Multi-omics assays offer even greater opportunities to understand cellular states and biological processes. The problem of integrating different omics data with very different dimensionality and statistical properties remains, however, quite challenging. A growing body of computational tools is being developed for this task, leveraging ideas ranging from machine translation to the theory of networks, and represents another frontier on the interface of biology and data science. Our goal in this review is to provide a comprehensive, up-to-date survey of computational techniques for the integration of single-cell multi-omics data, while making the concepts behind each algorithm approachable to a non-expert audience.Recently developed technologies to generate  Single-cell sequencing technologies have opened the door to investigating biological processes at an unprecedentedly high resolution. Techniques such as Drop-seq Recently, however, a number of experimental techniques capable of assaying multiple modalities simultaneously from the same set of single cells have been developed. Cellular indexing of transcriptomes and epitopes by sequencing (CITE-seq) The application of data fusion algorithms for multi-omics sequencing data predates single-cell technologies; bulk-level data have been integrated using a variety of computational tools as reviewed previously e.g., neural network)-based methods, and network-based methods. The scheme of these methods is illustrated in The integration methods for multi-modal data assayed from the same set of single cells can be conceptualized as “vertical integration”, which was mentioned in an earlier review Xi  then matrix factorization decomposes it as the product of a shared matrix H across all omics data types, and omics-specific matrix Wi , together with random noise εi  as:Matrix factorization-based methods aim to describe each cell as the product between a vector that describes each omics element  and a vector of reduced and common features (factors) capturing its basic properties A. MathemSuch methods are simple and easily interpretable since the cell and omics factors can be associated with omics features, but may lack the ability to capture nonlinear effects. We describe the variations in this type of method below. MOFA+ Single-cell aggregation and inference (scAI) X1 represents the transcriptomic data, X2 represent the epigenomic data, H is the common (cell-specific) factor matrix, W1 and W2 are the assay-specific factor matrices, Z is the cell–cell similarity matrix, and entries of R are Bernoulli-distributed random variables, and hyperparameters X2 (Z・R), rather than directly factoring the epigenetic data X2. After the learning is complete, the matrix of cell factors is used to cluster the cells and the importance of genes and epigenetic marks is ranked using the magnitude of the values in loading matrices. In order to jointly visualize different factors, scAI implements a novel VscAI algorithm utilizing Sammon mappings Here Although neural networks are generally well-suited for supervised tasks, a class of neural networks called autoencoders is commonly used for unsupervised learning, such as the multi-omics integration problem in single cells. Deep autoencoders perform nonlinear dimensionality reduction by squeezing the input through a lower-dimensional hidden layer (bottleneck) and attempting to reconstruct the original input as the output of the neural network B. They cSingle-cell multimodal variational autoencoder (scMVAE) This model incorporates the task of constructing shared representations of the multi-modal data with clustering. Namely, one of the latent variables is constructed to correspond to the cluster identifier. Furthermore, the model incorporates tools to deal with tasks such as data imputation and can be used for studying the association between epigenetics and gene expression. scMVAE was applied to integrate two real datasets assaying mRNA and chromatin accessibility using SNARE-seq method, as well as simulated data generated by Splatter Deep cross-omics cycle attention (DCCA) model is another method in this category for joint analysis of single-cell multi-omics data totalVI LIBRA vice versa.BABEL BABEL provides a promising generic framework for multi-omics inference at a single-cell level from single-omics data, by using the model that was previously trained on multi-omics data sequenced from the same single cells. The modular nature of BABEL provides additional flexibility, as the model can be extended to work with additional modalities when the corresponding data becomes available. Despite the potential for generalization, one should be cautioned that if the training is conducted on cell types that are very different, the transfer learning using BABEL is not very successful.DeepMAPS Network-based methods represent the relationships between different cells using a weighted graph, where cells serve as nodes C. IntegrciteFUSE Joint diffusion k nearest neighboring nodes. Cell-specific coefficients determining the relative importance of different omics are then learned by considering the accuracy of inter-modality and cross-modality predictions by nearest neighbor graphs. Lastly, a linear combination of data from different omics is done, using the coefficients learned in the previous step. The nearest neighbors with respect to those linear combinations are then connected to build the WNN graph. Seurat v4 was applied to a CITE-seq-based transcriptomic and proteomic dataset, and several other datasets involving mRNA, proteins, and chromatin accessibility. The authors compared this method with MOFA+ and totalVI, using correlations (Pearson and Spearman) between the data corresponding to a cell and the average of its nearest latent space neighbors, and claimed that it performed better than MOFA+ or totalVI.Seurat v4 BREM-SC SCHEMA Compared to multi-omics data, it is experimentally much easier to obtain multiple modalities of data where each modality is obtained from similar but different cells of the same tissue. The task to harmonize these data is called alignment , and it Clonealign MUSIC Manifold alignment methods aim to infer a lower-dimensional structure within multiple complex datasets B. Once tMATCHER Maximum mean discrepancy-based manifold alignment (MMD-MA) t-distributed stochastic neighbor embedding (t-SNE) Distance-based matching methods represent a class of methods performing unsupervised alignment of different omics datasets by matching the structure of the datasets . RepreseLimited benchmarking was performed in the original studies in the distance-based matching methods. UNION-Com compared favorably with Seurat v3 and MMD-MA when evaluated on the quality of labels transferred between gene expression, methylation, and chromatin accessibility data Neural networks, including autoencoders and generative adversarial networks (GAN), have been used for the unsupervised task of the alignment of omics datasets. Autoencoders have been described earlier. GANs typically consist of two parts: the generator network and the discriminator network. The generator tries to produce outputs of a form resembling a certain target dataset, and the discriminator is optimized to learn the difference between the generator’s outputs and the elements of the target dataset. In this section, we summarize the relevant neural network methods below.SCIM MULTIGRATE MAGAN Some of the methods previously developed for aligning different scRNA-seq datasets, could in principle be repurposed for single-cell multiple omics alignment as well. In such cases, different omics data are aggregated over genes and converted into gene activity scores, sharing the same format with scRNA-seq data. Here we cover two of such methods, LIGER and Seurat, due to their wide popularity. A caveat of this approach is the lack of the ability to individually model the omics data. Due to the space limitation, we recommend readers to earlier benchmark studies . Seurat v3 Canonical correlation analysis (CCA) based methods reduce the dimensionality of data by selecting the degrees of freedom that are correlated between the datasetsLIGER The landscape of experimental techniques for omics sequencing and analyzing the data has grown significantly in the last few years. Accompanying the thrust of technological advancement, an increasing body of computational methods to handle multi-omics data integration or alignment have been proposed. Geared toward computational biologists and genomics scientists, here we reviewed in-depth and extensively these computational methods by their working principles. Among these methods, AI and machine learning-based methods account for the majority, demonstrating the influence in single-cell computational biology. Other approaches using matrix factorization and Bayiean’s methods have also been proposed. As demonstrated in a range of methods, the integration of multi-omics data at the single-cell level improves the quality of downstream biological interpretation steps, such as clustering. With the advent of technologies for sequencing multi-omics data from the same single cells, efficient multi-omics integration methods to provide further biological and medical insights at larger scales will be in continued demand.etc., and as a result, careful consideration of these steps and their impacts on the model performances is needed. Oftentimes, the integration methods were developed with one specific application/assay in mind, generalization of these methods with the emergence of new technologies needs to be demonstrated. Fortunately, some benchmarking studies have been conducted in other sub-fields of single-cell computational biology for references, such as those focused on the integration of data from different cells and atlas study Meanwhile, the rapidly growing number of computational methods pose an urgent need for benchmarking studies on their performances, in order to provide guidelines to choose appropriate methods for specific datasets. Current comparisons are either incomplete or using a small set of benchmark datasets, with inconsistent metrics in various studies, impeding the selection of appropriate methods for the dataset to analyze. This is made more difficult by the generally unsupervised nature of the integration task, where commonly required ground truths are not known for certain. Moreover, different methods have different prerequisites regarding preprocessing steps, normalization, e.g., hematoxilin and eosin stain, or H&E image). In the data types with spatial measurements, the spatial relationships need to be considered in addition to the feature matrix. We refer readers to other recent reviews covering this area https://github.com/lanagarmire/multiomics_review_manubot; accessed on July 18, 2022). We encourage the community to contribute to this open document to keep the review up-to-date.Due to the scope, one area that we did not cover in this review is the integration between single-cell omics with other modalities of data. For example, integrative analysis between scRNA-seq and spatial omics data Stefan Stanojevic: Writing - original draft, Writing - review & editing. Yijun Li: Writing - original draft, Writing - review & editing. Aleksandar Ristivojevic: Writing - review & editing. Lana X. Garmire: Supervision, Writing - review & editing. All authors have read and approved the final manuscript.The authors have declared no competing interests.


