization factors. With the normalization factors jR estimated this way, the median fold change in normalized relative frequencies over these 104 genes will be one between any sample j and the pseudo sample.Let jR, we fit a log-linear negative binomial regression model to each row i (one gene) of the read count matrix (separately for each experiment) to assess DE between treatment groups (we suppressed the subscript i in the model equation below):j = 1, …, n, where ϕ is the overdispersion parameter capturing the commonly observed extra-Poisson variation in the read count data, and (jkx) is the model matrix. We chose the model matrix such that the fitted value of β0 will correspond to the log mean relative count of the control group, and the fitted regression coefficients β1, …, pβ will correspond to log fold changes between a treatment group and the control group. We used our own NBPSeq package to fit such a log-linear regression model  and jasmonic acid (JA). As a plant hormone, ET is commercially important due to its regulation on fruit ripening . JA actshttp://amigo.geneontology.org/amigo/landing) to search for the list of genes involved, and then identify the subset of genes in our data set that belong to the pathway through cross-reference. Genes with a fold change of <2 under all treatment conditions are filtered out. The name, GO accession number, and the number of genes in each pathway are listed in For each pathway, we first use AmiGO 2  results with MclustDA. Finally, we lay out our strategy for reducing data dimensionality with the ultimate goal of simplifying navigation of scatterplots.G, is assumed to be known. For probabilistic DA methods, it is assumed that observations in class k follow a class specific probability distribution kf(·). Let kτ represent the proportion of observations in class k. According to Bayes’s theorem, it follows thaty is assigned to the most probable class.In discriminant analysis (DA), known classifications of some observations are used to classify others. The number of classes, Commonly used DA methods, including Fisher’s linear discriminant analysis (LDA) and quadratic discriminant analysis (QDA), assume a multivariate normal density for each class:k = Σ for k = 1, …, G), and is called QDA if the class covariances are allowed to vary.The method is called LDA if the covariance matrices for all classes coincide  via the EM algorithm , which iIn our study, MclustDA is chosen over LDA/QDA as the classifier due to its greater flexibility in describing the data. In RNA-Seq analysis, we typically assume that the majority of genes are not differentially expressed, and therefore we expect to see a cluster of points around the origin. Since MclustDA proposes to fit more than one normal component to each class, it readily captures the cluster of non-DE genes as well as any abnormalities that might be of interest.In Class JA is fitted with a component centered near the origin, representing genes with low expression levels under both treatments, as well as a component centered at  that encompasses relatively active genes. Class ET is represented by a single normal component centered at .In comparison, due to model assumptions, LDA fitted a bivariate normal density to each class with covariances being equal, and in this case, the estimated centers almost coincide with each other. The fitted normal densities are only able to capture the general shape and orientation of each class, while MclustDA provides us with a more detailed anatomy of geometric and distributional properties in each class.Our definition of group separation measure is motivated by the relationship between visualized separation and misclassification probability (from a model-based classifier).π1 and π2. Let X =  denote the p-dimensional measurement vector of an observation. We assume that densities f1(x) and f2(x) describe the variability of the two populations. Let p1 and p2 denote prior probability of each population. Define c(1|2) and c(2|1) as costs of misclassifying an object from class 2(1) as class 1(2). Here we let c(1|2) = c(2|1) = 1 to simplify the formulation. Let Ω denote the entire sample space, and Ω = R1 ∪ R2, where R1 is the set of values of x for which we classify objects into π1, and R2 = Ω − R1.Suppose we wish to separate two populations π1 as π2 is:The probability of misclassifying an object from By definition, we can calculate the probability of misclassifying any object:π1 object or misclassifying a π2 object, that is,The total probability of misclassification (TPM) is defined as the probability of either misclassifying a Y = {Y1, …, NY1} ∼ π1 and Z = {Z1, …, NZ2} ∼ π2 are two i.i.d samples from the two populations. Assume that a classification system has been trained and tested on this data set, and results in the confusion matrix in Suppose Then the misclassification error rate (MER), that is, probability of misclassifying any object, is given by:π1 objects, N2|1, follows a Binomial distribution with parameters ). Likewise, the number of misclassified π2 objects, N1|2, follows a Binomial distribution with parameters ). The ML estimators