There are a few reports on the correlation between the 3Foxp altered expression level and single-nucleotide polymorphisms within the 3Foxp locus. Moreover, some studies showed the importance of 3Foxp expression in the same diseases. Therefore, to explore the possible effects of single-nucleotide polymorphisms, here, we evaluated the association of IVS9+459/rs2280883 (T>C) and −2383/rs3761549 (C>T) 3Foxp polymorphisms with systemic lupus erythematosus. Moreover, through machine-learning and deep-learning methods, we assessed the connection of the expression level of the gene with the disease. Single-nucleotide polymorphisms of 3Foxp (IVS9+459/rs2280883 (T>C) and −2383/rs3761549 (C>T)) were, respectively, genotyped using allele-specific PCR and direct sequencing and polymerase chain reaction-restriction fragment length polymorphism, in 199 systemic lupus erythematosus patients and 206 healthy age- and sex-matched controls. The Statistical Package for the Social Sciences version 19 and Fisher’s exact and chi-square tests were used to analyze the data. Moreover, six machine-learning models and two sequential deep-learning models were designed to classify patients from normal people in the E-MTAB-11191 dataset through the expression level of 3Foxp and its correlated genes. The allele and genotype frequencies of both polymorphisms in question were found to be significantly associated with an increased risk of systemic lupus erythematosus. Furthermore, both of the two single-nucleotide polymorphisms were associated with some systemic-lupus-erythematosus-related risk factors. Three SVM models and the logistic regression model showed an 81% accuracy in classification problems. In addition, the first deep-learning model showed an 83% and 89% accuracy for the training and validation data, respectively, while the second model had an 85% and 79% accuracy for the training and validation datasets. In this study, we are prompted to represent the predisposing loci for systemic lupus erythematosus pathogenesis and strived to provide evidence-based support to the application of machine learning for the identification of systemic lupus erythematosus. It is predicted that the recruiting of machine-learning algorithms with the simultaneous measurement of the applied single nucleotide polymorphisms will increased the diagnostic accuracy of systemic lupus erythematosus, which will be very helpful in providing sufficient predictive value about individual subjects with systemic lupus erythematosus.The impaired suppressive function of regulatory T cells is well-understood in systemic lupus erythematosus. This is likely due to changes in  These specialized lymphocytes, with regulatory functions in restraining immune responses [25), and the forkhead box P3 (Foxp3) transcription factor [3 controls the regulation, differentiation, and suppressor function of Treg cells. In contrast, function-impaired Treg cells develop systemic autoimmune diseases which have been found to be associated with mutations on the 3Foxp gene (located on the X chromosome in the Xp11.23 position) [3Foxp gene which can alter its expression level and impair the suppressive function of Tregs [3Foxp have been reported to be associated with autoimmune disease risk [To avoid responsiveness against self-antigens and reduce autoimmunity risk, the immune system has evolved immunological tolerance mechanisms which are categorized as central and peripheral tolerance. The primary deletion of autoreactive T or B cells take place by central tolerance, within the primary (thymus and bone marrow) lymphoid organs. Nevertheless, central tolerance is imperfect and self-reactive cells continuously escape into the periphery. Peripheral tolerance is the inactivation key of autoantigen-recognizing T or B cells which appear in the periphery ,2. A uniesponses ,4,5, arin factor . The masosition) ,8,9,10. osition) ,13. Impaase risk .Furthermore, gene expression analysis advances our understanding about the underlying molecular mechanisms of SLE. Nowadays, machine learning is a developing area that is known as a revolution in science. Machine learning and its more developed field called deep learning could be represent a solution for the big data interpretation challenge, and used to obtain understandable knowledge from massive gene expression data and facilitate the ability to predict changes in SLE disease . There aThe core finding from the present functional study may fill the existing gaps in our understanding about genetic factors predisposing to SLE and provide a promising way to utilize genetic computational methods for the prediction of risk for SLE.3Foxp polymorphisms and also the association of the expression of 3Foxp with SLE through in vitro and machine-learning methods.To shed new light on the molecular mechanism underlying the development of SLE, the present study aimed to realize the probable association of IVS9+459/rs2280883 (T>C) and −2383/rs3761549 (C>T) For our study, 199 SLE blood samples were collected from patients whose disease had been diagnosed by rheumatologist  findings and immunological evidence  at Hafez Hospital Lupus Clinic . Blood samples were also collected from 206 age- and sex-matched healthy subjects (controls) from the organization of the blood transfusion . All samples were kept in the Autoimmune Diseases Research Center of Shiraz University of Medical Sciences  until experimental analysis. Subjects with other co-occurrent autoimmune and underlying diseases were excluded. The study protocol was approved by the Ethics Committee of the Islamic Azad University—Kazerun Branch (IR.IAU.KAU.REC.1398.044) and written informed consent was provided to gain consent of research participation.Genomic DNA was extracted from a total blood sample volume of 200 µL using the DNP™ DNA Extraction kit  and was stored frozen at −20 °C for later use. NanoDrop ND-2000  was used for DNA concentration and quality assessment.Selected polymorphic sites (IVS9+459/rs2280883 (T>C) and −2383/rs3761549 (C>T)) were genotyped by two independent PCR methods.BseNI (BsrI) restriction enzyme, 2.5 µL buffer, and 18µL nuclease-free water. The mixture then incubated for 4 h at 65 °C. Next, 15 µL of each digested PCR product containing a 3 µL loading buffer was loaded into a lane of the 3% agarose gel. The DNA bands were then visualized on the UV transilluminator and images were taken with a gel documentation system . Finally, the genotypes of −2383/rs3761549 (C>T) SNP were determined.The −2383/rs3761549 (C>T) polymorphism was amplified by restriction fragment length polymorphism (RFLP) technique. Amplification program, primers, restriction enzyme, and product sizes are shown in IVS9+459/rs2280883 (T>C) was genotyped through allele-specific PCR (AS-PCR)  and GEO (https://www.ncbi.nlm.nih.gov/geo) databases on 7 July 2022, in the current study. Various datasets were selected as our first-level candidates; among them, we chose the E-MTAB-11191 dataset from the ArrayExpress database. The selection criteria were based on the number of samples, study design, and the platform in use. The platform in use in the current study was Affymetrix Human Genome U133 Plus 2.0 Array. We first downloaded raw CEL files and then generated the expression matrix through the RMA method in the affy package in the R environment. The package is developed to generate and modify expression matrices from the Affymetrix platform series. The data values were then normalized and scaled into log2 + 1 format. The matrix was then annotated with Ensembl IDs, Gene Symbols, and Entrez IDs. We did not remove any genes through typical methods such as CPM (counts per million) because we had a specific target gene to study.We searched for microarray expression datasets in the ArrayExpress , and rows were our labels . We had 101 samples; among them, 17 were normal, and 84 were patients. The data were first scaled between zero and one (a common method in machine-learning models) by the following formula:G represents the expression value of the gene in the patients i, and min and max values of G are the minimum and maximum values of the gene among all patients.First of all, we extracted the expression level of the 3Foxp gene, including linear regression (LR), support vector machine (SVM) with RBF (SVM_1), linear (SVM_2), and poly (SVM_3) kernels, decision tree (DT), and extra-tree classifier (ETC). To train the models, we shuffled and divided 70% of the data into the training datasets and 30% into the testing datasets. For that purpose, we used the train_test_split function from the sklearn library in Python. Each model was first trained on the training dataset and then evaluated on the test datasets.Six machine-learning models were created to classify them based on the expression level of the 3Foxp, the co-expression network analysis was performed. The expression matrix of 3Foxp was extracted. Afterwards, the Pearson correlation test was executed between the gene and all other genes in the main expression matrix. Those genes with a correlation coefficient (CC) > 0.8 and CC < −0.8 were selected.In order to find genes associated to 3Foxp probe IDs as our features. The model had 2 hidden layers with 10 and 5 units, respectively. Moreover, there was another output layer with one unit. The activation function for hidden layers was carried out then, and the output layer was sigmoid. Bias for all layers was considered zero at the first epoch, and the weights were random numbers. Adam was considered as the model optimizer, and, because it was a binary classification, we considered binary cross-entropy to calculate our loss. Moreover, the learning rate was set at a 0.0001 value. The model was trained with 2000 epochs, and the validation dataset was considered 0.25 of the total number of train samples. In addition, at the end of the training, the model was evaluated by the test dataset.Two deep-learning models were designed. We used both the Keras and the TensorFlow libraries in the Python environment. Keras is a branched library from TensorFlow that is developed for deep-learning usages. It generally supports two types of models, including sequential and functional models. In the current study, both models were sequential models. In the first model, we only considered 3Foxp. We had three hidden layers in the second model with 25, 25, and 12 units, respectively. Other parameters were similar to the first model. However, in this model, because of the large number of features, we did not consider the test dataset, and only the validation dataset with 33% of total samples was considered. We utilized this method because, if the number of samples became less than the number of features, the model could not classify very well.For the second model, we considered all genes with a correlation coefficient > 0.8 or <−0.8 with https://colab.research.google.com/) environment on 15 July 2022. The runtime was set on TPU, which is developed for better execution of machine-learning projects. Moreover, figures were depicted using Python and the matplotlib library.All statistical analysis for the genotyping part was performed in SPSS Statistics 19 software. The significance differences in genotype and allelic frequencies between two groups were verified