Weighted gene co-expression network analysis (WGCNA) revealed activation of T cell-mediated response in ER positive samples and Interleukin and Interferons in ER negative samples. WGCNA analysis also identified unique pathways for each individual, suggesting that rare mutations/expression signatures can be used to design personalised treatment.Genetic heterogeneity influences the prognosis and therapy of breast cancer. The cause of disease progression varies and can be addressed individually. To identify the mutations and their impact on disease progression at an individual level, we sequenced exome and transcriptome from matched normal-tumor samples. We utilised DawnRank to prioritise driver genes and identify specific mutations in Indian patients. Mutations in the C3 and HLA genes were identified as drivers of disease progression, indicating the involvement of the innate immune system. We performed immune profiling on 16 matched normal/tumor samples using CIBERSORTx. We identified CD8+ve T cells, M2 macrophages, and neutrophils to be enriched in luminal A and T cells CD4 The routine treatment regime is based on histopathology, TNM  staging, and proliferation index according to the Ki67 and molecular subtype . Even th methods  has led  methods . The use methods , and the methods .Exome-seq data is used to identify variants across the exonic regions of the genome. In contrast, RNA-seq is usually used for expression profiling and to study events like splicing and RNA editing . An inteDawnRank was selected for integrating the exome and transcriptome data. DawnRank is one tool that can give an insight into driver mutations at both levels, patient and overall . This toCancer incidence has been increasing in India, with more female than male cases reported in 2020 . Among fThis study is focused on understanding the molecular mechanisms that govern different breast cancer subtypes through integrating exome and transcriptome data.The breast cancer patient samples used for the study were procured from BGS Global hospital, Bengaluru, Karnataka, India. The patients/participants provided their written informed consent to participate in this study. The tumor tissue and their respective matched normal samples were collected in RNA later. Trizol was added to the samples and stored at −80 °C until further processing. Here, we analysed the exome and transcriptome data obtained from tumor samples of breast cancer patients of Indian origin to understand the underlying molecular mechanism involved. Total RNA was extracted using the standard Trizol method from matched tumors and normal samples. RNA was quantitated using QUBIT, and quality was checked using Tapestation. mRNA libraries were prepared using Illumina TruSeq RNA Library Prep Kit v2 as described . BrieflyTo obtain clean data, filtering was done on raw reads output from the Illumina Hiseq2500 platform. The sequencing depth for each sample was >10 million reads. As described , the quaAs stated before, the samples were collected in RNA Later solution. The tissue was then homogenised in Trizol reagent. After RNA extraction, DNA extraction was done using Back Extraction Buffer (BEB) . BrieflyA total of ~200 ng of genomic DNA isolated from Indian breast cancer patient samples was used as input for library preparation. 260/280 ratio for each sample was calculated, and samples with a ratio of 1.8–2.0 were chosen. dsDNA fragments with 3′ or 5′ overhangs of 150–200 bp (peak size) were generated using Covaris. End repair was done using T4 DNA polymerase and T4 polynucleotide kinase enzyme to generate blunt ends. A total of 3′ ends were then adenylated to prevent them from ligating one another during the adapter ligation reaction. After adapter ligation, enrichment of the DNA library was done . After cThe quality of the data obtained was checked using the FastQC tool. The reads were further processed, aligned and variants were called as detailed in the study mentioned . BrieflyAfter analysing the application of different tools identified from the literature, DawnRank was selected for integrating the exome and transcriptome data . This toTo determine the average immune cell fractions in all the samples using their transcriptome profiles, paired tumor/matched normal samples were used. The immune cell fractions were subsequently compared across the samples using the online tool CIBERSORTx , which hTo correlate gene expression data of samples with their respective subtypes, we used the R package WGCNA . It starp value < 0.05; Here we analysed the data for samples which had both exome-seq and mRNA-seq data. More than 12 million reads with ~60–90% alignment were obtained for mRNA-seq, and more than 29 million reads with ~84–98% alignment were obtained for exome-seq . Tumor aFurther to correlate mutations with expression using DawnRank, exome-seq data was analysed for mutations, and a mutation matrix was created taking all protein-coding mutations. RNA-seq data was processed, and the counts were normalised (TPM), the network data used was the one provided by the authors of DawnRank.HLA-A), nuclear receptors (ex. HNF1A) and kinase activators (ex. CCDN1). They were followed by those involved in catalytic activities such as CDKN1B, a cyclin-dependent kinase inhibitor. The next category of genes consists of transcription regulators and transducers, including EPAS1, POU2F1, TRRAP, HNF1A, HNF4A, PPARG and STAT6. Of these top 60 genes in aggregate result, 26 genes were previously reported in the Cancer Gene Census, of which 11 were present in the gold standard list provided in the tool. These genes and their ranks are shown in The initial analysis was based on the top 60 genes, based on the F1 score, and the precision and recall measures for the Top N genes were reported . These getc.) represented in Exome seq analysis gave a list of different types of mutations summarised in DawnRank ranks mutated genes based on their potential to be a driver gene in cancer. Here, we analysed the top 60 genes for overlapping pathways using GSEA , for whiHLA-A, HLA-B and HLA-C, whereas the major MHC Class II genes include HLA-DP, HLA-DQ and HLA-DR. Three of the HLA genes, HLA-A, HLA-B and HLA-DRB1, were ranked in the top 60 genes and had missense variants across all four samples, as shown in the plot , also known as the Human Leukocyte Antigen (HLA) complex, consists of a group of related proteins that help the immune system to distinguish “self” from “non-self” peptides. The major MHC Class I genes in humans consist of the plot . The preThe HLA-A mutation Q78R belongs to the MHC class I alpha chain domain, as reported in C3 was reported to be downregulated  and possth position. SIFT , identified by an algorithm described in on. SIFT  and Polyon. SIFT ), a commATF1) gene causes a splice region variant, which was observed in all samples reported by id rs4986837. The role of ATF1 in breast cancer has been identified as a tumor suppressor  cells activated, T follicular helper (Tfh) cells, dendritic cells activated, and neutrophils compared to the matched normal was observed. A lower fraction of M1 macrophage was observed in TNBC  and Macrophages.We further performed gene co-expression network analysis to correlate the BC subtypes with the immune microenvironment.p-value < 0.01. Similarly, the MEgreen module is the most significant with 81% correlation in only estrogen positive BC. Among all the subtypes, the highest and most significant correlation was in the TNBC subtype  class I molecules play a vital role as antigen-presenting molecules for cytotoxic T lymphocytes (CTLs), and HLA class II molecules (HLA-DR and HLA-DQ) are essential for peptide presentation to T-helper lymphocytes , migration and invasiveness of tumor cells . The exoCDKN2A was identified as a cancer mutation hotspot. This tells us that the integration of exome and transcriptome data is important to understand the exact impact of genes in cancer. This also suggests that the innate immune system and cell cycle might have a significant role to play in Indian breast cancer.ATF1, a reported tumor suppressor , carriedCancer’s well-known hallmarks are immune modulation, selective growth and proliferative advantage . Based ovs the Indian cohort. γδT are unconventional T cells that migrate to peripheral tissues and function independently of major histocompatibility complex (MHC)-dependent antigen presentation (The ER status guides the risk of relapse and chemotherapy response. In ER-ve tumors, the presence of CD+ve T cells and activated memory T-cells was associated with a reduced risk of relapse, and neoadjuvant chemotherapy response can be predicted based on the presence of T follicular helper cells . In the entation . γδT exhentation .In ER +ve tumors, M0 macrophage in the TCGA cohort was associated with poor prognosis ; in the The innate immune system has been studied in cancer, and recent research has even established the roles of cytokines in breast cancer progression and invasion . Immunot10.7717/peerj.16033/supp-1Supplemental Information 1Additional data showing interactors and the variantsClick here for additional data file.10.7717/peerj.16033/supp-2Supplemental Information 2Click here for additional data file.10.7717/peerj.16033/supp-3Supplemental Information 3Click here for additional data file.