for P(2|1) and P(1|2) can be easily computed:Under the assumption that each object is independently classified, the number of misclassified p1 = N1/(N1 + N2) and p2 = N2/(N1 + N2) as prior probabilities for π1 and π2, then under independence assumption, it follows thatNow, if we set In practice, however, the MER tends to underestimate TPM because the same data has been used for both training and testing. In this study, we use CV to address this issue.K-fold CV, the original data is randomly split into K equally sized subsamples, of which K − 1 (training set) are used to train a classifier and the remaining one  is used to test the trained classifier. For a binary classification problem, the MER, as defined in K folds, each time using a different subsample as validation set, and the resulting K MER values are averaged. In stratified CV, the folds are selected so that they contain approximately the same proportion of classes as the original data. It has been shown in previous studies that stratified CV tends to perform uniformly better than CV, in terms of both bias and variance . For small K, less data is used to train the classifier and therefore the error estimate tends to be biased. For large K, the estimator becomes less biased due to more data being used in training, but its variance is inflated due to higher correlation between different training folds. C = 10 considering the amount of computation required as well as the specs of our hardware.Let  C and K . IncreasWe define the group separation index (GSI) asIntuitively, for a chosen feature subset, a small CV error indicates that the data can be more easily classified when projected onto these dimensions, which, in our expectation, can be reflected in the graphical representation of the data by showing that different classes can be more easily distinguished through simple visualization.In this section, we describe the data in each pathway with a low dimensional representation for easier interpretation by selecting a parsimonious subset of features (treatment-control contrasts) that contain as much information on pathway classification/separation as possible. In other words, we hope to find the dimensions to project the data onto such that the separation between two pathways is as large as possible. We use GSI, as defined in Step 1: Determine the number of features M to keep. Choose M from {2, 3, 4}.Step 2: List all M-subsets of features exhaustively. Call this collection of subsets ℱM.Step 3: For each member of ℱM, subset the data accordingly. Calculate and record a 10 × 10 stratified CV error rate  with MclustDA as classifier on each subsetted data. For each fold of CV, use MER as measure of fit.–jG ≡ G = 2. Then, use the same fitted model  for every fold of CV.CV model fitting: First fit a MclustDA model to the entire subsetted data, setting maximum number of components as Step 4: Rank the feature subsets in ℱM according to their GSI values. Feature subsets with higher GSI values are ranked higher.Step 5: Repeat above steps for other values of M.In order to find the optimal feature subset in terms of group separation, we designed and implemented the following algorithm:G = 5 in R function MclustDA, and discovered that in some situations the number of model parameters became too large for the algorithm to produce a meaningful point estimate. The same problem occurred for G = 4 and G = 3, especially when we looked at three- and four-dimensional data. Therefore, we settled on using G = 2 for our implementation.Concerning the choice of maximum number of components in Step 3, we initially attempted to use the default value For the purpose of finding “good” angles for data visualization, we will examine the scatterplots and scatterplot matrices generated by top-ranked feature subsets. The results will be discussed in “Results.”Step 1: Choose a list of 50 random number seeds. Partition the list into five batches of 10 seeds.Step 2: For each feature subset, run 10-fold stratified CV for 50 times, each time using a different seed from the list.Step 3: Average results within each of five batches of 10 random seeds to obtain 10 × 10 stratified CV result. For instance, average of seeds 1–10 results serves as first run of 10 × 10 RCV; average of seeds 11–20 serves as second run, etc.To ensure reproducibility of our results, for each of 2-, 3- and 4-subset selection process, we followed the following protocol to set random number seeds:As discussed in “Mixture discriminant analysis via MclustDA,” LDA fits only one multivariate normal component to observations in each class. In gene expression data such as ours, a majority of genes are expected to be expressed at a low level, meaning we are likely to observe a cluster of data points around the origin, regardless of the class they belong to. Meanwhile, any aberrant patterns demonstrated by individual data points are often not captured by fitting LDA model.To see whether our method can still discover interesting visualization angles with LDA as classifier, we modified and implemented the GSI calculation algorithm accordingly, and applied it to our data. Results