by the Hardy–Weinberg (HW) equilibrium and chi-square test. Bonferroni corrections were applied to correct for multiple comparisons, and the threshold for statistical significance was set at ≤0.05. In the machine-learning part, all mathematical and statistical calculations were performed in R and Python environments. We applied R version 4.0.1 and R Studio for data preparation and basic statistical tests. We applied Python for deep learning, machine learning, and model evaluation in the Google Colab  and −2383/rs3761549 (C>T)) gene polymorphisms and SLE risk, and (2) the 81% accuracy of the three SVM models and the logistic regression model when performing classifications based on gene expression data in biological challenges about genetic factors predisposing to SLE.The results showed that the statistical power in our study were: (1) the associations between both 2 = 3.2, df = 2, HWE p-value = 0.201; and patient group, X2 = 4.7, df = 2, HWE p-value = 0.095). The CC, CT, and TT genotype of the −2383/rs3761549 (C>T) polymorphism is shown in 3Foxp rs3761549 SNP is summarized in The −2383/rs3761549 (C>T) genotype distribution was in accordance with the Hardy–Weinberg equilibrium . An evaluation of the Hardy–Weinberg equilibrium for the rs2280883 polymorphic loci showed a nonsignificant deviation in both the control and patient population , we only considered two layers but a more extensive training time for that (2000 epochs). The model showed an 83% and 89% accuracy for the training and validation datasets, respectively. The loss for both datasets was at the minimum level of its function, and the training was precisely stopped at this point. On the other hand, for the second model, we considered 76 genes that had the highest CC with 3Foxp  could be a risk allele and the CT and TT genotypes were associated with developing SLE. Other findings are in agreement with our result; for example, in a Brazilian population, the rs2232368 polymorphism T allele was found to have an association with endometriosis-related infertility [3Foxp rs2280883 was found with the risk of connective-tissue-disease-associated ILD [3Foxp-polymorphism-associated genetic effect on the risk of SLE identified in this study, confirm our hypothesis that 3Foxp polymorphisms might be a proper candidate for use in autoimmune disease screening, including for SLE. However, no evidence for the 3Foxp gene polymorphism association with Graves’ disease and autoimmune Addison’s disease has been found in the UK population [In the present study, the role of ertility . The assertility . Moreovepulation . It is c3Foxp gene expression level in patient classification was evaluated. Our present result is similar to the findings of a previous study which indicate machine-learning algorithms could potentially be applied to identify the gene expression features and subjects with higher degrees of disease activity [3Foxp expression levels might classify both groups considerably. A comparison among the deep-learning and machine-learning models shows that the first deep-learning model had the best performance with about 90% accuracy. In this model, we only considered 3Foxp as our feature. We believe that the better performance of the model is due to the number of samples, as the rules of deep learning say the number of features should be much less than the sample number to obtain the best result. On the other hand, among machine-learning models, logistic regression and all support vector machine models showed the same result with an accuracy of 81%. Here, again, we think that the same results are because of the number of control samples. Definitely, if we increase this number, the results would be changed. Therefore, we cannot decide which one of the machine-learning models could classify better. Considering a larger sample size to evaluate the association between these polymorphisms in question with SLE in future studies will resolve the present study’s limitation. Likewise, further studies on patients in a variety of ethnic populations are still required to increase our knowledge base for this gene. It is advantageous that other genetic association studies evaluate other potential mediators, such as DNA methylation.On the other hand, in the current study, the potential of the activity . Moreoveactivity . The dat3Foxp in autoimmunopathies have attracted interest in numerous genetic studies, the present study has been attempted to detect 3Foxp gene expression features and its related polymorphisms as more plausible genetic risk factors for SLE. The present data provide an approach to considering the 3Foxp gene as a strong genetic component with high clinical significance for SLE which could potentially be used to identify the subjects with higher disease susceptibility.To date, although the role of


A limitation of current deep learning (DL) approaches for single-cell RNA sequencing (scRNAseq) analysis is the lack of interpretability. Moreover, existing pipelines are designed and trained for specific tasks used disjointly for different stages of analysis. We present scANNA, a novel interpretable DL model for scRNAseq studies that leverages neural attention to learn gene associations. After training, the learned gene importance (interpretability) is used to perform downstream analyses  without retraining. ScANNA’s performance is comparable to or better than state-of-the-art methods designed and trained for specific standard scRNAseq analyses even though scANNA was not trained for these tasks explicitly. ScANNA enables researchers to discover meaningful results without extensive prior knowledge or training separate task-specific models, saving time and enhancing scRNAseq analyses.  Single-cell RNA sequencing (scRNAseq) technologies have been instrumental in studying biological patterns and processes in development and disease . ScRNAseThe major advance of scANNA is the innovative use of a simple neural attention module within a three-module DL core see . This DLAdditive Attention module, which learns optimal weights for each gene based on their contribution to the auxiliary objective. These weights are used to calculate gene scores, a scaled version of the raw counts. After training scANNA’s DL core, the gene attention weights from the Additive Attention Module are used as input for most standard downstream tasks. This common training is achieved by inputting the gene scores into the second component, the Deep Projection Blocks, which are an ensemble of operators learning a nonlinear mapping between gene scores. This mapping is designed to increase model capacity and connect the gene associations to the auxiliary objective. A concatenated representation of the ensemble defined in this step forms the input to scANNA’s third component, the Configuration Module. The Configuration Module is the last layer of the DL core made to align with the chosen auxiliary objective function, allowing for flexibility and potential adjustments based on the dataset, (e.g. number of neurons that correspond to the number of known populations).The first component of scANNA is the These weights are used to calculate gene scores, a scaled version of the raw counts. These gene scores serve as inputs to the second component, the Deep Projection Blocks, which are an ensemble of operators learning a nonlinear mapping between gene scores to scANNA’s third component, the Configuration Module. The Configuration Module is made to align with the chosen auxiliary objective function, allowing for flexibility and potential adjustments based on the dataset (e.g. number of known populations) or desired downstream applications . After tIn this work, we compare scANNA to state-of-the-art methods on a variety of standard scRNAseq tasks using nine public single-cell datasets. We show that scANNA attains comparable to better performance despite not being explicitly trained for these standard tasks. Based on our findings, we propose scANNA as an accurate and effective method for a variety of scRNAseq analysis settings. In large-scale studies with limited prior knowledge, scANNA’s unbiased pipelines can rapidly and accurately identify new and noteworthy genes. For small-scale studies (min 2000 cells), scANNA’s DL core can be pre-trained on existing atlases to transfer knowledge from existing repositories. As such, scANNA is a valuable tool for novice and expert users in the initial steps of scRNAseq analysis.1 on five complex datasets (four human datasets with distinct disease conditions and one mouse dataset). ScANNA was trained on quality-controlled raw data  modelsraw data , and forraw data , scPred raw data , SingleCraw data , scClassraw data , CHETAH raw data ) while p2 (2) trained the DL core to predict pseudo-labels, and (3) extracted attention weights from the Attention Module or fine-tuned the Configuration Module if transferring the learnings to a different biological context , unsupervised annotations (5 datasets), and transfer learning from large-scale data to small datasets (2 pairs of datasets). For each scRNASeq data set we considered, we trained scANNA once and then applied it to each corresponding downstream task without retraining the core DL model. To train scANNA in these unsupervised analysis tasks, for each data set we: (1) Generated pseudo-labels of cell types using an unsupervised clusteringtext see .3, scANNA’s Attention Module implicitly performs feature selection by assigning weights to each gene during training. After training, we extracted attention values and ranked “top” genes accordingly . As sucquencing .Next, we set out to perform cell type annotation, another critical challenge in scRNAseq studies , in an uOur results  show thaLastly, we considered the application of scANNA to transfer learning, the accurate and robust annotation transfer of knowledge from a larger reference set to a smaller query set. Linear machine learning methods have had broad applicability due to their interpretability . In contTo simulate small-scale studies and to test TL capabilities, we fine-tuned scANNA’s Configuration Module on only 20% of target datasets (5911 and 11520 cells) and used 80% for testing (23705 and 46020 cells) . We alsoWe presented scANNA, a DL model employing a novel core that leverages simple neural attention for multiple scRNAseq analyses. We show that scANNA performs comparably or better than state-of-the-art methods designed and trained for specific standard scRNAseq tasks , even though scANNA was not trained for these tasks explicitly. We have demonstrated scANNA’s effectiveness at identifying cell types in a supervised and unsupervised manner, reducing subjectivity while minimizing the time for annotating scRNAseq datasets. Our results indicate that leveraging attention in global feature selection outperforms current methods in identifying features that explain the most variance in a dataset. Lastly, we demonstrated that scANNA outperforms state-of-the-art models in TL tasks, highlighting the importance of interpretable and generalized models in the scRNAseq space. Moreover, scANNA’s unique flexibility extends beyond using cell-type pseudo-labels (as we did in this work), enabling the utilization of other groupings for learning the desired gene associations, such