Therapy resistance in cancer is often driven by a subpopulation of cells that are temporarily arrested in a non-proliferative G0 state, which is difficult to capture and whose mutational drivers remain largely unknown.TP53 integrity and lack the hallmarks of DNA damage repair deficiency, while presenting increased APOBEC mutagenesis. We employ machine learning to uncover novel genomic dependencies of this process and validate the role of the centrosomal gene CEP89 as a modulator of proliferation and G0 arrest capacity. Lastly, we demonstrate that G0 arrest underlies unfavourable responses to various therapies exploiting cell cycle, kinase signalling and epigenetic mechanisms in single-cell data.We develop methodology to robustly identify this state from transcriptomic signals and characterise its prevalence and genomic constraints in solid primary tumours. We show that G0 arrest preferentially emerges in the context of more stable, less mutated genomes which maintain We propose a G0 arrest transcriptional signature that is linked with therapeutic resistance and can be used to further study and clinically track this state.The online version contains supplementary material available at 10.1186/s13059-023-02963-4. Tumour proliferation is one of the main hallmarks of cancer development  and has MYC amplification [Although G0 arrest is a widely conserved cellular state, essential for the normal development and homeostasis of eukaryotes , 19, andfication  or alterfication .Despite these advances, the identification of G0-arrested cells within tumours presents an ongoing challenge due to their scarcity and lack of universal, easily measurable markers for the activation and maintenance of this state. As they are often defined by a lack of proliferative markers , 32, difFurthermore, our understanding of how cancer evolution is shaped by proliferation and G0 arrest decisions is limited. The proliferative heterogeneity of cancer cell populations has been previously described and linked with FAK/AKT1 signalling , but theTo address these challenges, we have developed a new method to reliably quantify G0 arrest in cancer using transcriptomic data, and employed it to characterise this phenomenon in bulk and single-cell datasets from a variety of solid tumours. We describe the spectrum of proliferation and G0 arrest decisions in primary tumours, which reflects a range of stress adaptation mechanisms during the course of cancer development from early to advanced disease. We identify and validate mutational constraints for the emergence of G0 arrest, hinting at potential new therapeutic targets that could exploit this mechanism. We also demonstrate the relevance of G0 arrest to responses to a range of compounds targeting cell cycle, kinase signalling and epigenetic mechanisms in single-cell datasets and propose an expression signature that could be employed to detect treatment resistance induced by G0 arrested tumour cells.We hypothesised that primary tumours contain varying numbers of cells temporarily or permanently arrested in the cell cycle, which reflect evolutionary adaptations to cellular stress and may determine their ability to overcome antiproliferative therapies. To capture this elusive phenotype, we developed a computational framework that would allow us to quantify G0 arrest signals in bulk and single-cell sequenced cancer samples Fig. a. To defTo validate this signature and select the optimal method to score G0 arrest in individual samples amongst different enrichment/rank-based scoring methodologies –43, we uWe further experimentally validated our methodology in nine lung adenocarcinoma cell lines. We estimated the fraction of G0 cells in each of these cell lines using quantitative, single-cell imaging of phospho-Ser807/811-Rb  and 24-There was a remarkably good correlation between our predicted G0 arrest levels based on the expression of these cell lines from the Cancer Cell Line Encyclopedia (CCLE) and the fraction of G0 cells in the experiment as assessed by lack of EdU incorporation over a 24-h period (EdU incorporation only occurs during S phase) but particularly by lack of Rb phosphorylation. Phosphorylation and inactivation of the retinoblastoma protein is often used to define the boundary between G0 and G1 and was specifically shown to distinguish the G0 state recently by Stallaert et al. . FurtherHaving established a robust framework for quantifying G0 cell cycle arrest in cancer, we next profiled 8005 primary tumour samples across 31 solid cancer tissues from The Cancer Genome Atlas (TCGA). After accounting for potential confounding signals of non-cycling non-tumour cells from the microenvironment by correcting for tumour purity see ‘a. While Our score showed strong negative correlations with the expression of proliferation markers Fig. d, suggesTP53 or the components of the DREAM complex, as well as those with higher p21 expression, had elevated G0 arrest levels across numerous tissues  either in slow cycling or fast proliferating tumours Fig. a. Reassu and MYC , 29. We  and MYC , 69. FifFollowing the initial prioritisation of putative genomic constraints of G0 arrest, we employed machine learning to identify those events that could best distinguish slow cycling tumours with higher abundance of G0 arrested cells from fast proliferating ones, while accounting for tissue effects. An ensemble elastic net selection approach similar to the one described by Pich et al.  was applTP53, lack of MYC amplification and lower mutation rates  deletions, one of the frequent early events during cancer evolution [RB1 deletions and amplifications were both associated with a reduction in G0 arrest, which might reflect the dual role of RB1 in regulating proliferation and apoptosis [Overall, the genomic dependencies of G0 arrest mainly comprised genes involved in cell cycle pathways, p53 regulation and ubiquitination (most likely of cell cycle targets), and RUNX3 regulation, which have previously been shown to play a role in controlling proliferation and cell cycle entry   [CEP89 expression was prognostic across multiple cancer tissues  cell line treated with the EGFR inhibitor erlotinib [Similarly, using single-cell data from an rlotinib , we predrlotinib , 13. Furrlotinib , which mThus, G0 arrest appears to explain resistance to broad acting chemotherapy agents as well as targeted molecular inhibitors of the Ras/MAPK signalling pathway, being either selected for, or induced immediately upon treatment, and gradually waning over time as cells start re-entering the cell cycle. Using massively multiplexed chemical transcriptomic data, we also analysed responses to 188 small molecule inhibitors in cell lines at single-cell resolution  Additio: Fig. S9predicting resistance in these studies  and showed comparable profiles of resistance to treatment , as even their definitions can be contentious at times both in the context of human cancers , 107–109X9, RARβ , 113 andThe versatility of our signature is evidenced by high classification accuracies across a variety of solid cancer datasets. More variable performance was observed when applied to haematopoietic stem cells as it was not designed to capture signals in this context  selection of genes with a unidirectional change of expression across all five forms of quiescence; (2) removal of genes involved in other cell cycle stages included in the ‘KEGG_CELL_CYCLE’ gene list deposited at MSigDB; (3) removal of genes showing low standard deviation and low levels of expression within the TCGA dataset, or which showed low correlation with the pan-cancer expression of the transcriptional targets of the DREAM complex, the main effector of quiescence, in TCGA. The resulting 139-gene signature is presented in Additional file Differential expression analysis results comparing cycling immortalised, non-transformed human epithelial cells and cells in five different forms of quiescence  were obtained from Min and Spencer . A totalg steps:  selectiop-value cut-off of 0.05. The gene lists were subjected to filtering steps 2 and 3 described above. Following the refinement steps, 10 upregulated and 10 downregulated genes with highest log2 fold changes were selected for each stress response type.Gene lists representing spontaneous quiescence, contact inhibition, serum starvation, CDK4/6 inhibition and MEK inhibition programmes were obtained using genes differentially expressed in each individual quiescence form using an adjusted GSVA R package was used to implement the combined Z-score [singscore R package. In addition to these, we also calculated a mean scaled G0 arrest score based on the refined list of genes upregulated and downregulated in quiescence, as well as a curated housekeeping genes from the ‘HSIAO_HOUSEKEEPING_GENES’ list deposited at MSigDB, as follows:The  Z-score , ssGSEA  Z-score  and GSVA Z-score  gene set Z-score  was implG0m = mean scale G0 arrest scoreGU = expression of genes upregulated in quiescenceGD = expression of genes downregulated in quiescenceGH = expression of housekeeping genesn = number of genes in each gene setG0 arrest scores for the TCGA cohort were derived from expression data scaled by tumour purity estimates. The pan-cancer TCGA samples were also classified into groups with ‘high’ or ‘low’ levels of G0 arrest based on k-means clustering (k = 2) on the expression data of 139 G0 biomarker genes, following the removal of tissue-specific expression differences using the ComBat function from the sva R package [ package .We employed the GSE124109 dataset from Fujimaki et al.  where raSingleCellExperiment [scater [scran [Datasets were obtained from the ArrayExpress and Gene Expression Omnibus (GEO) databases though the following GEO Series accession numbers: GSE83142, GSE75367, GSE137912, GSE139013, GSE90742 and E-MTAB-4547. Quality control analysis was standardised using the periment  and scat [scater  R packagr [scran  R packagGeoTcgaData R package. All normalised datasets were log-transformed before further analysis.Datasets were obtained from the GEO database through the following GEO Series accession numbers: GSE93391, GSE114012, GSE131594, GSE152699, GSE124854, GSE135215, GSE99116, GSE124109, GSE61130, GSE64553 and GSE63577. GSE114012 count data were normalised to TPM values using the plotROC R package.The accuracy with which the G0 arrest scoring methods could separate proliferating and quiescent samples within the validation datasets was determined by calculating the area under the curve of the receiver operating characteristic (ROC) curves, using the The average fraction of cancer cells spontaneously entering