are presented in “Using fisher LDA as classifier.”Principal component analysis (PCA) maps the data onto a lower dimensional space in such a way that the variance of the data in the low-dimensional representation is maximized. As a dimension reduction technique, usually only the first few principal components (PCs) are used. Despite its popularity in the field of data visualization, the formulation of PCA does not involve any class information in the data, which implies that the projected directions corresponding to the largest variance may not contain the best separability information.To verify this observation, using the expression data from all five experiments, we calculated its PCs, and treat them as the new (projected) features. Then for the first two, three and four PCs, respectively, we calculated the GSI for each case using 10 × 10-CV with MclustDA and compare the results with ours.With the secondary purpose of testing the stability of repeated CV, we executed multiple runs for each of the 2-, 3-, and 4-subset feature selection procedures. The top ranked feature subsets as well as their corresponding GSI values are presented in Although the top ranked feature subsets sometimes differ between multiple RCV runs, we are still able to observe high degree of overlap between the results:For 4-subset , , by calculating M = 2,000 GSI values from permuted data, and obtained the empirical p-value of 0.0055, indicating the significance of this pair of features.We were advised on whether we can assign a measure of significance for the top ranked feature set found by our method. Our interpretation of “significance” in this context is as follows: Under the assumption that the feature pair contain no group information on the genes, what is the probability of obtaining a GSI value as high as or higher than the value computed by our method (i.e., a As shown in “Quantification of group separation,” CV was used for the calculation of MER. A recent study  points o10.7717/peerj.5199/supp-1Supplemental Information 1Click here for additional data file.


BRAF, SMAD4 and TP53 mutations and MYC amplification. Finally, we show that this signature is a predictor of the failure of PD-1 blockade and outperforms previously-proposed biomarkers. Thus, our findings identify a distinct transcriptional pattern of ECM genes in operation across cancers that may be potentially targeted, pending preclinical validation, using TGF-β blockade to enhance responses to immune-checkpoint blockade.The extracellular matrix (ECM) is a key determinant of cancer progression and prognosis. Here we report findings from one of the largest pan-cancer analyses of ECM gene dysregulation in cancer. We define a distinct set of ECM genes upregulated in cancer (C-ECM) and linked to worse prognosis. We found that the C-ECM transcriptional programme dysregulation is correlated with the activation of TGF-β signalling in cancer-associated fibroblasts and is linked to immunosuppression in otherwise immunologically active tumours. Cancers that activate this programme carry distinct genomic profiles, such as  Changes in ECM are of predictive value in pancreatic and colorectal cancer prognosis. Here, the authors perform a pan-cancer analysis and find a subset of ECM genes that is linked to TGF-β signalling signature and is correlated with immunotherapy failure. Moreover, cancer-associated fibroblasts (CAFs) produce key growth factors and cytokines as components of the ECM that fuel tumour growth, metastasis and chemoresistance and immune response4. Further, ECM changes also predict prognosis in pancreatic5 and colorectal cancers7.The ability to disseminate, invade and successfully colonise other tissues is a critical hallmark of cancer that involves remodelling of the extracellular matrix (ECM) laid down by fibroblastsHere we examine the pan-cancer landscape of ECM gene dysregulation and find that a subset of ECM genes is dysregulated specifically in cancer and is enriched among transcriptional changes that distinguish normal from malignant tissue. We further show that the high expression of this subset of genes is adversely prognostic in pan-cancer analyses. Then, using deconvolution and analyses of transcriptional profiles from dissociated tumour fractions, we show that these genes are modulated in CAFs.8, cytolytic activity (CYT)9, TGF-β expression alone, a CAF signature10 or a T cell-inflamed signature11. We have thus identified a novel signature of immune evasion that is a potential target for pharmacological modulation and may facilitate effective patient stratification in precision immunotherapy, pending preclinical validation.Subsequently, based on multiplatform analysis of The Cancer Genome Atlas (TCGA) data, we correlated these profiles to transforming growth factor (TGF)-β signalling in the tumour microenvironment and show that this transcriptional programme is enriched in immunologically active cancers, suggesting a possible role in immune evasion/adaptation. Finally, we demonstrate that this transcriptional programme predicts responses to immune checkpoint blockade better than mutation burdenn = 