Cancers develop and progress as mutations accumulate, and with the advent of single-cell DNA and RNA sequencing, researchers can observe these mutations and their transcriptomic effects and predict proteomic changes with remarkable temporal and spatial precision. However, to connect genomic mutations with their transcriptomic and proteomic consequences, cells with either only DNA data or only RNA data must be mapped to a common domain. For this purpose, we present MaCroDNA, a method that uses maximum weighted bipartite matching of per-gene read counts from single-cell DNA and RNA-seq data. Using ground truth information from colorectal cancer data, we demonstrate the advantage of MaCroDNA over existing methods in accuracy and speed. Exemplifying the utility of single-cell data integration in cancer research, we suggest, based on results derived using MaCroDNA, that genomic mutations of large effect size increasingly contribute to differential expression between cells as Barrett’s esophagus progresses to esophageal cancer, reaffirming the findings of the previous studies. Here, the authors develop MaCroDNA, an algorithm to integrate single-cell DNA and RNA sequencing data from the same tissue. They use MaCroDNA to show—in agreement with previous studies—that copy number changes can predict progression from Barrett’s esophagus to esophageal adenocarcinoma. These technologies have changed our understanding of different fields of biology, including developmental biology, immunology, microbiology, and cancer biology.Over the last decade, single-cell sequencing (SCS) has grown dramatically. SCS can now provide data with much higher throughput and quality with a diverse range of protocols that can assay single cells’ genomic, transcriptomic, epigenomic, and proteomic contents7.SCS technologies can shed light on our understanding of the genotype-phenotype relationship. In particular, single-cell multi-omic assays sequencing RNA and DNA from the same single cells are of great potential to unravel the underlying mechanisms by which genomic alterations, including single-nucleotide variations, copy number aberrations (CNAs), and other structural variations, might impact transcriptomic programs at the single-cell level. This would lead to further understanding of clonal development in healthy and diseased tissues, especially in cancer therapies where drug responses are affected in part by phenotypes induced by genomic mutations8, DR-seq9, and scTrio-seq10, are of low throughput and face scalability issues. On the other hand, high-throughput sequencing technologies such as 10X genomics single-cell RNA sequencing (scRNA-seq)11 or Direct Library Preparation (DLP)12 can measure either genomic or transcriptomic content of single cells imposing the computational challenge of associating cells across different modalities. Among such computational problems, the cell association problem in high-throughput SCS data where for each single cell, either CNA measurements or gene expression values are provided is relatively less studied. There is a plethora of methods developed for the integrative analysis of SCS multi-omic data, which mostly integrate the single-cell chromatin accessibility—scATAC-seq—or DNA methylation measurements with the gene expression data from scRNA-seq such as20, to name a few. However, there are yet, a handful of methods that specifically address the cell association problem between scDNA-seq and scRNA-seq data, such as clonealign21, Cardelino22, CCNMF23, and SCATrEx24 among which clonealign, CCNMF, and SCATrEx are developed for the integration of copy number and gene expression data. In the following, we review clonealign, CCNMF, Seurat19, and SCATrEx.Despite being ideal for such studies, SCS technologies that measure both DNA and RNA from the same cells, such as G&T-seq21 is a statistical method aiming to assign single cells whose gene expression values are provided by scRNA-seq to cancer clones inferred from low-coverage single-cell CNA data. Here, the clones are the clades obtained by defining a cut-off on a phylogenetic tree reconstructed from CNA data. clonealign’s dosage compensation function is predicated on the assumption that an increase (decrease) in the copy number value of a gene would yield a higher (lower) gene expression value at that gene. This assumption was established based on the previously observed relationship between the genes’ expressions and their corresponding copy number values in bulk and single-cell assays26. Given the clone-specific copy number profiles, clonealign predicts the assignment of the cells measured using scRNA-seq to cancer clones measured using scDNA-seq by approximating the posterior probability distribution of the data given the method parameters using variational inference27.clonealign19 is a manifold alignment algorithm to solve the integration of multiple modalities. In manifold alignment methods, it is assumed that the data points—cells in this context—from the two modalities share a low-dimensional space where each cell can be represented by a low-dimensional vector—interpreted as the underlying biological state of the cell. The cells from the two domains whose vector representations are either identical or adjacent to each other in the manifold are identified as the associated cells. To establish such a shared manifold between two different modalities, Seurat adopts canonical correlation analysis . This dimensionality reduction step is followed by the identification of mutual nearest neighbors—or anchors—across the two datasets. Anchors are the pairs of single cells, each from a different dataset, that neighbor each other in the shared low-dimensional space. The anchors are filtered, scored, and finally utilized for batch correction and further downstream analyses.Seurat’s integration method23, a reference-free method, CCNMF23, was put forward. CCNMF applies a non-negative matrix factorization technique (see refs. 30 for details about this technique) to the scRNA-seq and scDNA-seq data. Specifically, for each of the two SCS datasets, CCNMF infers a pair of matrices, including the cluster  centroids in a low-dimensional space as well as the soft clonal assignment of the single cells to their clones. The low-dimensional representations of the DNA and RNA clones are coupled by incorporating prior information about the relationship between CNAs and gene expression values, such as the information acquired by the linear regression modeling of CNAs and gene expression values measured from the paired RNA and DNA bulk sequencing data. Performing this coupling technique on the cluster centroids of the two datasets yields a co-clustering on both datasets. CCNMF’s unique co-clustering technique differentiates it from the other existing methods, such as clonealign and Seurat, as CCNMF can infer clones by itself, it does not accept the predefined clones as input. A more recent method is SCATrEx24. Given a CNA clonal tree, SCATrEx maps scRNA-seq cells to the CNA