quiescence was estimated for nine lung adenocarcinoma cell lines  using EdU and phospho-Rb staining proliferation assays.2. To calculate the quiescent fraction, A549 and NCIH460 cells were plated at a density of 500 cells/well, and all other cell lines at a density of 1000/well, in 384-well CellCarrier Ultra plates (PerkinElmer) in the relevant media. Twenty-four hours later, 5 μM EdU was added and cells were incubated for a further 24 h before fixing in a final concentration of 4% formaldehyde , permeabilization with PBS/0.5% Triton X-100  and blocking with 2% BSA in PBS . The EdU signal was detected using Click-iT chemistry, according to the manufacturer’s protocol (ThermoFisher). Cells were also labelled for phospho-Ser807/811 Rb (phospho-Rb) using Rabbit mAb 8516 (CST) at 1:2000 in blocking solution, overnight at 4 °C. Unbound primary antibody was washed three times in PBS and secondary Alexa-conjugated antibodies were used to detect the signal . Finally, nuclei were labelled with Hoechst 33258  before imaging on a high-content widefield Operetta microscope, 20 × N.A. 0.8. Automated image analysis  was used to segment and quantify nuclear signals in imaged cells. Quiescent cells were defined by the absence of EdU or phospho-Rb staining, determined by quantification of their nuclear expression . NCIH358, NCIH1299 and NCIH1563 were maintained in RPMI-1640 (Gibco) supplemented with 5 mM sodium pyruvate and 0.5% glucose. NCIH1944, NCIH1666, NCIH1650 and L23 were grown in RPMI-1640 ATCC formulation (Gibco). A427 were cultured in EMEM (ATCC). A549, NCIH460, H358, NCIH1299, NCIH1563, and A427 were supplemented with 10% heat inactivated FBS. NCIH1666 with 5% heat-inactivated FBS and all other cell lines with 10% non-heat inactivated FBS. All cell lines had penicillin–streptomycin (Gibco) added to 1%. Cells were maintained at 37 °C and 5% COEndogenous PCNA was labelled at the N-terminus with a cDNA encoding mRuby in both A549 and NCI-H1944 cells, using AAV-mediated gene-targeting, according to methods described in Zerjatke et al. [The G0 arrest scores for cancer cell lines were calculated using corresponding log-transformed RPKM normalised bulk RNA-seq data from the Cancer Cell Line Encyclopedia (CCLE) database .CEP89 was depleted by ON-Target siRNA Pool from Horizon. NCI-H1299 cells were reverse transfected in 384-well plates with 20 nM of non-targeting control (NTC) or CEP89-targeting siRNA using Lipofectamine RNAiMax (ThermoFisher), according to the manufacturer’s instructions. Cells were left for 24 h, before 5 μM EdU was added for the final 24 h and then cells were processed as above to determine the quiescent fraction. To determine the level of Cep89 depletion by western blot, cells were reverse transfected with siRNA in 24-well plates. Forty-eight hours after transfection, cells were lysed directly in 1 × SDS sample buffer with 1 mM DTT (ThermoFisher). Samples were separated on pre-cast 4–20% Tris-Glycine gels, transferred to PVDF using the iBlot2 system and membranes blocked in blocking buffer (5% milk in TBS) for 1 h at RT. The membrane was then cut and the upper half was incubated in 1:1000 Cep89 antibody , the bottom half in B-actin antibody 1:2000  diluted in blocking buffer overnight at 4 °C. Membranes were washed three times in TBS-0.05% TritonX-100 before being incubated in secondary anti-rabbit (Cep89) or anti-mouse (B-actin) HRP conjugated antibodies  diluted 1:2000 in blocking buffer for 1 h at RT. Membranes were washed three times again and signal detected using Clarity ECL solution (BioRad) and scanned on an Amersham ImageQuant 800 analyser.TCGABiolinks R package [FPKM normalised RNA-sequencing expression data, copy number variation gene-level data, RPPA levels for p27 as well as mutation annotation files aligned against the GRCh38 human reference genome from the Mutect2 pipeline were downloaded using the  package  for 9712 package  to accouThe mutation rates of all TCGA primary tumour samples were determined by log-transforming the total number of mutations in each sample divided by the length of the exome capture (38 Mb).TP53 functional status was assessed based on somatic mutation and copy number alterations as described in Zhang et al. [TP53 mutation and copy number for the TCGA tumours were downloaded from cBioPortal . Tumours with TP53 oncogenic mutations (annotated by OncoKB) and copy-number alterations (GISTIC score ≤  − 1) were assigned as TP53 mutant and CNV loss. Tumours without these TP53 alterations were assigned as TP53 wild type. The effects of the TP53 mutation status on G0 arrest were then determined with a linear model approach with the G0 arrest score as a dependent variable and mutational status as an independent variable. The P values were FDR-adjusted.g et al. . TP53 muAPOBEC mutagenesis enriched samples were determined through pan-cancer clustering of mutational signature contributions as described in Wiecek et al. . The APOAneuploidy scores and whole-genome duplication events across TCGA samples were obtained from Taylor et al. . MicrosaphateR R package [ComBat function from the sva R package [The  package  was used package  was usedThe mean stem cell division estimates for different cancer types used in this study were obtained from Tomasetti and Vogelstein .Mutational signature contributions were inferred as described in Wiecek et al. .The COSMIC database was used to source a list of 723 known drivers of tumorigenesis (tiers 1 + 2); 285 oncogenes and tumour suppressors from a curated list showed a significant enrichment or depletion of mutations or copy number variants in samples with high levels of G0 arrest either pan-cancer or within individual TCGA studies.caret R package was used to build an elastic net regression model 1000 times on the training dataset of 3753 TCGA primary tumour samples . Only samples with at least 50 mutations were used in the model, for which mutational signatures could be reliably estimated. For each of the 1000 iterations, we randomly selected 90% of the samples from the training dataset to build the model. Only features which were included in all 1000 model iterations were selected for further analysis. To test the performance of our approach, a linear regression model was built using the reduced list of genomic features and their corresponding coefficients averaged across the 1000 elastic net regression model iterations. When applying the resulting linear regression model on the internal validation dataset of 936 samples, we found a strong correlation between the observed and predicted G0 arrest scores .To classify G0 arrest-prone from fast proliferating tumours, the 285 genes were used as input features for an ensemble elastic net regression model along the tumour mutational rate, whole-genome doubling estimates, ploidy, aneuploidy scores and 15 mutational signatures, which showed a significant correlation with G0 arrest scores either pan-cancer or within individual TCGA studies. The fastshap R package.SHAP values for the linear regression model used to predict G0 arrest scores were obtained using the ReactomePA R package, as well as GeneMania [CEP89 and other cell cycle components were inferred using the list of cell cycle genes provided by cBioPortal and GeneMania to reconstruct the expanded network with direct interactors . Networks were visualised using Cytoscape [Gene set enrichment analysis was carried out using the eneMania  and ConseneMania . Interacytoscape .Genes associated with the G1 phase of the cell cycle were obtained from the curated ‘REACTOME_G1_PHASE’ list deposited at MSigDB. Genes associated with the G1/S and G2/M phases of the cell cycle were obtained from Tirosh et al. .Genes associated with apoptosis were obtained from the curated ‘HALLMARK_APOPTOSIS’ list deposited at MSigDB.Genes associated with the senescence-associated secretory phenotype were obtained from Basisty et al. . Lists oGenes associated with contact inhibition were obtained from the curated ‘contact inhibition’ gene ontology term. Genes associated with serum starvation were obtained from the curated ‘REACTOME_CELLULAR_RESPONSE_TO_STARVATION’ list deposited at MSigDB. MEK inhibition was assessed based on the activity of the MAPK pathway as determined using an expression signature (MPAS) consisting of 10 downstream MAPK transcripts .For elastic net model feature validation, RNA-seq data was downloaded for six cancer studies from cBioPortal , along wAn ANOVA-based feature importance classification was used and identified 30 genomic features most discriminative of samples with lower and higher than average G0 arrest scores. A random forest model was then built using the identified features and correctly classified samples according to their G0 arrest state with a mean accuracy of 74% across five randomly sampled test datasets from the cohort.coxph function from the survival R package. The optimal quiescence score cut-off value of 2.95 was determined pan-cancer using the surv_cutpoint function. We also used this function to determine optimal cut-offs for individual cancer types, as presented in Fig. Multivariate Cox proportional hazards analysis was carried out using the umap R package was used for dimensionality reduction with constant seed for reproducibility.Datasets have been obtained from the GEO database through the following GEO Series accession numbers for the cell line experiments: GSE134836, GSE134838, GSE134839, GSE137912, GSE149224, GSE124854, GSE135215, GSE99116, GSE152699, GSE178839, GSE139944, and the following accession numbers for the patient sample datasets: GSE191127, GSE109211, GSE50509, GSE65185, GSE66399, GSE68871, GSE99898  of a given cell based on the expression levels of the 139 genes in the signature. The Gini indices corresponding to each gene in the model were normalised to a range of values between 0 and 1, which would reflect how important an individual gene was for determining G0 arrest state relative to the other 138 genes. The procedure was repeated 1000 times for each of the three datasets, and the average Gini coefficients across iterations were stored.Prioritisation of gene subsets based on cumulative importance in the modelGenes were placed in the candidate subset if their importance metric was above a given threshold in at least one of the datasets. By gradually increasing the threshold from 0 to 1, different gene combinations were produced.External validation of candidate subsetsp = 0.016) showed the highest correlation with phospho-Rb measurements capturing short-lived G0 arrest, the more common state observed in single-cell treatment datasets. Therefore, this signature