as leveraging hierarchies for trajectory inference.Our results with scANNA demonstrate the potential of attention-based DL methods to offer significant improvement compared to traditional DL methods when applied to scRNAseq. Researchers can replace task-specific DL pipelines with scANNA, and potentially other interpretable DL methods that are likely to emerge. As attention-based DL methods are not yet widely used in scRNAseq analyses, our work suggests significant discoveries may yet exist in the abundance of existing public scRNAseq datasets. Finally, we note that scANNA’s architecture can be generalized to design further interpretable models for scRNAseq including spatial transcriptomics. We envision the use of attention layers in DL models will allow the field to transition from single-purpose DL models designed for specific tasks to interpretable multi-tools capable of enabling researchers without extensive computational training to accelerate the discovery process.branching projections. Multiple branching projections combined together form a projection block. ScANNA is a much simpler version of the popular Transformers models  denoting a linear neural network. The learned operator A is leveraged after training to identify salient genes for interpretability. Gene scores have the same dimension as input data, i.e., The first step in the DL core, the Attention Module, is used to calculate a gene-score matrix (weighted version of scRNAseq count matrix), representing expression data in later layers. These importance scores enable gene prominence quantification for the downstream task, allowing interpretation of the model’s decisionmaking. Given a gene expression matrix k =2 projection blocks with h =4 branches provide the appropriate balance of accuracy and efficiency. We hypothesized that adding residual connections from the gene scores to the input of each block would improve interpretability (by reducing the chance of learning a complex unrelated non-linear mapping). Through ablation studies, we found that the residual connections, followed by LayerNorm . The Configuration Module used for our work consisted of a linear layer mapping the gene space (number of highly variable genes) to the number of cell types, followed by a Leaky ReLU activation.lr =10−4 for 50 epochs. Our experiments showed training scANNA for more epochs can result in a slight increase in prediction accuracy; however, we chose to train all models for 50 epochs for additional computational efficiency. We also employed an exponential learning rate scheduling, starting at epoch 10 and decaying every 5 epochs after with γ = 0.95 to avoid overfitting .Results presented for all downstream tasks used one trained model, except for TL between reference and query datasets that had different numbers of cell populations. For all datasets, we trained scANNA by minimizing a standard cross entropy loss using the Adam gradient-based optimizer at a learning rate All data are publicly available from NCBI gene expression omnibus (GEO) and the Broad Institute Single Cell Portal (SCP), with links provided in n features, with n = {10, 25, 50, 100, 200, 300}, using K-Nearest Neighbors (KNNs), XGBoost and Nearest Centroid. As a baseline, we also trained each classifier using the 5000 HVGs. In our results, we only report KNN classification accuracy, since KNN on 5000 HVGs performed best for most datasets. Additionally, we computed the fraction of variance on the original gene space  and compared that with the different approaches. Based on the evidence provided in the SmaSH manuscript and our own validation, ensemble learning (XGBoost) provided the most accurate approach, which we employed in our experiments. Of note, minor but necessary adjustments were made to the SMaSH package (located at https://gitlab.com/cvejic-group/smash) to make SMaSH compatible with Tensorflow 2.11 . For a fair comparison across all methods, we modified SMaSH to use pre-defined train and test split, which were determined a priori. Our last minor modification was to allow for the ensemble method to train in parallel (by adding n_jobs=−1 to the XGBoostClassifer arguments in the ensemble_learning class method). For scGeneFit (https://github.com/solevillar/scGeneFit-python) with the same parameters as in https://github.com/alexmascension/triku) following the suggested usage protocol with only one modification (i.e. the parameter for tk.tl.triku function was set to use_raw=True). For Seurat and CellRanger, we leveraged scanpy’s function scanpy.pp.highly_variable_genes to identify important features based on the dispersion-based methods Seurat (Seurat) and CellRanger (CellRanger) . FollowcGeneFit , we usedlRanger) .https://github.com/SindiLab/ACTINN-PyTorch). Lastly, for Random Forest we used sklearn.ensemble.RandomForestClassifier function with default parameters. We generated five distinct train and test splits  for each dataset using the ShuffleSplit function from the Sci-Kit Learn package. Each model was applied to all splits with the following metric collected runtime, accuracy, weighted F1, and macro F1. Mean and standard deviation was calculated for each metric based on the dataset and model. Runtimes are presented in Seven models were compared against scANNA to evaluate performance on supervised classification ACTINN , scClassWe chose six large immune datasets to evaluate scANNA’s capabilities across multiple diseases and tissues. Five datasets consist of human cells and one of the mouse cells. The human datasets included three SARS-CoV-2 viral infection studies and a human cutaneous squamous cell carcinoma study. We included a mouse dataset to demonstrate our model’s effectiveness on non-human and non-immune datasets. All datasets were generated using the 10X Genomics platform. A summary for each dataset is provided in https://github.com/zqfang/GSEApy) enrichr method. We provide an overview of our workflow in Given that labels are not available in an unsupervised setting, pseudo-labels are used to keep the same supervised objective as in the dataset publications. Pseudo-labels can be generated using traditional methods, such as graph-based clustering, or self-supervised contrastive learning . To avoid any improvements in annotation not caused by scANNA, we generated pseudo-labels for each dataset using the same clustering approach described in the originating manuscript. After clustering, the arbitrary cluster numbers were used as pseudo-labels, and scANNA was trained to predict the cluster number given to a cell. No information about the cell types, known marker genes or common housekeeping genes were used during training. After training, we extracted the top n attentive genes and used those genes as markers for querying cell type. using GSEAPY’s  , it is pOur enrichment analysis for “proliferating lymphocytes” resulted in multiple significant populations, with the most prominent type being CD8+ proliferating T cells . IntuitiFor transfer learning, we focused on labeling two small-scale query datasets using larger source data (references). These experiments were as the following:As an initial assessment for transfer learning, we pre-trained scANNA on a PDAC atlas, an integration of five publicly available datasets see , which wAs a more challenging task, we aimed to perform TL from a broad T cell atlas (GSE188666) to a CD8+ T cell-specific dataset (GSE199565), which contains more subpopulations than the reference data. Similar to the PDAC experiment, we used 80% of the source data for pretraining (and 20% for testing the pre-training), 20% of the query target data for fine-tuning, and 80% for testing see .Fine-tuning scANNA consists of freezing all weights in the attention and projection modules, with the only trainable parameters being in the configuration module (the last layer of scANNA mapping projections to the corresponding cell types). We fine-tuned scANNA (and other tested models) for 10 or 50 epochs using the same hyperparameters as pre-training.https://scarches.readthedocs.io/); however, we were unable to use scGen due underlying maintenance issues, therefore all results presented in the manuscript are for scArches with scANVI (which uses scVI at its core). Though scGen method is recommended, we note that scANVI is also an appropriate method since it can be trained unsupervised and finetuned on a target data using labels, thus making the comparison relevant and fair. Using the source data, we trained the scVI core for 100 epochs, with an additional 10 epochs for the annotation which achieved desirable accuracy (comparable to other methods). Then, similar to scANNA, we fine-tuned the model for 10 and 50 epochs on the query data.ScArches  allows tWe hypothesized that scANNA’s advantage for TL stems from our architecture design. To test the importance of architecture, we applied our methodology for freezing weights and fine-tuning to an existing model, ACTINN, with the following rationale: If scANNA’s architecture is not unique and more beneficial for transfer learning, then a pre-trained ACTINN model (on the source data) should perform comparably to scANNA (once fine-tuned on a query dataset) given its comparable performance in the supervised annotation regime. Similar to the other experiments, we trained ACTINN-TL on source data for 50 epochs, then froze the weights in the hidden layers, and fine-tuned the last layer responsible for predicting the correct cell type. For simplicity, we call this approach ACTINN-TL.ScNym  model ishttps://singlecell.broadinstitute.org/single_cell.SCP1361 consists of aortic cell scRNAseq from mice fed a normal diet or a high-fat diet, resulting in 24K cells (after processing) . The autImmuneCSF (GSE163005) profiles scRNAseq data in cerebrospinal fluid . Cells in = 3), moderate COVID (n = 5), acute respiratory distress syndrome , and recovering , resulting in 69K cells. After pre-processing the dataset, we retained 64K cells. The authors identified 9 populations in the dataset. Raw data can be downloaded from Gene Expression Omnibus (GEO) with accession number GSE154567.GSE154567 evaluates the transcriptional immune dysfunction in patients triggered during moderate and severe COVID-19 using scRNAseq . Periphen = 10), resulting in 48K cells and 7 major cell populations. We retained 47K cells after pre-processing. The myeloid cell population (CD14+Hi) is composed of various subpopulations. Raw data can be downloaded from Gene Expression Omnibus (GEO) with accession number GSE144236.GSE144236 evaluates scRNAseq of normal skin and cutaneous squamous cell carcinoma (cSCC) tumors . Normal n = 12 total), resulting in 39K cells and 9 cell populations. We retained 39K cells after pre-processing. Raw data is available from the European Genome-Phenome Archive (EGA) with study id EGAS00001004419.Lukassen (EGAS00001004419) evaluates single nuclei RNA sequencing of lung tissue to evaluate the expression of ACE2 and TMPRSS1 . PrimaryPDAC atlas consists of five scRNAseq published datasets  from norPDAC small (GSE154778) is a specific PDAC study consisting of individual cells (57K with 10 subpopulations) from dissociated primary tumors or metastatic biopsies obtained from patients with PDAC . Raw datT-cell atlas (GSE188666) evaluates CD8 T cell exhaustion during viral infection by scRNAseq resulting in 96K cells, (retained 96K cells after pre-processing) . Raw datCD8 specific data (GSE199565) evaluates CD8+ T cell temporal differentiation by scRNAseq resulting in 29K cells (retained 29K cells after pre-processing) . The aut1