8043) and normal tissues (n = 704) accounting for tumour type (n = 15) from TCGA and tested for enrichment of an ECM-associated gene-set we curated based on gene ontology terms  and downregulated  genes in malignant tissues )  while downregulated C-ECM genes were not  scorespes Fig. . We thenp < 8.5e−5, Cox regression, two-sided).We also performed survival analyses where the quartiles of up-and-down scores were combined into single categories. This showed that cancers with the highest quartile of the up-score (Q4) and the lowest quartile of the down-score (Q1) had markedly increased risk of death  and purity estimates independently computed using allele-specific copy number profiles using ASCAT19, downloaded from COSMIC20 . The lower correlation of the median VAF with ECM scores is expected given the confounding influence of ploidy on the relationship between cancer cell fraction and VAF21.We found tumour purity estimated using ABSOLUTE, which jointly estimates cancer cell fractions of variants, purity and ploidy using copy-number data and whole-exome datares Fig. , S2A. ThThe breakdown of correlations between C-ECM scores and purity estimates for different methods by tumour type have been presented in Supplementary Figure 22 (GSE40595) resulted in clustering by sample type with strong stromal expression , CD8 T cells (CD8A expression), CAFs (ACTA2 expression) and monocytes (CD14 expression) whereupon we noticed strong, consistent agreement Notably, the CAF specificity of C-ECM transcription was further indicated by the absence of expression in the leukocyte compartment in these data sets, suggesting that while monocyte enrichment and CD8 infiltration co-occur with C-ECM upregulation, they are not the source of C-ECM transcriptional changes  profiled in the study24. We found markedly higher expression of C-ECM genes in CAFs, which clustered together when the signature was projected onto the data set  < 0.05, Wilcoxon’s Rank Sum Test) and 10 genes were significantly underexpressed in CAFs compared to other cell types , which we selected owing to the large collection of CAFs  while the down-signature was negatively correlated   Fig. . Similar26, and found significant associations  relative to M2 (immunosuppressive) macrophages , FDR < 0.01, Supplementary Data Additionally, we assessed macrophage polarisation using CIBERSORTNext, since our data suggest that the C-ECM-up signature associated with the presence of CAFs and not with normal stroma Fig. , we endeSMAD transcription factors, AP1 complex members that associate with SMADs28 and SMARCA429  and identified 13 differentially abundant peptides between upper and lower quartiles of the ECM-up score  data , BMPs (BMP1 and BMP8A) and the local sequestrators of TGF-β, FBP1 and LTBP1. Further, we compiled a collection of TGF-β upregulated target genes across various tissues and across species from MSigDB (C2 collection) while excluding C-ECM genes and found a very strong correlation between C-ECM-up scores and this set , further strengthening the notion that C-ECM-up gene dysregulation is associated with TGF-β signalling in CAFs. However, C-ECM-down genes were not significantly enriched among downregulated genes following TGF-β stimulation, suggesting that C-ECM-up genes represent TGF-β activation in CAFs, while C-ECM-down genes represent more normal fibroblasts.This revealed marked enrichment for C-ECM-up genes among differentially expressed genes (DEGs)  counts from whole-exome data from pre-treatment biopsies.Finally, we tested whether C-ECM dysregulation is an immune-evasion mechanism in the context of PD-1/PD-L1 blockade, where immunologically ‘hot’ tumours are associated with responses39, the C-ECM-up score was significantly higher in progressors . This was also true in pooled logistic regression accounting for cancer type, CYT, mutational load, a T cell-inflamed signature11, cohort, antibody and prior anti-CTLA4 treatment ent Fig. .Fig. 4C-40 showed that models with C-ECM ssGSEA scores significantly outperformed those involving CYT, a T cell-inflamed signature and mutation load alone  , and when C-ECM scores, the CAF signature score and TGFB1/2 expression are all included in a joint model, the CAF score loses significance while the C-ECM signature shows even stronger associations   for TGFB1 expression and the Tirosh CAF ssGSEA score. We predicted that CAF-high TGFB-high cancers would display the highest C-ECM-up score, that CAF-low TGFB-low cancers would display the lowest enrichment, while the other two combinations would display significantly lower expression than CAF-high TGFB-high cancers because both factors are necessary but insufficient alone. Statistical comparisons  confirmed our prediction Fig. .In this study, we have identified a pan-cancer role for ECM dysregulation. Using a range of approaches, we show that ECM dysregulation is associated with the presence of CAFs and the activity of TGF-β, among other regulators. Our model fits a scenario where the C-ECM-down signature represents normal/normal-like fibroblasts, whereas the TGF-β-driven C-ECM-up signature identifies a poor prognosis CAF