was deemed to achieve the best trade-off between gene numbers and signal capture.The gene combinations in (2) were tested for their ability to predict G0 arrest. For this, a separate validation dataset was utilized, which contained gene expression levels for the 139 genes in the 10 lung cancer cell lines previously employed for experimental validation, along with the quiescence state of the lines as inferred by phospho-Rb and EdU staining. For each gene subset, a combined Z-score of G0 arrest was calculated from the expression levels as described previously. The correlations between this Z-score and the two experimental measurements of quiescence were used to establish the ability of a gene combination to predict quiescence. Among the top performing subsets, a 35 gene signature with a mean correlation of 78% between predicted and measured G0 arrest levels in the test data (We investigated if a subset of the 139 G0 phase-related genes could act as a more reliable marker of cell cycle arrest that would bypass dropout issues in single-cell data. This was performed in three steps:The optimised gene signature is provided in Additional file t test, Wilcoxon rank-sum test or ANOVA, as appropriate. p-values were adjusted for multiple testing where appropriate using the Benjamini–Hochberg method. Graphs were generated using the ggplot2 and ggpubr R packages.Groups were compared using a two-sided Student’s Additional file 1: Table S1. The 139-gene signature of G0 arrest. The up- or downregulation status in G0 arrest is indicated for each gene. Table S2. Summary of external G0 arrest score validation datasets. Table S3. Summary of external cancer cell line treatment response data. Table S4. Results of the signature optimisation analysis.Additional file 2: Fig. S1. G0 arrest score evaluation and validation. Fig. S2. Expression and genomic patterns of G0 arrest in tumours. Fig. S3. Modelling and validating a pan-cancer classifier of G0 arrest. Fig. S4. Genomic landscape of G0 arrest in breast cancer. Fig. S5. CEP89 expression is associated with G0 arrest and has prognostic value. Fig. S6. Stress response programme validation and links with p53 status. Fig. S7. Relevance of G0 arrest to clinical outcome in cancer. Fig. S8. G0 arrest signatures of drug tolerance in single cell data. Fig. S9. G0 arrest dynamics upon various treatment modalities. Fig. S10. G0 arrest levels in patient samples compared between responders and non-responders to various cancer treatments. Fig. S11. Application of the reduced G0 arrest signature to scRNA-seq data.Additional file 3. Review history.


Solanum to test hypotheses about the evolutionary forces acting during mating system shifts. These comparisons allow us to highlight the power of CAGEE, demonstrating its utility for use in any empirical system and for the analysis of most morphological traits. Our software is available at https://github.com/hahnlab/CAGEE/.Despite the increasing abundance of whole transcriptome data, few methods are available to analyze global gene expression across phylogenies. Here, we present a new software package  for inferring patterns of increases and decreases in gene expression across a phylogenetic tree, as well as the rate at which these changes occur. In contrast to previous methods that treat each gene independently, CAGEE can calculate genome-wide rates of gene expression, along with ancestral states for each gene. The statistical approach developed here makes it possible to infer lineage-specific shifts in rates of evolution across the genome, in addition to possible differences in rates among multiple tissues sampled from the same species. We demonstrate the accuracy and robustness of our method on simulated data and apply it to a data set of ovule gene expression collected from multiple self-compatible and self-incompatible species in the genus  Early studies of gene expression in single genes revealed widespread and frequent changes in the levels, timing, and breadth of expression across species , provides a robust set of methods for analyzing expression data across a species tree. CAGEE estimates ancestral states and rates, with rates shared by all or subsets of genes . We show that lineage-specific and tissue-specific (or condition-specific) rates can be accurately inferred, and we provide principled statistical approaches for model selection. Our current implementation uses a bounded Brownian motion (BBM) model and assumes expression data are accurate, but the architecture and codebase will easily allow for future extensions that relax these and other assumptions., a model that includes a force constraining traits about the mean. However, to our knowledge, the OU model has only been compared against an unbounded Brownian motion model , making fair comparisons difficult. In addition, OU models may be frequently and incorrectly favored over simpler models due to several biases , especially when the number of tips in a tree is small . Therefore, the initial version of our software models gene expression with the BBM process, which naturally bounds possible values without invoking an additional constraining force.We model gene expression evolution as a BBM process on a known species tree cf. . Our modi in species j. We assume that log-transformed expression Let er bound .The second major feature of our model (as implemented in CAGEE) is that many genes can share the evolutionary rate parameter, T, and a set t conditional on having log expression t on the same lineage is CAGEE infers the most likely value(s) of lgorithm . The keyStarting with the known tip distributions, the pruning algorithm propagates back to the tips’ parent nodes. The distribution at the parent node is then the product of the two backward-propagated child node distributions. Proceeding iteratively across the tree, we ultimately obtain the gene-specific probability density for expression value at the root where The default prior https://github.com/hahnlab/CAGEE/blob/main/docs/manual/troubleshooting_and_technical.md).The required inputs for CAGEE are a Newick-formatted, rooted, ultrametric tree (with branch lengths) and a tab-delimited data file containing the expression levels of all species or taxa being studied. The data file can consist of data on one gene/transcript or thousands of different genes. The first line of the data file should contain the species’ names (matching those used in the Newick tree). In addition, headers for gene names, gene descriptions, and sample IDs (see next section for an explanation of “samples” in CAGEE) can be used. Subsequent lines each correspond to a single gene and contain expression levels for each species. Missing data can be denoted using multiple characters (-/?/N). Examples of Newick trees and corresponding data files can be found in the online user manual ; we also estimated N = 500 . This indicates that standard statistical procedures should adequately control the false positive rate when fitting multi-sample Each additional sample requires another criteria , twice tn taxa, from 1 to 2n-2 parameters can be specified, and branches can be grouped together in any way. For instance, a two-parameter model can have all branches that share a rate adjacent to one another in the tree  has two different populations represented , the ancestral state in the family Solanaceae . Self-inSolanum . Self-coSolanum: . Such paSolanum:  but are Solanum: . These cSolanum: . Mating Solanum species sampled here represent two independent transitions from SI to SC, with one of the transitions (in accession S. pennellii LA0716) occurring recently enough that different populations within this species have different incompatibility systems  fitting significantly better. To further examine the evolution of S. pennellii LA0716, model D fits a three-parameter model, with this lineage assigned its own rate of evolution. This model is a significantly better fit than model C  and demonstrates that S. pennellii LA0716 has a rate of evolution ; other published data sets also use this normalization  and counts per million (CPM)  . Each noon (CPM) . Converson (CPM)  make the. Although OU models may be artifactually preferred over unbounded Brownian motion models due to a number of nonbiological factors (see discussion in New Approaches), it would still be helpful to be able to compare such a model with the BBM model used here. However, fitting such a model to genome-wide data is nontrivial: each gene must have its own mean expression value (μ) but possibly shared constraint parameters (α) across genes. We have the goal of implementing such a model in the near future, as well as other models commonly used in comparative methods research . Implementation of multiple models will not only allow for the analysis of different types of traits—each of which may be evolving under different regimes—but will also allow users to test the sensitivity of their analyses to model choice. For instance, it is not currently clear how different the inferred ancestral states or rates of evolution will be under different models  and therefore how different the conclusions drawn from any such analyses might be. Ideally, qualitative results will be similar, even when there are slight quantitative differences.CAGEE currently has multiple limitations, both in the available models that can be applied and in the types of data that can be analyzed. As mentioned earlier, many researchers have modeled gene expression using an OU process Beyond the evolutionary model applied to any data set, there are multiple additional sources of variation that could be modeled. For instance, we have previously accounted for measurement error in a likelihood framework, using an empirically parameterized error model . We can ne trees . This unne trees  and shoun tips is 2n-2, so that the number of calculations scales linearly with the number of species. This makes the pruning algorithm ideal for comparative data sets with large numbers of taxa . However, we also envision different ways to represent and model gene expression data, including as a ratio . Such a ratio, after log2-transformation, would be most appropriately modeled by an unbounded Brownian motion model since both negative and positive values are possible. This and other data types will be supported in future releases. Moreover, CAGEE does not have to analyze whole-genome or even molecular data: it can be applied to any single trait for which the BBM model is appropriate, even morphological traits. One intriguing application of CAGEE could be to suites of morphological traits that are hypothesized to share a common