Molecular subtyping by integrative modeling of multi-omics and clinical data can help the identification of robust and clinically actionable disease subgroups; an essential step in developing precision medicine approaches.We developed a novel outcome-guided molecular subgrouping framework, called Deep Multi-Omics Integrative Subtyping by Maximizing Correlation (DeepMOIS-MC), for integrative learning from multi-omics data by maximizing correlation between all input -omics views. DeepMOIS-MC consists of two parts: clustering and classification. In the clustering part, the preprocessed high-dimensional multi-omics views are input into two-layer fully connected neural networks. The outputs of individual networks are subjected to Generalized Canonical Correlation Analysis loss to learn the shared representation. Next, the learned representation is filtered by a regression model to select features that are related to a covariate clinical variable, for example, a survival/outcome. The filtered features are used for clustering to determine the optimal cluster assignments. In the classification stage, the original feature matrix of one of the -omics view is scaled and discretized based on equal frequency binning, and then subjected to feature selection using RandomForest. Using these selected features, classification models  are built to predict the molecular subgroups that were identified at clustering stage. We applied DeepMOIS-MC on lung and liver cancers, using TCGA datasets. In comparative analysis, we found that DeepMOIS-MC outperformed traditional approaches in patient stratification. Finally, we validated the robustness and generalizability of the classification models on independent datasets. We anticipate that the DeepMOIS-MC can be adopted to many multi-omics integrative analyses tasks.https://github.com/duttaprat/DeepMOIS-MC).Source codes for PyTorch implementation of DGCCA and other DeepMOIS-MC modules are available at GitHub (Bioinformatics Advances online. Advances in high-throughput technologies have facilitated generation of multiple -omics datasets, such as genomic, epigenomic, transcriptomic and proteomic measures, on same biosamples. Indeed, analyses of -omics data on hundreds of cancer tissues, profiled by The Cancer Genome Atlas (TCGA), International Cancer Genome Consortium (ICGC) and many other laboratories around the world, have led to the identification of clinically relevant subgroups of various cancers. While majority of the studies utilized microarray or RNA-Seq-based expression profiling data , a novel deep learning-based method that achieves multi-omics integration and subtyping of cancer by finding a low-dimensional shared representation that maximizes the correlation between multiple views. DeepMOIS-MC extends DGCCA  (https://xena.ucsc.edu/) using the R package UCSCXenaTools  were obtained in total, including RNA-seq (UNC IlluminaHiSeq_RNASeqV2), miRNA-seq (BCGSC IlluminaHiSeq_miRNASeq) and methylation array (JHU-USC HumanMethylation450) data. Data was preprocessed in a similar fashion to previous work  patients (n = 243) (n = 225 HCC patients (We obtained TCGA level-3 datasets from UCSC Xena database (enaTools . Three tn = 243)  which coDeepMOIS-MC  is dividCanonical correlation analysis (CCA)  finds liA (GCCA)  can be eThe final shared representation ReLU activation function throughout all views  were preserved. The selected features were then used as input to K-means clustering with 100 initialization points and 2000 iterations, where the best number of clusters (k) was determined by combination of visual analysis of the silhouette plot, the average silhouette width and the Calinski–Harabasz score. We applied log-rank test to determine the statistical significance of prognostic stratification of the subtypes derived. We plotted Kaplan–Meier survival curves and performed Cox-PH analysis using R survival and survminer packages.The DGCCA algorithm outputs a 100-dimensional vector embedding, which reflects the nonlinear maximally correlated shared representation. These embeddings were then subjected to a univariate Cox-PH feature selection process prior to clustering. Essentially, each coordinate of the 100-dimensional embedding was used as a feature and input to a univariate Cox-PH model, and only features with significant log-rank We benchmarked DeepMOIS-MC with several most widely used multi-omics integration and subtyping methods, including iClusterBayes . Among the 438 patients, 406 contains all three types of -omics data  while 22 has at least one type of -omics data missing. Contrary to other similar studies .P < 0.05). Upon univariate Cox-PH filtering, eight variables were retained for k-means clustering analysis with cluster number from two to six. The silhouette index shows both k = 2 and 6 could be the optimal number of k  has a lot of samples with negative silhouette width  stacked autoencoder with concatenated inputs, i.e. to combine input views and analyze through a single neural network (AE); (ii) stacked autoencoder with separated input views, processed through separated neural networks, then concatenated the latent representation/embedding (AE_concat); (iii) denoising autoencoder (dropout at input layer to corrupt some input) with concatenated inputs (DAE); (iv) denoising autoencoder with concatenated embedding (DAE_concat); (v) denoising autoencoder, concatenated inputs with additional dropout at every hidden layer (DAE_full_dropout); (vi) denoising autoencoder, concatenated embedding with additional dropout at every hidden layer (DAE_full_dropout_concat); (vii) variational autoencoder, concatenated inputs (VAE); and (viii) variational autoencoder, concatenated embedding (VAE_concat). To ensure consistency with previous literatures and with DGCCA, we used same network architecture for the fully connected layers  throughout all experiments. We also used hyperbolic tangent (tanh) as activation function as this was most widely used in previous studies for autoencoders  at 10 epochs (log-rank P = 9.58e–5), which we believe was closest to the reported implementation and results by Chaudhary et al . Nevertheless, this is still much less significant than the subtypes identified using DGCCA representation (P = 8.89e–7) we obtained at the end of 20-epoch training.We generated Kaplan–Meier survival curves for the 2 identified HCC subtypes for all 8 autoencoder settings at both 10 and 20 epochs . DespiteP-value (P < 0.05) in k = 2–6 among all methods, including PINSPlus . DeepMOIS-MC (labeled DGCCA) was the only method that resulted in significant Cox P = 3.71e–8 for BRCA and P = 1.96e–4 for LUAD; We further extended our comparison to the other two types of cancer, including breast adenocarcinoma (BRCA) and lung adenocarcinoma (LUAD) in TCGA. Even without altering any training parameters and network architecture, DeepMOIS-MC consistently identified two subtypes in both types of cancer that were significantly separated in survival  and GEO (GSE14520), the first being on RNA-seq platform and second being a gene expression microarray dataset. 15 189 and 10 125 genes out of 15 588 in TCGA-LIHC training set were found in the two validation sets respectively. To eliminate the noise related to platform bias and batch effects, we applied equal frequency data discretization on both training and validation data after scaling (Section 2). The number of bins was a hyperparameter to choose and was determined by whether finer or coarser binning enhanced performance of the model . We usedFinally, we examined whether DeepMOIS-MC can be readily extensible to additional -omics data by bringing new modality in the DGCCA stage. Since genomic alterations are another source of heterogeneity across patient samples and were frequently used in subtyping studies in the past, we decided to include copy number variation (CNV) as a fourth view and investigate how that could change our results. We have performed combinatorial experiments between the four types of -omics data and reported the subtypes extracted in each experiment on LIHC, BRCA and LUAD data . Though In this study, we proposed a novel deep learning-based multi-omics integrative cancer subtyping pipeline to derive a shared representation that simultaneously reconstructs the nonlinear transformations of all input views by maximizing the correlation across views. In theory, the biggest advantage of using a DGCCA-based representation as opposed to an autoencoder-based one is that it considers the relationship and attempts to extract only the common, coherent features among all views, rather than preserving and reconstructing all features of the views without explicitly considering how they are related to one another. Essentially, DGCCA finds the intersection of the nonlinear subspaces formed independently by the neural network outputs of all views  may also be simply integrated using DeepMOIS-MC to obtain potentially better subtypes with even more clinical value, given that DGCCA supports the input of an arbitrary number of views. Meanwhile, the fact that each -omics is processed through a separate network offers an additional advantage in network selection as different most suitable network architecture could be selected for individual view. Furthermore, our ability to incorporate data points with partially missing -omics also greatly extends the flexibility and applicability, especially when data is limited.Notwithstanding, certain caveats exist in the current proposed model. First, although DGCCA specializes in extracting the common features across multiple views through maximizing correlation, the assumption that there are always some common patterns shared across the views is not guaranteed in every case. In a multi-omics scenario, if the quality of the training data for at least one platform is poor, there could be very weak consistency between the different -omics levels. In such cases, it is anticipated that DGCCA will not perform well since there is little or no common features to extract across views. Meanwhile, DGCCA could also be biased toward finding only common features across all views but ignoring some strong features that only present in single view. It is therefore necessary to balance the tradeoff between preserving single -omics features and finding common features shared across platforms. Moreover, the current study is limited by availability of public validation data for -omics other than expression that (i) simultaneously contains the -omics data and survival data, (ii) matches the exact platforms used in our training data and (iii) is not part of TCGA or its overlap with other consortiums, which will be addressed in future studies. Finally, as an outcome-guided subtyping approach, DeepMOIS-MC relies on high quality and comprehensiveness of survival data used as input for DGCCA model training to ensure generalizability of subtypes obtained across different cohorts.vbad075_Supplementary_DataClick here for additional data file.