activation phenotype that is upregulated pan-cancer. We further show that tumours that are otherwise 'immunologically hot' tend to display higher levels of the C-ECM-up programme and possess genomic alterations that may minimise the fitness costs of the high levels of TGF-β signalling required to sustain the C-ECM-up programme. These statistical associations serve as suggestive early evidence supporting the continued experimental investigation of TGF-β in immune modulation across tissue types.41. This suggests approaches that seek to normalise the aberrant transcriptome in fibroblasts, possibly through TGF-β blockade, are likely to offer a more promising route to boost the efficacy of checkpoint blockade. Consistent with this, recent preclinical studies have uncovered evidence that simultaneous targeting of both TGF-β and PD-L1 can result in markedly better tumour control in multiple mouse models42. Moreover, recent studies using genetically reconstituted murine colorectal cancers43, and those based on transcriptional analyses of bladder cancers treated with PD-L1 blockade7, have arrived at similar conclusions and have demonstrated that TGF-β blockade can markedly potentiate antitumour immunity by modulating CAF-mediated T cell-exclusion phenotypes.Given this, the depletion of CAFs may be a potential approach to enhance checkpoint blockade; however, in some cases, CAF depletion per se is paradoxically associated with worse outcomes33. The widespread occurrence of the C-ECM programme across cancer types may help explain, at least partially, why this is the case.Our pan-cancer analyses establish the presence of a TGF-β-associated C-ECM programme that is correlated with immunotherapy failure and indicate the existence of subsets of C-ECM-high cancers independent of tissue type. Relevantly, prior work has suggested that negative selection in cancer is generally weak as a pan-cancer phenomenon, suggesting that the depletion of immunogenic mutations through immunoediting is weakOur results suggest that tumours with elevated C-ECM programme across cancer types may likely benefit from combination immunotherapy with PD-1 blockade and TGF-β blockade to restore immune control of tumours. Future tissue-agnostic, C-ECM biomarker-guided basket trials are necessary to validate this hypothesis.Finally, our findings linking TGF-β activity, CAFs, C-ECM signature and immunosuppression of otherwise immune ‘hot’ tumours are associative and further experiments would be required to prove a causal link.All tests were two sided and were performed for unmatched samples measured once.RNA-seq data were obtained in the form of RSEM estimates from SAGE Synapse. This was reduced to 15 cancer types that had >10 normal samples available and low expressed genes were filtered (average <1 CPM).44 was then used to compute DEGs between normal and cancer samples while controlling for cancer type at thresholds of FDR < 0.01, 2FC. Controlling for the cancer type was explicitly used in order to minimise the effects of class imbalance and also to derive a picture of ECM gene dysregulation independent of cancer type.Limma-trendA reference gene set of extracellular matrix genes was derived using the gene ontology term 'extracellular matrix' (GO:0031032) biological process category (used by UniprotKB) and downloaded from geneontology.org. Gene ontology terms and enrichments in overlap were computed using Fisher’s Exact Test.15 for each sample. Clinical data were then derived from SAGE synapse for a large subset of these tumours (Accession: syn7343873) and ECM-up and -down scores were divided into quartiles for categorisation. Validation at the protein level was performed using Spearman’s Rank Correlation between RNA-seq and mass spectrometry for matched BRCA and OVCA samples profiled by TCGA and CPTAC, with the mass spectrometric data derived from the corresponding publications.Significant upregulated and downregulated ECM genes were used to define gene sets whose expression was summarised using ssGSEAA stratified Cox regression model was of the form Survival ~ ECM-up-quartile + ECM-down-quartile + strata(cancer type) + strata(stage) was fit to estimate impact on prognosis. Similarly, a combined analysis was performed by fusing ECM-up and -down quartile categories.18 was used to derive purity and ploidy estimates for n = cancers. ECM scores were tested for association with purity using Spearman’s Rank Correlations. This analysis was then repeated using purity estimates from ASCAT19 derived from COSMIC and the median VAF of mutations was obtained from the MC3 MAF (Synapse:syn7214402)45.ABSOLUTE46. C-ECM genes were then projected onto the data set to visualise clustering by phenotype. Significant probes were then identified for cancer epithelium versus cancer stroma and cancer stroma versus cancer epithelium using limma. Fisher’s Exact Tests were used to test for enrichment of ECM signatures among DEGs (defined using limma).An ovarian cancer data set was then obtained from GEO (GSE40595) and normalised using fRMAACTA2, CD14, CD8A and CYT) using Spearman’s Rank Correlation. Validation of CAF association