evolutionary rate parameter. If, for instance, there is a shift in body plan along some lineages, then multiple traits may all increase or decrease their rate of evolution at once, and CAGEE can be used to estimate these shared parameters. Even in the context of single-trait analyses, the pruning algorithm has been hailed as a solution for large-scale comparative analyses . Importaxa e.g., .The analysis of data from a clade of wild tomatoes revealed a possibly unexpected result: the rate of ovule gene expression evolution among SC species is twice as high as the rate among SI species . This fiSolanum pimpinellifolium and Solanum lycopersicon—domesticated tomato) have significantly larger seeds than most of the SI lineages and SC S. pennellii (unpubl. data). Indeed, individual genes identified in our GO analysis are known to directly influence ovule and/or seed size in Solanum . This approach gives,Without the reflecting boundary, M is tridiagonal with M.where CAGEE is written in C++ and is compatible with the C++11 standard. A comprehensive manual and extensive unit tests facilitate further code development and maintenance. CAGEE is organized into modular components. A “clade” class, with references to a parent clade and any number of descendant clades, represents a tree structure, and a “gene_transcript” class represents the expression levels observed in the various species. These two classes comprise the fundamental data structures upon which CAGEE performs its analysis  online.Calculations are carried out by additional classes. The “optimizer” class has the responsibility of determining the ire tree  online.M) requires calculation of eigenvalues and eigenvectors and is computationally expensive. This work is performed by the Eigen linear algebra library (https://eigen.tuxfamily.org); various internal data structures also take advantage of Eigen classes. To enable faster searching, the matrix for an ancestral state vector of length 200 (the default in CAGEE) has been precomputed and is included with CAGEE. Users who wish to use vectors of different lengths can specify this as an option.Performing the likelihood calculations requires extensive matrix operations; it is recommended (though not required) that these be passed off to a specialized library such as Intel's MKL or Nvidia's CUBLAS. If no external library is available, CAGEE will carry out these calculations (slowly) by itself. Creating the diffusion matrix (https://github.com/doctest/doctest). At the time of writing, more than 200 unit tests had been created, comprising more than 1,200 individual assertions. For complex logging and debugging cases, CAGEE uses the EasyLogging framework (https://github.com/amrayn/easyloggingpp). C++ development is always made easier by using the Boost C++ libraries (https://www.boost.org/), so we include them as well in CAGEE.Unit-testing is performed using the doctest testing framework . Further details are given in We briefly describe here the data collected from seven accessions of wild tomatoes (To construct a species tree for use with CAGEE, we started with the topology given in Molecular Biology and Evolution online.msad106_Supplementary_DataClick here for additional data file.


Episignatures are popular tools for the diagnosis of rare neurodevelopmental disorders. They are commonly based on a set of differentially methylated CpGs used in combination with a support vector machine model. DNA methylation (DNAm) data often include missing values due to changes in data generation technology and batch effects. While many normalization methods exist for DNAm data, their impact on episignature performance have never been assessed. In addition, technologies to quantify DNAm evolve quickly and this may lead to poor transposition of existing episignatures generated on deprecated array versions to new ones. Indeed, probe removal between array versions, technologies or during preprocessing leads to missing values. Thus, the effect of missing data on episignature performance must also be carefully evaluated and addressed through imputation or an innovative approach to episignatures design. In this paper, we used data from patients suffering from Kabuki and Sotos syndrome to evaluate the influence of normalization methods, classification models and missing data on the prediction performances of two existing episignatures. We compare how six popular normalization methods for methylarray data affect episignature classification performances in Kabuki and Sotos syndromes and provide best practice suggestions when building new episignatures. In this setting, we show that Illumina, Noob or Funnorm normalization methods achieved higher classification performances on the testing sets compared to Quantile, Raw and Swan normalization methods. We further show that penalized logistic regression and support vector machines perform best in the classification of Kabuki and Sotos syndrome patients. Then, we describe a new paradigm to build episignatures based on the detection of differentially methylated regions (DMRs) and evaluate their performance compared to classical differentially methylated cytosines (DMCs)-based episignatures in the presence of missing data. We show that the performance of classical DMC-based episignatures suffers from the presence of missing data more than the DMR-based approach. We present a comprehensive evaluation of how the normalization of DNA methylation data affects episignature performance, using three popular classification models. We further evaluate how missing data affect those models’ predictions. Finally, we propose a novel methodology to develop episignatures based on differentially methylated regions identification and show how this method slightly outperforms classical episignatures in the presence of missing data.The online version contains supplementary material available at 10.1007/s00439-023-02609-2. U test and the addition of an effect threshold on the difference between controls and cases beta-values are applied to highlight DMCs. The resulting set of DMCs beta-values is then used to train a classification model such as support vector machines (SVM), random forest (RF) or penalized logistic regression (PLR)  of the 5th carbon of cytosine sitting in cytosine-guanine (CpG) context is the most studied epigenetic process. Identification of differentially methylated cytosines (DMCs) is a promising area to improve diagnosis and gain knowledge on the etiology of diseases (Reichard and Zimmer-Bensch DMC) and Sotos (SotosDMC) have been described before in two separate studies . Indeed, we noticed that both SotosDMC_Raw and SotosDMC_Swan failed to completely separate patients and controls, as two cases  were clustered with the controls. Moreover, those two cases are clustered together even when normalizing data with the other methods and noticeably display a different methylation profile than the rest of the case-cohort . Interestingly, those two samples are described in the original paper as sharing the same mutation at the end of exon 22 of NSD1, which could explain this behavior. Dimensionality reduction using UMAP allowed clear separation of the different samples for both signatures .The DMC-esig for Kabuki (KabukiDMR) and Kabuki (KabukiDMR) syndromes, we applied the bumphunter method from champ. DMR on the training data from the two aforementioned studies normalized with the 6 different methods in minfi. For each DMR found, according to each normalized dataset, several parameters are reported in Additional Files 1 and 2 for Sotos and Kabuki syndrome, respectively, including the length of the DMR (width) and the number of CpGs included in the region (L). The resulting number of DMRs varied between both syndromes and normalization methods . The mean number of DMRs identified was higher in Sotos (n = 51) than in Kabuki (n = 38). However, this was mainly due to the Illumina normalized dataset that showed the highest number of DMRs in both syndromes . For each dataset, the median methylation level per DMR was computed using the beta-values from the CpGs located within the region. The resulting set of median DMR methylation values constitutes the DMR-esig. We applied unsupervised hierarchical clustering and showed that similarly to DMC-esig, SotosDMR and KabukiDMR were able to discriminate between cases and controls using all the normalization methods , support vector machine (SVM), and penalized logistic regression (PLR) models on all six normalized training sets, using the DMC-esig and the corresponding DMR-esig (see Methods). After performing LOOCV to find the optimal hyperparameters, the trained SVM, RF, and PLR classifiers were tested on both IM450K testing set from the original studies  on the Kabuki cohort (training set + testing sets) and the best Kabuki predictive model (SVM) on the Sotos cohort. All the samples in the Kabuki dataset were predicted as controls by the best Sotos predictive model and all the samples in the Sotos dataset were predicted as controls by the best Kabuki predictive model, regardless of the normalization method adopted, thus showing high inter-syndrome specificity Fig. .Fig. 3ThPLR achieved a specificity of 100% in both IM450K, IMEPIC and IMEPICv2 samples for all three best normalization methods. Instead, the best Kabuki predictive model (KabukiSVM) achieved 100% of specificity only when using the model trained on data normalized with Illumina normalization method  was consistently predicted as positive by the best Sotos predictive model with a prediction probability of 0.87, 0.96, and 0.87 when using Funnorm, Illumina, and Noob functions, respectively . Both GA functional analysis was performed to elucidate the pathophysiology of Kabuki and Sotos Syndromes. The genomic locations of the DMR-esigs for Illumina, Noob, and Funnorm normalization methods show that the DMRs are located mostly in the gene bodies and promoters. Furthermore, the genomic partition analysis shows an enrichment of CpGs overlapping gene promoters and regions 1–5 kb upstream the TSS compared to the training sets used for both the Kabuki and Sotos datasets Fig. .Fig. 5A DMR episignatures. This subfamily of genes encodes for large transmembrane proteins that are critical for processes such as cell-signaling . This could be due to the fact that the effect size in those two syndromes were close to the threshold at which bumphunter performs best . However, due to their relative novelty, no framework on how to build them has been described. Nevertheless, efforts from one group lead to the first guidelines on how to properly design cohorts for episignature