Despite the success of recent machine learning algorithms’ applications to survival analysis, their black-box nature hinders interpretability, which is arguably the most important aspect. Similarly, multi-omics data integration for survival analysis is often constrained by the underlying relationships and correlations that are rarely well understood. The goal of this work is to alleviate the interpretability problem in machine learning approaches for survival analysis and also demonstrate how multi-omics data integration improves survival analysis and pathway enrichment. We use meta-learning, a machine-learning algorithm that is trained on a variety of related datasets and allows quick adaptations to new tasks, to perform survival analysis and pathway enrichment on pan-cancer datasets. In recent machine learning research, meta-learning has been effectively used for knowledge transfer among multiple related datasets.We use meta-learning with Cox hazard loss to show that the integration of TCGA pan-cancer data increases the performance of survival analysis. We also apply advanced model interpretability method called DeepLIFT (Deep Learning Important FeaTures) to show different sets of enriched pathways for multi-omics and transcriptomics data. Our results show that multi-omics cancer survival analysis enhances performance compared with using transcriptomics or clinical data alone. Additionally, we show a correlation between variable importance assignment from DeepLIFT and gene coenrichment, suggesting that genes with higher and similar contribution scores are more likely to be enriched together in the same enrichment sets.https://github.com/berkuva/TCGA-omics-integration. Traditionally, survival analysis has usually been done by means of statistical analyses that aim to identify the distributions of event times and the statistical properties of the estimated parameters. In comparison, machine learning algorithms aim to produce more accurate survival prediction by combining established statistical methods with machine learning methods. Yet, a high ratio of missing survival information, data sparsity, missing features, and labels can cause significant loss of performance even with some of the most recent machine learning algorithms. In particular, deep neural network machine learning approaches, which have shown promising results in various aspects of biomedical studies, require a large amount of well-organized and complete data for training, which is rare in biomedical settings.Recently, high throughput techniques together with the continuously decreasing cost of sequencing have resulted in a wide availability of multiomics data. Because different molecular processes starting on DNA and resulting in protein products are intricately interconnected, omics data derived from different stages of gene and protein expression are likely to contain complementary information. However, the explicit relationships among multiomics data are complex and remain poorly understood. Moreover, many omics data suffer from the problem of ‘big P, small N’—having significantly higher number of features (P) than the number of data samples (N). This makes integrating and interpreting multiomics data even more challenging.As a result of those challenges, many existing works on survival analysis use a single omics dataset, such as clinical or transcriptomics  , proteomics, and clinical datasets. These datasets contain information in different molecular stages: proteins are translated from RNA, and the functional mechanisms of cells are determined from proteins, leading to various clinically relevant outcomes.For the clinical and the proteomics datasets, we imputed missing numeric feature values using the k-nearest neighbors (KNN) method, with k = 1. We used label encoding to encode categorical features. In the clinical dataset, we manually removed the feature that contains patients’ vital status, which has a high correlation with their survival status. The transcriptomics dataset required no imputation. We then applied z-score transformation for each dataset after imputation. Finally, in order to remove features with high correlation to each other, we filtered out features with over 0.7 Pearson correlation to at least one other feature.Post-imputation, scaling, and feature engineering, the transcriptomics, the clinical, and the proteomics datasets in the TCGA comprised 11 068, 8490, and 5853 patients, respectively, and 13 960, 10 039, and 227 features. To integrate the multiple omics datasets, we reapplied z-scale transformation and filtered out features with a correlation of over 0.7 to another feature in the integrated dataset.Although there are 33 cancer types in TCGA, the variations among them can result in high bias and noise when all are used to construct the input for the learning model. Therefore, we carefully selected 17 cancer types that satisfy the following two conditions: (1) sufficient number of patients in all three datasets and (2) long follow-up times. We reviewed  fewer assumptions and (ii) no distributional constraints on survival times.x is a set of covariates. This means the hazard ratio does not depend on the baseline hazard and remains constant. This leads to one of the most widely used time-to-event analysis, Cox Proportional Hazard (Cox-PH) method. Cox-PH is a semi-parametric model that calculates the probability of an event occurring in relation to a time variable.Given many collected features in a dataset, Cox regression models determine which features conduce to a probability of survival. By taking the natural logarithm of the hazard function, we obtain i, The Cox hazard loss Recently, the Cox-PH model has been combined with various forms of artificial deep neural networks, allowing flexible model selection and thereby enhancing the performance compared to regularized Cox-PH methods, such as in L, allowing quick adaptation to new tasks.Meta-learning is an algorithm that allows quick adaptation across multiple similar datasets. It is first trained on related source data, followed by fine-tuning and evaluation on target tasks. Back-propagation of the gradients generated from the loss incurred from each task leads to the optimal values of The meta-learning model used in our survival analysis is Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks (MAML)  applying a variable importance score cutoff and inputting the resulting gene list into a pathway enrichment tool and (2) using all annotated genes in the genome and their associated scores to arrive at enriched pathways.For the first approach, we used g: Profiler to find functionally enriched pathways on the limited gene list. For the second approach, we performed gene set enrichment analysis (GSEA) by using a ranked list of genes with scores. The selection of genes and the assignment of scores were done by applying DeepLIFT (Deep Learning Important FeaTures) to our meta-learning model that estimates the patients’ probability of survival by optimizing cox-loss. DeepLIFT is a recently developed method for gaining interpretability for deep neural networks. Interpretability methods applicable for deep neural networks such as DeepLIFT largely consist of two methods: forward propagation and backward propagation methods. Forward propagation methods, such as , generatDeepLIFT first assigns reference values, or null values, to the input neurons in the network. It forward propagates the difference between the value and its reference value. Then, it calculates how much each input affects its subsequent neuron, or it ‘blames’ the difference from reference of the output on the difference from reference of the input. This difference is then allocated (or blamed) to each input neuron by back-propagation, assigning contribution scores to all neurons in the network. Related interpretability methods, such as integrated gradients , calculaWe also studied whether DeepLIFT importance analyses are correlated with gene coenrichment using STRING  measures the relative order of predicted patients’ hazard times to the actual order. Hence, it is one of the most widely used evaluation metrics for Cox loss-based survival analyses. It is calculated by dividing the number of concordant pairs by the sum of concordant and discordant patient pairs. A pair of patients is concordant if the predicted order of the event is the true order; otherwise, it is a discordant pair. We evaluated the C-index of the meta-learning model on the target tasks on two conditions: using transcriptomics dataset alone and using different combinations of the three datasets.A metric for evaluating the error of survival prediction includes the integrated Brier score. It is calculated by the mean squared differences between predicted and ground truth survival probabilities at a given time step. Therefore, we use integrated Brier score  to evaluGiven a list of enriched genes and attribution scores, GSEA calculates the number of statistically significantly enriched molecular pathways differentially expressed between survived and deceased patients. The higher the attribution scores are for the genes that are coenriched in a pathway for a group of patients, the more statistically significant the pathways. However, there exists no standard for objectively comparing the goodness of enriched pathways. Therefore, we provide literature support for a few selected pathways, supporting their enrichment status for cancer.As a follow-up study for interpreting DeepLIFT scores and pathway analysis, we compare how genes with similar DeepLIFT attribution scores appear in the same STRING enrichment sets with how genes with different attribution scores do. We queried STRING with genes with the highest attribution scores in the 50th, 70th, and 90th percentiles to observe correlation between attribution scores and gene coenrichment. Finally, we studied how the distribution of categories of enriched pathways change with different percentiles of DeepLIFT attribution scores.In M trained on each dataset d as c, t, and p indicate the clinical, the transcriptomics, and the proteomics, respectively, and any combination of two or all three of these subscripts indicates dataset integration. Similarly, we denote the direct learning baseline model trained on c, t, p as For convenience, we denote our meta-learning model Compared with We then ran survival analysis on pairwise integrated datasets. To perform data integration, we merged the features from each pair of datasets and removed features with higher than 0.7 Pearson correlation to at least one other feature. The resulting dimensions after integrating and removing the feature were 23 994 for the clinical and the transcriptomics datasets, 13 724 for the proteomics and the transcriptomics datasets, and 10 266 for the proteomics and the clinical datasets.Finally, we expanded our survival analysis by integrating all three datasets. As we did to the paired datasets, we also removed features with 0.7 or higher Pearson correlation, resulting in 24 218 features. Our results summarized in We tried four DeepLIFT reference values: the median and the mean feature values for deceased patients and survived patients individually. The median feature values for deceased patients yielded higher number of enriched molecular pathways.In For a number of pathways identified in The VEGF-VEGFR2 signaling pathway plays a critical role in the development and progression of cancer. Vascular endothelial growth factor (VEGF) stimulates angiogenesis (the formation of new blood vessels), which is necessary for tumors to grow and spread . VasculaSimilarly, research suggests that oxidation by cytochrome P450 and ABC transporters are also related to cancer. Specifically, cytochrome P450 is a group of enzymes that are involved in the metabolism of drugs, hormones, and other substances in the body. They are also involved in the metabolism of carcinogens, which are substances that can cause cancer .TLR4 signaling pathway is involved in the development and progression of cancer and has been linked to inflammation and tumorigenesis (In addition, we used STRING to find the correlation between genes in the 50th, 70th, and 90th percentiles of DeepLIFT contribution scores and gene sets contained within STRING representing genes where protein products interact and form pathways. With 13 960 genes in our transcriptomics dataset, genes in the 50th, 70th, and 90th percentiles represent 6980, 4188, and 1396 genes, respectively, and genes in the different percentiles are independently assigned as input to STRING. To ensure proper analysis of enrichment sets and genes’ DeepLIFT scores, we filtered the enrichment sets with at least 30 genes.After running our pretrained metalearning model from survival analysis on each target cancer type data, we sorted the genes by DeepLIFT scores and set the first gene from each enrichment set as the anchor gene. We then counted how many genes in the same enrichment set appear near the anchor gene in the sorted list. In this process, a standard for how near we look around the anchor gene becomes necessary, which we refer to as the window size. If a gene is within On BLCA, with genes in the 50th, 70th, and 90th percentile of DeepLIFT scores, 18.8%, 19.7%, and 19.2% of genes in each enrichment sets had similar DeepLIFT scores, respectively, to the anchor gene in the sorted list. On the other hand, only 9.4%, 5.0%, and 2.4% genes were near the anchor gene in a randomly sorted list. Clearly, the more similar genes’ DeepLIFT scores, the more likely they were coenriched in functional sets. This indicates that using a metalearning model trained using Cox-loss on the transcriptomics genes, genes that are coenriched in the same enrichment sets were assigned similar DeepLIFT contribution scores. Since these enrichment sets are categorized by their functional attributions, this result indicates that the model captures functional and semantic relationships among genes without any prior knowledge. Results for each of the three cancer types are shown in Although data integration and transfer of knowledge have been shown to be effective in other machine learning areas, omics data integration in comparison has only recently been explored considerably due to data sparsity, complexity, and extremely large feature space. Toward the goal of advancing omics data integration for survival analysis and pathway enrichment analysis, we used metalearning to show how multi-omics dataset integration improves cancer survival analysis. Whereas transcriptomics dataset is the most widely used, our results show that complementing it with clinical and proteomics datasets enhances performance of survival analysis. Furthermore, we combined metalearning with variable importance analysis methods of DeepLIFT, compared pathway enrichment using g: Profiler and GSEA, and compared enriched molecular pathways using the transcriptomics data alone and using integrated multi-omics data. Finally, we demonstrated how genes with similar, high DeepLIFT attribution scores are more likely to be coenriched in functional enrichment sets, which implies that training a meta-learning model can learn functional relationships of genes without prior knowledge.Financial Support: None declared.Conflict of interest: None declared.