was performed in single-cell RNA-seq data from HNSCC, selected owing to the availability of large numbers of CAFs (n = 1440) (GSE103322) by projecting ECM signatures onto log2(TPM + 1) transformed matrices. Data were obtained in a TPM matrix from GEO and the cell-type allocations were taken from the corresponding publication, wherein known cellular markers were used to define populations. ssGSEA scores were computed and Mann–Whitney tests were used to test for differential expression.Cellular deconvolution analyses were carried out using estimated cellular fractions produced using MethylCIBERSORT using Spearman’s Rank Correlations between the ECM-up and -down scores. These findings were validated using gene expression of associated markers 47. Topiary (https://github.com/openvax/topiary) was then used in combination with the MC3 set of TCGA mutation calls (Synapse:syn7214402) to define variants and potential neoantigens, using nonamers and thresholds of binding affinity <500 nM. Mutation loads were also computed for the same set of samples.HLA type for MHC class I alleles was retrieved from The Cancer Immunome Atlas27.Spearman’s correlation and negative binomial models were used to test for associations between these genomic counts and ECM scores after adjusting for cancer type. M1/M2 macrophage fractions were computed using CIBERSORT48.The expression of immune checkpoints was computed as part of whole-transcriptome analyses from differential expression between the top and bottom quartiles of the ECM-up score, adjusting for cancer type. Mismatch repair analyses were carried out using TCGA-allocated status based on Sanger sequencing published previouslyFor RNA-seq and RPPA data, limma-trend was used to compute differentially regulated genes/proteins at thresholds of 2FC, FDR < 0.01 and 1.3FC, FDR < 0.01 by comparing samples in the top and bottom quartiles of ECM-up score, respectively.IPA was used to perform a core pathway analysis using interactions experimentally verified in human tissues in general. Causal network analysis results were restricted to those themselves differentially expressed, while upstream regulatory analyses were not.33 (positively selected) in cancer and carried out linear regression against ECM-up score with cancer type for a covariate. For copy-number data, we generated GISTIC34 calls pan-cancer at intensity thresholds of 0.3 and FDR < 0.01. Events for each GISTIC peak were dichotomised into altered/wild type and were regressed against ECM-up scores using a linear model with cancer type as covariate.For mutation analyses, we retrieved a previously published catalogue of driver mutationsWe assembled RNA-seq, mutation and neoantigen burden data from multiple immunotherapy data sets and standardised the expression data to consider transcripts quantified in all data sets. Then we computed ssGSEA scores for the C-ECM-up and -down scores for each data set and examined association with response  by Response Evaluation Criteria in Solid Tumours criteria using Mann–Whitney tests. A pooled logistic regression was conducted using the C-ECM scores from the three data sets with cancer type and treatment as covariates.40 were carried out to evaluate the performance of logistic regression and Cohen’s unweighted Kappa was used to evaluate model performance. For Random Forest-based analyses, we first subtracted study-specific effects using a linear model via the removeBatchEffects function in the limma R package. Mann–Whitney tests were used to compare model performance across resamples. The models fit were C-ECM + CYT, C-ECM alone, TGFB1 alone, Mutational load + CYT and C-ECM, CYT and mutational load, a CAF signature derived from Tirosh et al.10 and an interferon-induced signature11 . Limma-trend was used to identify ECM genes differentially expressed between nonresponders and responders using restricted hypothesis testing at FDR < 0.1. Finally, for analysis of mechanistic hypotheses surrounding the relative contributions of CAFs, TGF-β and the C-ECM-up score to immunotherapy failure, we fit the following logistic regression models. (i) Response ~ TGFB1 + TGFB2 + log2(MutLoad) + T cell-inflamed GEP score + Cohort, (ii) Response ~ Tirosh CAF signature score + log2(MutLoad) + T cell-inflamed GEP score + Cohort, (iii) Response ~ C-ECM-up score + Tirosh CAF signature score + TGFB1 + TGFB2 + log2(MutLoad) + T cell-inflamed GEP score + Cohort. To test whether both TGFB1 and CAFs were required for activation of the C-ECM-up signature, we defined the lowest quartile of the Tirosh CAF signature score, and the lowest quartile of TGFB1 expression, as low and the rest as high. Pairwise Mann–Whitney tests were computed between the four groups produced thus with Benjamini–Hochberg correction for FDR.Finally, 100 iterations of 0.632 bootstrappingKnit HTML R markdowns of the code used to generate the results are available on Zenodo at 10.5281/zenodo.1410639.Further information on research design is available in the Supplementary InformationDescription of Additional Supplementary FilesSupplementary Data 1Supplementary Data 2Supplementary Data 3Reporting Summary