discovery  when possible. Indeed, being able to access features importance allows to better characterize the underlying biological mechanisms of the episignature. Second, the choice of normalization method is necessary and must be done carefully when training a model. Overall, from our analysis, it is preferable to use Funnorm, Noob or Illumina as normalization functions and avoid the use of Raw, Quantile, and Swan. The first three have been shown to maximize the accuracy independently of the type of model or disease. Finally, the use of DMRs instead of DMCs as features to train a classification model has been demonstrated to be a valid, accurate, and robust alternative to currently adopted episignatures. This new approach does not need any imputation algorithm to deal with missing data, nor, when a new Illumina array version is released, to repeat the procedure of building a new model that is trained on common CpGs between the old and the new array version.The study includes peripheral blood from 26 samples collected at the ULB Erasme Hospital Center for Human Genetics . Informed consent was obtained from all research participants according to the protocol approved by the Ethics committee of the Erasme Hospital. These are composed of 22 controls, 1 patient with a confirmed diagnosis of Kabuki syndrome (OMIM: #147920) and 3 patients with a confirmed diagnosis of Sotos syndrome (OMIM: #117550) through the identification of class IV or V variants by genetic testing. Control specimens were healthy individuals without any developmental delay, intellectual disability, or congenital anomalies. Additional peripheral blood datasets were retrieved from the gene expression omnibus. They include data used to generate the Kabuki  and Sotos  episignatures , while the control group is composed of 12 females and 7 males with an average age at sample collection of 10.94 ± 5.45 years (range 3–18 years) . The Kabuki case training group is composed of two females and nine males with an average age at sample collection of 13.64 ± 5.64 years (range 1–20 years), while the control group is composed of two females and nine males with an average age at sample collection of 10 ± 3.43 years (range 5.5–13 years) . The testing cohort includes the rest of the respective datasets without the samples with variants of unknown significance (VUS), as well as the data from Erasme Hospital.minfi library in R , cross-reactive probes, probes harboring single nucleotide polymorphisms (SNPs), and probes on sex chromosomes were removed. The cross-reactive probes were removed using the R library maxprobes. The total number of probes retained for each dataset is shown in Table minfi using default parameters: Noob  as the distance metric to cluster samples, which is preferred for Euclidean distance for high-dimensional application  . The classifiers were then tested on the test sets to assess their performances on new, unknown samples. The prediction probabilities were also extracted from the results. Matthew’s correlation coefficient (MCC) was used to evaluate the models’ performances. Indeed, MCC is preferred to the F1 score in binary classification tasks due to its higher robustness to imbalanced datasets , Random Forest (RF), and Logistic Regression regularized with penalization term (PLR) were trained either on the beta-values of the DMC-esig, or on the median beta-values of the DMRs constituting the DMR-esig. Moreover, for each syndrome, the models were trained on each of the six normalized training sets as described above. The optimization algorithm of PLR was set as nan resulting from CpGs removal  were imputed using pandas.fillna(method = ‘ffill’). In order to test the robustness of the different classifiers, we also removed from all the testing datasets 5, 10, 20 or 30% of CpGs from the whole array after normalization. We then imputed the missing probes with the same procedure adopted above. This process simulates a scenario in which the release of new technology and the removal of low-quality signal probes introduce missing values in the samples to be classified with existing models. In the DMR-esig, no imputation was performed and for each DMR the median methylation value has been computed on the remaining probes within that DMR. Then, prediction performances and probabilities for each model have been extracted in order to evaluate the robustness of both approaches. We repeated this process ten times, using different random seeds to select the CpGs to remove and computed the mean and the standard deviation of the MCC from all individual performance evaluations.To avoid missing values in the DMC-esig, dasen function and Illumina GenomeStudio, respectively, as described in the original studies , 656 IM450K control samples (GSE40279) and 4 additional IMEPICv2 control samples (GSE222919) were used. Furthermore, the models were applied to a cohort of 489 IM450K unresolved cases (GSE89353). Data from GSE89353, GSE222919, GSE152026, and GSE40279 were retrieved already preprocessed and normalized using BMIQ (Quantile), Illumina GenomeStudio, the wateRmelon R (version 4.1.2). For both Kabuki and Sotos DMR-esigs using Illumina, Noob and Funnorm normalization methods, we extracted the CpGs belonging to the DMRs of each episignature. Then, the CpGs were annotated to the genome assembly GRCh37 (hg19) using annotatr (v. 1.24.0). Genic annotations included regions 1-5 Kb upstream of the transcription start site (TSS), gene promoters (< 1 Kb upstream of the TSS), intergenic regions, 5’UTRs and 3’UTRs, exons, introns and intron–exon boundaries, using the following built-in annotations: ‘hg19_basicgenes’, ‘hg19_genes_intergenic’ and ‘hg19_genes_intronexonboundaries’. The UTRs, exons, introns and intron–exon boundaries were considered part of the “gene body” category. The CpGs genomic annotations of the episignatures were then compared to the CpGs genomic annotations of the entire corresponding training set in order to understand which regions are most enriched in the DMR/esigs.All analyses were performed using DAVID .Gene ontology enrichment analysis was performed using Analyses were performed either in Python (version: 3.8.10) or R (version 4.1.2).minfi (version 1.40.0); maxprobes (version 0.0.2); ChAMP (version 2.24.0); seaborn (version 0.12.2); umap (version 0.5.3); scikit-learn (version: 1.2.2); pandas (version: 1.5.3).The following version of the packages were used: Supplementary file1 (ZIP 4431 KB)Below is the link to the electronic supplementary material.


Kernels offer a nonlinear version of any linear algorithm solely based on dot products. The kernelized version of principal component analysis is a valid nonlinear alternative to tackle the nonlinearity of biological sample spaces. This paper proposes a novel methodology to obtain a data-driven feature importance based on the The proposed method, kernel PCA Interpretable Gradient (KPCA-IG), provides a data-driven feature importance that is computationally fast and based solely on linear algebra calculations. It has been compared with existing methods on three benchmark datasets. The accuracy obtained using KPCA-IG selected features is equal to or greater than the other methods’ average. Also, the computational complexity required demonstrates the high efficiency of the method. An exhaustive literature search has been conducted on the selected genes from a publicly available Hepatocellular carcinoma dataset to validate the retained features from a biological point of view. The results once again remark on the appropriateness of the computed ranking.The black-box nature of kernel PCA needs new methods to interpret the original features. Our proposed methodology KPCA-IG proved to be a valid alternative to select influential variables in high-dimensional high-throughput datasets, potentially unravelling new biological and medical biomarkers. Big Data era, offering researchers new perspectives to analyse biological systems to discover new genotype-phenotype interactions.The recent advancement in high-throughput biotechnologies is making large multi-omics datasets easily available. Bioinformatics has recently entered the Consequently, new ad-hoc methods to optimise post-genomic data analysis are needed, considering the high complexity and heterogeneity involved. For instance, multi-omics datasets pose the additional difficulty of dealing with a multilayered framework making data integration extremely challenging.In this context, kernel methods offer a natural theoretical framework for the high dimensionality and heterogeneous nature of omics data, addressing their peculiar convoluted nature . These mThis work will focus on the kernelized version of Principal Component Analysis, KPCA, that provides a nonlinear alternative to the standard PCA to reduce the sample space dimensions.pre-image problem arises since data points are only addressed through the kernel function, causing the original features to be lost during the data embedding process. The initial information contained in the original variables is summarised in the pairwise kernel similarity scores among data sample points. Thus, retrieving the original input dimensions is highly challenging when it comes to identifying the most prominent features. Even if it is possible for certain specific kernels to solve the pre-image problem through a fixed-point iteration method, the provided solution is typically numerically unstable since it involves a non-convex optimisation problem KPCA-IG ae kernel .u whose tangent vectors in t are h.The idea is to look for the curves In the previous section, we showed how to represent the projection of every mapped generic point mentclass2pt{minimu(t) curves can be projected into the subspace of the kernel PCA. We define Similarly, the h i.e. the tangent vector field of u(t) into the KPCA solution. Formally, the tangent vector at an initial condition Now we can define the induced curve in the KPCA axes with the row vector:f takes the linear form j-th component, we obtain the same expression as in [j-th variable asIn this case,  becomes6jf(x)and :7\documeon as in 8\documen can use  to compuj for the generic point If we take as kernel the radial basis kernel 2), then  becomes,j-th variable for each input point.If we consider that the j for each sample point and then compute the mean value of these n contributions. The score that we obtain suggests the relevance of the j variable in the KPCA solution.Thus, the idea is to first compute the norm of this partial derivative with respect to the variable i-th row and k-th column of n rows, resulting in n values n sample points, it can give