Gliomas are primary malignant brain tumors with poor survival and high resistance to available treatments. Improving the molecular understanding of glioma and disclosing novel biomarkers of tumor development and progression could help to find novel targeted therapies for this type of cancer. Public databases such as The Cancer Genome Atlas (TCGA) provide an invaluable source of molecular information on cancer tissues. Machine learning tools show promise in dealing with the high dimension of omics data and extracting relevant information from it. In this work, network inference and clustering methods, namely Joint Graphical lasso and Robust Sparse K-means Clustering, were applied to RNA-sequencing data from TCGA glioma patients to identify shared and distinct gene networks among different types of glioma  and disclose new patient groups and the relevant genes behind groups’ separation. The results obtained suggest that astrocytoma and oligodendroglioma have more similarities compared with glioblastoma, highlighting the molecular differences between glioblastoma and the others glioma subtypes. After a comprehensive literature search on the relevant genes pointed our from our analysis, we identified potential candidates for biomarkers of glioma. Further molecular validation of these genes is encouraged to understand their potential role in diagnosis and in the design of novel therapies.The online version contains supplementary material available at 10.1186/s13040-023-00341-1. Gliomas are primary malignant brain tumors, accounting for 28% of all brain tumors and 80% of malignant ones . The larThe World Health Organization (WHO) classification of the Central Nervous System (CNS) tumors has been changing throughout the years regarding the classification of glioma. The classification of gliomas has evolved from histological-based  to increThe technological advances are responsible for the generation of large amounts of genetic information. With an increasing larger number of molecular features than samples, machine learning stands as a powerful tool to retrieve relevant information from these complex datasets. A relevant machine learning task to cope with ’omics data involves dimensionality reduction using, e.g., feature selection methods. Model regularization is a promising way to select features and improve model interpretability by adding constraints to the solutions. Methods like the least absolute shrinkage and selection operator (lasso)  and furt to zero , making  to zero .Biological networks are one of the most studied types of networks used to decipher the molecular structures involved in disease development and progression . BiologiGraphical lasso (glasso)  is a metBesides the relevance of identifying key network features in known cancer subtypes, the discovery of new patient groups from the increasingly available omics data is also encouraged. This approach aims to evaluate whether the information extracted from available cancer-type-specific molecular data correlates with the established clinical/molecular groups, or supports further cancer reclassification efforts. Finding groups of patients based on molecular information can be tackled by clustering methods. In the context of high-dimensional data, a shape-based method for sparse clustering, SPARCL, was proposed to allow clustering-based feature selection. The motivation behind this technique is to divide observations into a pre-specified number of groups, using only a subset of representative features. Robust K-means clustering (RSKC) is an extension of SPARCL that can handle outliers in the data. A pre-specified proportion of outliers is admitted by the method, which considers that the observations that are not so close to each cluster centers are not representative of any condition . The abiThe goal of this work is to identify, through sparse methods, transcriptomic network biomarkers of heterogeneity in gliomas. Although differences in glioma types have been investigated in the past –28, thesIn a first stage of the network-based methodology proposed, RNA-seq data from glioma patients were obtained from The Cancer Genome Atlas (TCGA), the largest repository of multiple omics data concerning cancer in humans . The TCGThe RNA-seq data used were collected by the TCGA Research Network. We downloaded TCGA-GBM , 31 and TCGAbiolinks package [huge R package [The final dataset comprises of 622 patients, divided as 264 astrocytoma, 220 oligodendroglioma and 138 GBM. As required from JGL, only normally distributed variables were considered in our dataset. To ensure this assumption, we selected the features having normal distribution in accordance with the Jarque-Bera test , leading package , 37. The package . For the package  was usedn and p denote the number of observations and the number of features, respectively. If all the features are independent and identically distributed, glasso algorithm estimates the precision matrix D distinct but related datasets Dp features are common to all the D classes. Features are independent and identically distributed within each class. The JGL [D precision matrices, each one defining the undirected network existing in the corresponding dataset. These networks are estimated jointly, by inducing sparsity and similarity across the different dataset through a penalty function. The authors of JGL method proposed two different penalty functions, the Group Graphical Lasso (GGL), leading to similar pattern of sparsity, and Fused Graphical Lasso (FGL), encouraging similarity between the edges. In this work, we selected FGL, which, beside providing generally better performances in various applications [D datasets by the parameter Let X be the data matrix, features . Let us  The JGL  algorithications , was morn observations into K clusters L1  [K-means clustering divides the utliers) . This alinduced) .silhouette and Calinski-Harabasz scores.A mathematical validation with random baseline of the RSKC results has been performed. For each case of study, we generated 1000 random datasets with the same dimension, and we applied RSKC, by fixing The analysis started by data preprocessing , and visualization. The latter has been performed by using the Uniform Manifold Approximation and Projection (UMAP), a nonlivs. GBM’ (case A), ‘Astrocytoma vs. Oligodendroglioma’ (case B), and ‘Astrocytoma vs. Oligodendroglioma vs. GBM’ (case C).Three case studies were created to allow the comparison of different glioma subtypes, namely, ‘LGG RSKC [L1 has been considered in L1 lead to stronger regularization). To set the number of expected clusters K, we observed that the defined cases of study contain two glioma types in case A and B, and 3 glioma types in case C. However, in case C, astrocytoma and oligodendroglioma cases could be also considered as unique class (LGG), so we decided to test silhouette score [Calinski-Harabasz index [The following step consisted of applying JGL to all three cases. JGL was applied using the R package JGL . For cas authors . Given tthe RSKC , by testte score  and the sz index , widely sz index , 49–52. The datasets and R code used for this study will be made available upon request.A first visual inspection of glioma transcriptomics data was performed in a 2-dimensional space obtained via UMAP, in order to capture potential preexisting patterns. In this representation Fig. , we can Figure vs. GBM’ case , but most of the estimated connections are exclusive for LGG (n = 14) and GBM (n = 6). A large subnetwork can be observed on the right hand side, containing 10 genes and both exclusive (green and blue) and shared connections between LGG and GBM (yellow). The genes included in this subnetwork are TMEM125, ERMN, GJB1, CARNS1, KLK6, MAG, MOG, MBP, MOBP and CNDP1. Half of them are involved in relations which are common to the two classes, while CNDP1 is exclusive to GBM, and TMEM125, ERMN, GJB1, and CARNS1 are nodes in the LGG network.For the ‘LGG ase Fig. A the algvs. Oligodendroglioma’ case . There are only a few edges exclusive to one of the two subtypes, namely n = 9 for astrocytoma (green) and n = 1 for oligodendroglioma (blue). The network highlights the presence of a large subnetwork on the right hand side, represented by genes BUB1B, CENPF, TPX2, AURKB, BIRC5, BUB1, CKAP2L, FAM64A, GTSE1, HJURP, KIFC1, MKI67, NCAPG, NCAPH, NUSAP1, PBK, TOP2A, TROAP, TTK and UBE2C. All these genes are involved in relations described in both datasets, except for BUB1B, CENPF, TPX2, which are exclusive to astrocytoma.The network obtained for the ‘Astrocytoma ase Fig. B is compvs. Oligodendroglioma vs. GBM’ case , and by all three subtypes . Only one edge is shared between GBM and astrocytoma (green), as well one edge has been estimated only in GBM dataset (yellow). There are no exclusive edges of astrocytoma or oligodendroglioma, and shared edges between oligodendroglioma and GBM. A subnetwork of shared edges can be observed, composed by the following genes: TMEM125, ERMN, GJB1, MOG, CARNS1, KLK6, MAG, MBP, and MOBP.The ‘Astrocytoma ase Fig. C resultshubs, are listed in Table For each case, the 5 genes with the highest number of connections were selected. These genes, referred to as RPSA and RPSAP58 appears as potentially relevant for GBM. On the other hand, two subnetworks related to LGG are detected, i.e., the one constituted by PBK, FAM64A and KIFC1, and the one involving UBE2C and AURKB. While the role of RPSA in GBM has not yet been investigated, the LGG genes we detected are all known in the context of glioma [UBE2C and AURKB genes on glioma histology [To further explore the estimated joint networks we focused on case C, i.e., the one considering the three glioma types. Figure f glioma –59. Inteistology , which iK and L1). For all combination of parameters, the best performance was obtained for silhouette and the Calinski-Harabasz scores, which have been calculated by considering all cases, including the ones that the method identified as outliers. Larger values of the silhouette were obtained when removing the outliers from the dataset, as expected , the identified clusters support the defined glioma types, since cluster 1 and 2 are mainly composed by LGG and GBM cases, respectively. In case B, clustering places the majority of oligodendroglioma samples into cluster 2, while cluster 1 is mainly composed by astrocytoma samples. However, K = 2), while in cases B and C (K = 3) are associated to very low values.To quantify how much the identified clusters are in agreement with the diagnostic labels, we computed the Average Rate Index (ARI) in each case of study, by considering the combination of parameters leading to the best results. ARI score provides a measure of how much the clusters agree or disagree with the known labels, by varying in a range of entclass1pt{minimaL1 = 2. We observed that, for K = 2, the silhouette score computed by considering the complete dataset with was totally comparable with the one related to cases A and C . In all these cases, the values are higher than 0.7  we are able to slightly improve the quality of clustering (Table SK = 3) is considerably low , the one computed for the clustering taking into account the complete set of variables was very close to the random assignment . Overall, clustering results have been used as a validation of JGL variable selection. Indeed, both the considered scores confirmed good clustering performances, suggesting that a representative subset of genes might have been identified. Clustering outcomes also indicate that the expression of few genes can distinguish different glioma conditions and disclose new groups of patients based on transcriptomics data, since better performances were obtained with lower values of L1. Interestingly, in case C, which compares the three glioma types, the best clustering was obtained by considering only K = 3). Indeed, despite our variable selection provides a slight improvement, this is not enough to obtain a good distinction of the three glioma types. For future studies, it would be interesting to compare the present results with the ones using an updated dataset according to the 2021 classification, to evaluate whether the latest classification yields better separation between known glioma types or if it might reveal new findings. Moreover, multinomial classification models based on transcriptomics data, possibly combined with relevant clinical data  will enable assessing the concordance of the updated glioma classes with the groups here estimated in an unsupervised way, and further evaluating the features explaining the differences between the groups.This work aimed at finding potential biomarkers of glioma heterogeneity. The results obtained confirm that astrocytoma and oligodendroglioma are more similar to each other at a transcriptomics level compared to GBM. In particular, our estimated networks show many common relations between the two LGG subtypes, while GBM shares few edges. The K-means clustering also confirms this outcome, since the lowest Although our study leads to a list of potentially interesting genes, further analysis is necessary to sustain the already performed literature search. Indeed, on one hand, the existence of previous studies about the role of the identified genes in glioma processes can be seen as a preliminary validation, supporting our findings and the great potentiality of this study. On the other hand, the genes that have not been yet described in the context of glioma might be regarded as candidates for experimental validation and therapy research. Biologically testing the most promising candidates will be the natural next step to validate their role in the genesis, development, and progression of glioma.Additional file 1. Supplementary Material.


The rapid development of single-cell transcriptomics has revolutionized the study of complex tissues. Single-cell RNA-sequencing (scRNA-seq) can profile tens-of-thousands of dissociated cells from a tissue sample, enabling researchers to identify cell types, phenotypes and interactions that control tissue structure and function. A key requirement of these applications is the accurate estimation of cell surface protein abundance. Although technologies to directly quantify surface proteins are available, these data are uncommon and limited to proteins with available antibodies. While supervised methods that are trained on Cellular Indexing of Transcriptomes and Epitopes by Sequencing data can provide the best performance, these training data are limited by available antibodies and may not exist for the tissue under investigation. In the absence of protein measurements, researchers must estimate receptor abundance from scRNA-seq data. Therefore, we developed a new unsupervised method for receptor abundance estimation using scRNA-seq data called SPECK (Surface Protein abundance Estimation using CKmeans-based clustered thresholding) and primarily evaluated its performance against unsupervised approaches for at least 25 human receptors and multiple tissue types. This analysis reveals that techniques based on a thresholded reduced rank reconstruction of scRNA-seq data are effective for receptor abundance estimation, with SPECK providing the best overall performance.https://CRAN.R-project.org/package=SPECK.SPECK is freely available at Bioinformatics Advances online. Transcriptome profiling has conventionally been performed using RNA sequencing (RNA-seq) of bulk tissue samples  tool . Similar to ALRA, the SPECK method utilizes a singular value decomposition (SVD)-based RRR but includes a novel approach for thresholding of the reconstructed gene expression matrix that improves receptor abundance estimation. A second important contribution of this article is a comprehensive evaluation of unsupervised receptor abundance estimation performance across at least 25 human cell surface receptors and multiple tissue types.m cells and n genes in a m × n matrix of scRNA-seq counts using the procedure outlined below. See The SPECK method estimates abundance profiles for Algorithm 1 SPECK Algorithm1: Rank-k Selection and Singular Value Decomposition2: 3: 4: 5: 6: 7: 8: Clustered Thresholdingforn do        ▹ Threshold each gene.9: 10:   11:   ifthen12:   13:    14:    end if15:   end for16: Given a k was then selected to represent a numeric value, ranging from 1 to 100, for which the absolute value of the difference between consecutive standard deviation estimates was at least 0.01 for two or more estimate pairs. Although this rank selection procedure is a heuristic method, motivated by the commonly used elbow method for determining the number of principal components, we find that it works well in practice. The rsvd-based decomposition was subsequently used to generate a rank k reconstruction of the To perform the RRR, we leveraged the randomized SVD algorithm implemented in the rsvd R package , which compares with O(qknp) for standard k-means algorithm, where q defines the number of iterations and p specifies the dimensionality  clustering algorithm from the Ckmeans.1d.dp package  to perfoionality . We seleComparative evaluation of the SPECK method was performed against four other approaches described below, which include three unsupervised approaches and one supervised receptor abundance estimation strategy.k, given an upper bound of k<100, such that the gap between consecutive singular values ks is significantly different from the mean and standard deviation of typical noise spacings, defined to be ALRA: Receptor abundance was estimated using the imputed value of the associated transcript generated by the ALRA method with v.1.0.0  that contains 32 648 cells profiled with 102 mouse antibodies. Each dataset was individually processed using Seurat v.4.1.0   for a large set of human receptors. In addition, we evaluated SPECK using the Mouse Spleen and Lymph Nodes dataset for ∼100 receptors, which further indicates SPECK’s potential as a receptor abundance estimation strategy for both human and the mouse specimens. This comparative evaluation demonstrates that SPECK generates more accurate receptor abundance estimates over the RRR-based imputation methods, including ALRA and MAGIC, or the direct use of normalized RNA transcript.An important contribution of SPECK is a novel strategy for cluster-based thresholding of the reconstructed gene expression values. Our proposed thresholding mechanism differs from existing thresholding schemes, e.g. the ALRA thresholding approach, in two ways. First, our strategy does not always threshold a gene, and, second, it does not necessarily apply the same quantile to threshold each gene, thereby enabling recovery of more accurate, estimated abundance profiles. A second important contribution of this work is an extensive evaluation strategy for benchmarking the effectiveness of unsupervised methods for estimating receptor abundance using scRNA-seq data. With comparisons performed across multiple datasets from different tissue sources and species, this evaluation strategy provides considerable information on the relative performance of unsupervised methods across a wide range of receptors.One limitation of our proposed approach is that SPECK is not necessarily the best abundance estimation strategy for all receptors. For example, SPECK produces a negative correlation value for CD69 for both the PBMC and the BMMC datasets as indicated by In conclusion, SPECK is a promising approach for unsupervised estimation of surface receptor abundance for scRNA-seq data, which addresses limitations of existing imputation methods, such as ALRA and MAGIC. The cell surface receptor abundance profiles generated by SPECK have important scientific utility for the analysis of single-cell data with specific relevance to the identification of the cell (sub)types, cell phenotypes and cell–cell signaling present in a tissue. Improved support for these single-cell analysis tasks will have a meaningful impact on basic research supporting precision medicine applications, especially in the immunology domain.vbad073_Supplementary_DataClick here for additional data file.


Correlation metrics are widely utilized in genomics analysis and often implemented with little regard to assumptions of normality, homoscedasticity, and independence of values. This is especially true when comparing values between replicated sequencing experiments that probe chromatin accessibility, such as assays for transposase-accessible chromatin via sequencing (ATAC-seq). Such data can possess several regions across the human genome with little to no sequencing depth and are thus non-normal with a large portion of zero values. Despite distributed use in the epigenomics field, few studies have evaluated and benchmarked how correlation and association statistics behave across ATAC-seq experiments with known differences or the effects of removing specific outliers from the data. Here, we developed a computational simulation of ATAC-seq data to elucidate the behavior of correlation statistics and to compare their accuracy under set conditions of reproducibility.R and Spearman’s RRUsing these simulations, we monitored the behavior of several correlation statistics, including the Pearson’s Collectively, this study demonstrates how measures of correlation and association can behave in epigenomics experiments. We provide improved strategies for quantifying relationships in these increasingly prevalent and important chromatin accessibility assays. Epigenetic modifications play an important role in regulating multiple cellular processes ranging from DNA replication to gene expression. These covalent additions to DNA and histone proteins do not alter the underlying DNA sequence, but rather, help modulate chromatin structure resulting in distinctive phenotypes. Genome-wide epigenetic modifications can be determined using several techniques: the gold-standard is chromatin immunoprecipitation followed by sequencing (ChIP-seq) –3. ChromTo ensure significance and consistency of identified peaks, best practices have been defined for quantifying reproducibility across experimental replicates , 10. TheR or the coefficient of determination  followed by the Top–Down statistic  between samples. For these analyses, additional experiments were downloaded from the ENCODE project public repository . These iRRRRRRp-value After removing co-zeros, the mentclass2pt{minimRRRRp-value To quantify which statistic  via normalized mutual information with binned, Fpkm counts rounded to the nearest whole integer, after the removal of co-zero values as input. In choosing a correlation statistic, after removing co-zero values, our results indicate little difference in the outputs from the Pearson’s As part of this study, we generated highly correlated, new ATAC-seq experimental replicates of the A549 cell line. Our data highly correlates with previously published ATAC-seq data of the A549 cell line generated by the ENCODE project. Using these data, we generated a novel simulation that utilizes down sampling to generate replicates with known varying signals. While similar simulation studies have been conducted on Hi-C sequencing data , to our In our simulations, we observed that most statistics overestimate the correlation of signal between replicates. One specific strategy we investigated to reduce this inflation was the removal of co-zeros, which is an option present in several bioinformatic software suites , 31, 34.In epigenomics and chromatin accessibility data sets, biological interpretation of the data is dependent upon visualization of “peaks” where accumulation of sequenced reads denotes the presence of a modification or an accessible region. Regions with zero (or nearly zero) aligned sequenced reads are deemed unmodified or inaccessible and largely ignored when interpreting data. Correlation statistics should provide biologists with the confidence that replicates are truly comparable. As stated above, the inclusion of co-zeros seems to inflate values of most correlation and association statistics. Thus, removal of co-zeros formed by the genomic bins that overlap and account for inaccessible regions may be warranted.RRUsing our simulation, we also examined the behavior of three association statistics, which we distinguish from the set of correlation statistics as those metrics ranging in value from zero to one. These association statistics were the Curiously, Kendall’s W displayed the least sensitivity to the designed peak counts between synthetic replicates. This statistic was of interest given Kendall’s W is capable of simultaneously examining the ranks of more than two input samples , 50. Thiychology , 44. Forunctions .We also examined the effect of dropping co-zeros when estimating correlation between real ATAC-seq and ChIP-seq samples. Much like our results from analysis on simulated ATAC-seq replicates, expunging co-zero values from correlation (and association) calculations reduced the value of the