an indication of the overall influence of the j-th variable on the points.Analytically, the p variables, and after sorting them in descending order, it represents the ranking of the original features proposed by KPCA-IG. Every entry of Finally, we can repeat the procedure for all the p variables with The method is non-iterative, and it only requires linear algebra. Thus, it is not susceptible to numerical instability or local minimum problems. It variables representing the ranking of the original features proposed by KPCA-IG. Every entry ofis a score that indicates the impact of every variable on the kernel PCA representation of the data, it is then sorted decreasingly, from the most influential to the least important.is computationally very fast, and it can be applied to any kernel function that admits a first-order derivative. The described procedure has been implemented on R, and the code can be available upon request to the authors.Carcinom and Glioma, which are available in the Python package scikit-feature [GPL93 from the GEO, a public functional genomics data repository. Glioma contains the expression of 4434 genes for 50 patients, while Carcinom 9182 genes for 174 individuals. Both datasets have already been used as a benchmark in numerous studies including several methods comparisons, such as [GPL93 contains the expression of 12626 genes for 165 patients, and it has been chosen for its complexity and higher dimensionality.We conducted experiments on three benchmark datasets from the biological domain to assess the accuracy of the proposed unsupervised approach for feature selection. These datasets include two microarray datasets, named -feature  and the -feature , GPL93 f such as . Then, tKPCA-IG with existing unsupervised feature selection methods from diverse frameworks, as conducted in [lapl [lapl , to inclNDFS [NDFS , to add KPCA-permute in [mixKernel R package to include another methodology from the context of kernel PCA.rmute in  availablTo evaluate the selected features provided by the four methods, we measured the overall accuracy (ACC) and normalized mutual information (NMI) [d of selected features, with Glioma, Carcinom and GPL93 are characterized by 4, 11 and 4 groups respectively. Thus, the k-means clustering was computed using the correct number of clusters in the datasets to obtain a metric for the capability of the selected features to keep this nature.The idea is to compare the proposed methodology ucted in , 35:laplon (NMI)  based onNDFS method is implemented to explicitly obtain an optimum solution in terms of clustering, also requiring in advance the number of groups in the data. For each method, the k-means clustering was run 20 times to obtain a mean of the overall accuracy and normalized mutual information for each of the 30 subsets of selected features. Both our novel method KPCA-IG and KPCA-permute have been employed with a Gaussian kernel with a sigma value depending on the dataset. The selected features are, in both cases, based on the first 3, 5 and 3 kernel PC axes for Glioma, Carcinom and GPL93, respectively. The CPU time in seconds required to obtain the feature ranking for all the methods has also been observed. The experiment was conducted on a standard laptop Intel Core i5 with 16GB RAM.Note that only the d. For the first dataset Gliomalapl seems to show the best performance in terms of NMI and AUC, except when KPCA-IG is the highest, even if all the methods seem to behave very similarly in terms of ACC. Analyzing the results for the other two datasets Carcinom and GPL93 that are considerably bigger and possibly more complex in terms of sample space manifold, the two methods based on the kernel framework exhibit to surpass the lapl and NDFS approaches, especially in the GPL93 datasets. The comparison of the different approaches in terms of NMI and ACC of these two datasets can also be observed in Figs. In Table mentclass2pt{minimNDFS and the other cluster-based methods like MCFS and UDFS suffer if the user selects an incorrect decision for the a priori number of clusters. In our case, we show that the proposed methodology behaves similarly or even better to a method like NDFS that is specifically optimized for this cluster setting.Moreover, as shown in  NDFS andKPCA-permute and our novel method KPCA-IG, reveal an excellent performance in this setting, once again displaying the appropriateness of the kernel framework in the context of complex biological datasets. However, KPCA-IG can provide these above-average performances with a considerably lower CPU time.The two kernel-based approaches, namely lapl seems as fast as KPCA-IG while showing poorer results in the more complex scenario represented in this case by the GPL93 dataset. Other methods, such as the concrete autoencoder in [Only coder in , have prcoder in , were coLiver cancer is a global health challenge, and it is estimated that there will be over 1 million cases by 2025. Hepatocellular carcinoma (HCC) is the most common type of liver cancer, accounting for around of cases .KPCA-IG method, we used the expression profiling by array of an HCC dataset from the Gene expression Omnibus (series GSE102079). It contains the gene expression microarray profiles of 3 groups of patients. First, 152 patients with HCC who were treated with hepatic resection between 2006 and 2011 at Tokyo Medical and Dental University Hospital. Then, the gene expression of normal liver tissues of 14 patients as control [The most significant risk factors associated with HCC are, among others, chronic hepatitis B and C infections, nonalcoholic fatty disease, and chronic alcohol abuse . To anal control . The thi control  and scalTo show the potentiality of KPCA-IG, we first perform kernel PCA with radial basis kernel with For this reason, applying a method like the proposed KPCA-IG can enlighten the kernel component axes, possibly giving an interpretation of the genes’ influence on the sample points representation.The KPCA-IG provides a feature ranking based on the KPCA solution, in this case, based on the first two kernel Principal Components. As mentioned before, one of the main advantages of the proposed method is the fast computational time required, as with this high-dimensional dataset, the CPU time was 654.1 seconds. Table To obtain an indication of the significance of the variables selected by KPCA-IG in terms of retained information, we computed the Silhouette Coefficient, a metric used to assess the goodness of a clustering solution. The score values are in eparated . In thisStarting from the feature ranking given by KPCA-IG, we computed the silhouette scores for the KPCA solution for 5462 subsets in terms of original variables, i.e. datasets with the increasing number of features of From Fig. To see more in detail the behaviour of the curves for reduced datasets with a small number of features, which can be more relevant for practical biological use, Fig. Moreover, to check the generalization properties of KPCA-IG, we compared the explained variance captured by the selected variables on training and test data. More specifically, based on 5 different random train-test splits (192 train and 65 test points), we computed the feature ranking using KPCA-IG for each of the 5 training sets. Based on these features, we plotted the variance explained by KPCA. Again the analysis is made on different subsets with an increasing number of variables retained, namely Now, the variable ranking obtained by KPCA-IG on the training set is applied on the test sets. Thus, the computed KPCA explained variance on the test sets containing only those features is compared to the one obtained with KPCA applied on the training sets. In Fig. Another way to assess the relevance of the obtained ranking is to visualize the genes with the method proposed by  and to sFor instance, Fig. The direction of the arrows suggests an upper expression of the gene towards the cluster of patients that do not have liver cancer or patients whose liver tissue is not tumorous.To validate the procedure, we selected relevant literature about the gene TTC36. This gene, also known as HBP21, is a protein encoding gene. It has been shown that this gene’s encoded protein may function as a tumour suppressor in hepatocellular carcinoma (HCC) since it promotes apoptosis while it has been proven to be downregulated in HCC cases .Another gene that shows differential expression in the two groups is CDK1. In this case, Fig. The indication found in multiple studies is that the increased expression of this gene is indeed linked with a poorer prognosis or outcome, such as high tumour grade, invasion of lymphovascular or muscularis propria, and the presence of distant metastasis , 38, 66.ASPM was known initially as a gene involved in the control of the human brain development and in the cerebral cortical size , 77 whosLastly, for the group of upregulated genes in HCC, RRM2 has also been linked with low overall survival , 28, leaOn the other hand, the selected genes that manifest down-regulation in cancerous HCC tissues are LINC01093, OIT3, VIPR1, CLEC4G, CRHBP, STAB2, CLEC1B, FCN3, FCN2 and CLEC4M. The literature regarding these genes indicates that they work as suppressors in different cancerous situations, once again endorsing the selection provided by KPCA-IG for the upregulated genes.The few genes in the first 25 selected by KPCA-IG that do not exhibit differential expression using  method (We have seen how the unsupervised feature selection literature is narrower than its supervised counterpart. Moreover, algorithms that use the kernel principal component analysis for feature selection are reduced to a few works. In the present work, we have introduced a novel method to enhance variables’ interpretability in kernel PCA. Using benchmark datasets, we have proven the comparability in terms of accuracy with already existing and recognized methods, where the efficiency of KPCA-IG has proven to be competitive. The application on the real-life Hepatocellular carcinoma dataset and the validation obtained from the comparison of the selected variables by the method with the bio-medical literature have confirmed the effectiveness and strengths of the proposed methodology. In future works, further in-depth analysis will be realized to assess the impact of the choice of the kernel function on the feature ranking obtained by KPCA-IG. Moreover, the method will be adapted to other linear algorithms that are solely based on dot-products hence supporting a kernelized version, such as kernel Discriminant Analysis or kernel Partial Least-Squares Discriminant Analysis.