reported statistics between real samples. These effects were primarily seen in the correlation and association scores calculated between non-replicates within the examined assays. In particular, the correlation and association values between true H3K27ac and H3K4me3 replicates were unaffected by eliminating co-zeros. These correlation scores were high and remained high after excising co-zeros from calculations. This may be due to higher overall signal in these assays. Importantly, omitting co-zeros from analysis produced a larger difference in the average correlation between groups of replicates and non-replicates. Thus, excluding co-zeros from analysis is an important step for quality control procedures looking to identify errant samples.ROf the statistics examined here, the genetics –57. Regagenetics , 59. Forgenetics .To perform correlation and association analyses as seen here, we have generated python code and an executable for public use. These software, installation instructions, and a tutorial written as a jupyter notebook are hosted on the Github listed within the data availability section. We hope these tools will benefit investigators and students in their exploration of the mutual information statistic and the effect of excluding co-zero values in their epigenetic data.Sparsity and zero mapped sequenced reads are not unique properties of ATAC-seq data. These extend to genomic, Hi-C, ChIP-seq, and RNA-seq data sets. Imputation along with modified zero-inflated models have been used with success for studying RNA sequencing data sets and detecting regions with differential expression . SimulatFor this study, we produced eight ATAC-seq experiments using the A549 Cancer cell line. Across replicates, these ATAC-seq samples are well correlated and reproducible. For investigations of chromatin accessibility (particularly in the A549 cell line), these experiments are an additional resource for developing analysis pipelines, peak detection algorithms, and machine learning approaches.R, Spearman’s RLeveraging the A549 ATAC-seq experiments, we designed a computational simulation to generate simulated replicates. Specifically, synthetic replicates were coded that share a known, fixed portion of significantly enriched loci. Using these replicates, correlation metrics—the Pearson’s Removing specific outliers from ATAC-seq data, specifically the removal of co-zeros, improved estimates of correlation and association. We estimate that co-zero values, when comparing WFpkm counts between two real ATAC-seq experiments, occupy nearly five percent of a bi-variate distribution. While only a small portion of the total data, filtering these values from analysis greatly improves the measurements of most correlation and association statistics between samples, in simulation. Applied to real ATAC-seq and ChIP-seq data, removing co-zero values from comparison significantly reduced the reported correlation and association statistic, matching results from simulation.ROne of the association statistics examined here is normalized mutual information, an information theoretic approach that is less well known across the (epi)genomics field. After removing co-zero values, normalized mutual information displayed the lowest inflation relative to the similarity between simulated replicates. The ATAC-seq experimental libraries were generated using A549 human lung carcinoma epithelial cells  –65. ThreATAC-seq libraries were sequenced at the sequencing facility at Los Alamos National Laboratory on an Illumina NextSeq2000 sequencer in paired end mode (PE151) using P3 chemistry. With Fastp, raw reads were trimmed and filtered to remove Nextra adaptors and reads with repetitive sequences . Additioersion 2  via bwa ersion 2 . After aRaw ATAC-seq data, in the form of paired fastq.gz files, was downloaded from the ENCODE project for the A549, HepG2, RWPE2, GM12878, IMR-90, K562, and WTC11 cell lines . The ENCp-value For ChIP-seq experiments, twenty and ten assays of the H3K27ac and H3K4me3 epigenetic modifications (respectively) were downloaded  from the ENCODE project as raw alignments in bam file format. The ENCODE accession numbers of these files are listed in Additional file After filtering, sample alignments were analyzed to identify loci displaying significant enrichment of paired-end reads. This peak calling was conducted using MACS2 , 71. Spe-F 4 -F 256 -F 512 -F 1024 -F 2048 -q 30 and then passed to MACS2 in BAMPE mode , 73.Between true, biological replicates, reproducible peaks were identified via irreproducible discovery rate thresholding . Using Cplicates . In addiFor each of the eight ATAC-seq experiments of A549 cells generated in this study, synthetic replicates were generated by duplicating a given sample into two copies and then randomly, varying the total number of shared peaks between them. Specifically, for a given ATAC-seq experiment, a set portion of peaks was chosen at random, such that within one of the synthetic replicates, a given selected peak was depleted, randomly removing a portion of the alignments within the peak bounds (as defined by MACS2). These sets of peaks were randomly selected from the set of reproducible peaks for that sample and its associated biological replicates (see above). Three sets of simulations were conducted, removing 50, 85 and 95% of reads within selected peaks. This procedure results in two synthetic ATAC-seq replicates, generated from a single, true parent ATAC-seq data set. These synthetic ‘sister’ ATAC-seq data sets have identical genome-wide alignments except within a sub-set of loci that vary between them. From each true ATAC-seq data set, synthetic sister replicates were generated by varying the total percentage of shared peaks from 99 to 5%, with a delta of 5%. For each simulation, across the change in portion of shared peaks, a common random seed was used to preserve autocorrelation across this axis. This process was repeated fifteen times for each of the eight, A549 ATAC-seq samples, totaling a one hundred and twenty simulations.On both synthetic samples from simulation studies or replicates from (true) ATAC-seq experiments, a genomic binning approach was used to estimate correlation and association statistics between samples. For each chromosome, contiguous bins were established 5’–3’, every ten kilobases. Within each of these bins, the number of sequenced fragments is counted and standardized to fragments per kilobase per million. These counts were rounded up to their nearest whole integer generating standardized counts of whole fragments per kilobase per million (WFpkm).R, Spearman’s RR. The normalized mutual information statistic from pythons sklearn module [In python scripts, using the scipy-stats module , the Pean metric  and Kendn metric , 50 weren module  was usedR correlation statistic was calculated on WFpkm values between replicates with co-zeros removed. Similarly, co-zeros were removed prior to calculating correlation and association statistics between replicates of ATAC-seq data downloaded from the ENCODE project public repository.For correlation analysis on ATAC-seq experiments conducted here using A549 cells, the Pearson’s p-value. A significance level of 0.05 was used to reject the null hypothesis, HAcross simulations, values of correlation and associations statistics were calculated as a function of the designed portion of peaks between synthetic replicates. For each statistic tested, the 95% confidence interval of the average area under the curve was calculated via bootstrapping, with a thousand iterations. This was done for statistical profiles from simulations with and without co-zero values. For comparisons of the average area under the curve, either between statistics or within the same statistic after removing co-zeros, one thousand permutations were used to calculate the null distribution of the difference between the mean area under the curve . The proRA random forest model was built in python using the scikit learn module , 47. AssFor the testing and training of the model, test and training sets of the classes defined above were selected using a stratified, 40:60 split of the data. Additionally, ten-fold, stratified cross validation was used to train and test the model . A hundrAdditional file 1: Figure S1. Boxplots displaying the area under the curve (y-axis) across statistics (x-axis) with co-zeros retained and removed from analysis .Additional file 2: Figure S2. Bi-variate plot of WFpkm counts (across 10 kb genomic bins) between replicates of real, A549ATAC-seq experiments. Dark red to blue colors and marker size designate the density (log10 (WFpkmcounts)) of counts between replicates. Co-zero values appear as an orange dot in lower left corner. A dashedgrey line represents a one-to-one relationship between the two replicates.Additional file 3: Figure S3. The percent of co-zero values in bi-variate WFpkm distributions between real ATAC-seq experiments.Sample names are annotated along the x- and y-axis.Additional file 4: Figure S4. Correlation and association values (y-axis) as a function of percentage of shared peaks betweensynthetic replicates (x-axis). Red and grey curves depict the mean and 95% CI (respectively) values acrosssimulations. A grey, dashed line marks a one-to-one relationship between the x- and y-axis. Left and rightcolumns display change in values as a function of removing co-zeros. Results are from simulations with 50%paired reads within selected peaks removed.Additional file 5: Figure S5. Correlation and association values (y-axis) as a function of percentage of shared peaks betweensynthetic replicates (x-axis). Red and grey curves depict the mean and 95% CI (respectively) values acrosssimulations. A grey, dashed line marks a one-to-one relationship between the x- and y-axis. Left and rightcolumns display change in values as a function of removing co-zeros. Results are from simulations with 95%paired reads within selected peaks removed.Additional file 6: Figure S6. Correlation and association statistics across epigenomic experiments. For samples from AATAC-seq and ChIP-seq (assays for B H3K27ac and C H3K4me3 modifications) experiments, the Spearman’sρ, Pearson’s R, R2 coefficient, and normalized mutual information  were calculated on WFpkm counts between replicates, with (blue) and without co-zeros (orange).Additional file 7: Figure S7. The coefficient of determination (R2) versus the normalized mutual information  calculated on binned counts of WFpkm between ATAC-seq experiments. Blue triangles, orangeXs, and green circles mark comparisons between independent experiments, between independent experimentsusing the same cell line, or true experimental replicates, respectively.Additional file 8: Figure S8. The f1-scores, recall, and precision of the random forest model with ten-fold, stratified cross validation. Blue, orange, and green colorsdenote experimental relationship class.Additional file 9: Table S1. Read counts of ATAC-seq experiments.Additional file 10: Table S2. Fragment counts of ChIP-seq experiments from the ENCODE project.Additional file 11: Table S3. Difference of mean correlation and association values between replicates and non-replicates.