clones to obtain an augmented tree while accounting for two types of possible gene expression variations, including the gene expression variations influenced by clonal copy number changes along the tree, and the variations not related to the underlying clonal tree structure such as epigenetic events. The authors used discrete moves to search for new tree structures and employed mean-field variational inference to score each augmented tree.Both clonealign and Seurat are map-to-reference inference methods, meaning that the data from one domain is mapped to the clones inferred from another domain. The reference may differ in such methods. For example, in clonealign, the copy number profile of each clone is the reference, while in Seurat, the scRNA-seq data on the latent manifold is the reference. Since the choice of the reference in these methods might introduce systematic bias to the method31. We exploited the partially known ground truth information in this dataset to evaluate the performance of the methods for integration of independent single-cell gene expression and copy number data directly on empirical data. By taking advantage of the available ground-truth information and using a variety of clustering techniques, we measured the accuracy of clonealign, Seurat, and MaCroDNA in assigning the scRNA-seq cells to the scDNA-seq clones as well as predicting the clonal prevalences of the scRNA-seq cells. To demonstrate the insight that may be gained from integrated DNA and RNA single-cell data, we applied MaCroDNA to a previously published dataset from a study of Barrett’s esophagus (BE), where biopsies were taken from multiple patients and individual cells from those biopsies sequenced for either DNA or RNA32. BE is a metaplasia presumed to be caused by gastroesophageal reflux disease, where the squamous epithelium of the esophagus is replaced by metaplastic epithelium with intestine-like goblet cells33. Non-dysplastic BE (NDBE) may progress to low-grade dysplasia (LGD), high-grade dysplasia (HDG), or esophageal adenocarcinoma (EAC), although the exact relationship of this progression in terms of cellular descent remains uncharacterized34. While a diagnosis of EAC is devastating with dismal prospects for survival, most BE do not progress to EAC, and predicting when EAC will develop is very difficult35. To make useful predictions and improve patient outcomes, we must first understand why progenitor cells evolve into EAC or dysplastic BE instead of NDBE. Our MaCroDNA-based results suggest that in comparison to NDBE and LGD, HGD and EAC are associated with genomic mutations of large effect size, which are heterogeneously present within individual biopsies. This finding aligns with previous studies suggesting that the copy number changes are good predictors of progression from Barrett’s esophagus to esophageal adenocarcinoma38.Here we report on a method for the inference of cell association in SCS multi-omic data with CNA and gene expression measurements. Inspired by clonealign’s underlying assumption that the gene expression value of a gene is proportional to the corresponding CNA value at that gene, we hypothesize that the Pearson correlation coefficients between the gene expression measurements of scRNA-seq cells and the CNA profiles of scDNA-seq cells could be an effective metric for the cell association inference. We applied our method, MaCroDNA (Mapping Cross Domain Nucleic Acid) to a scTrio-seq2 datasetNG ≤ NC”).The inputs of MaCroDNA include the scRNA-seq gene expression read count tables  and the scDNA-seq absolute copy numbers  of the single cells sequenced from the same tissue .When the number of the scRNA-seq cells is smaller than the number of the scDNA-seq cells, MaCroDNA identifies a unique scDNA-seq cell for each scRNA-seq cell by viewing the correspondence problem as an instance of maximum weighted bipartite matching problem. This is a well-known problem that is polynomially solvableNG > NC”).When the number of the scRNA-seq cells is larger than the number of the scDNA-seq cells, some of the scRNA-seq cells would inevitably be matched to the same scDNA-seq cells. For this case, we devised a heuristic algorithm that breaks down the problem into multiple maximum weighted bipartite matching problems and solves them, one by one, in a sequential manner  are matched or not.Supposing the single cells are sampled from the same tissue, we assume that they share the same underlying clones, and therefore, the clonal prevalences in the two datasets are nearly identical. To respect such an assumption, MaCroDNA avoids assigning any two scRNA-seq cells to the same scDNA-seq cell as much as possible. To elaborate more on how MaCroDNA accounts for this constraint, let us consider the two following cases:Using the above correspondence matrix, we assign the scRNA-seq cells to the clones identified from scDNA-seq data. First, we perform a clustering technique of choice on the scDNA-seq cells to obtain the clonal assignments Fig. d. Given In the following, we will describe our scheme for evaluating the performance of MaCroDNA, Seurat, and clonealign when applying them to an empirical dataset.31. The CRC dataset consists of the scRNA-seq and scDNA-seq data of several patients. We decided to use three of these patients, namely CRC04, CRC10, and CRC1131. The remaining patients were excluded from our analysis because their transcriptomic data were obtained using a different library preparation protocol or their cell amount was insufficient (see “Description of CRC dataset”).To assess the performance of MaCroDNA and the other methods, we applied them to a colorectal cancer (CRC) dataset originally studied by Bian et al.The CRC dataset is particularly helpful for our evaluation purposes as it contains some cells for which both RNA and DNA measurements are provided. These cells can readily be used in our experiments as the ground truth data. In all our experiments, we exploited this ground truth information to evaluate the performance of the methods (see below). Of note, all the methods (including MaCroDNA) were oblivious to this information at the time of inference, and we used it only for the assessment. Given the limited ability to produce realistic synthetic data, this study assesses the accuracy of methods for integrating DNA and RNA data using this empirical dataset. While simulation-based analyses are widely used and useful, they cannot match the realism of this approach and results from empirical datasets without any ground truth can only be described rather than measured for accuracy.Table Cell-to-clone assignment accuracy: Given a clonal assignment identified on the scDNA-seq cells using a clustering algorithm, what is the accuracy of a method in assigning the scRNA-seq cells to the scDNA-seq clones? We measured the accuracy only for the scRNA-seq cells whose joint DNA measurement is also provided. For these scRNA-seq cells, we know their true corresponding scDNA-seq cell. Following this idea, the assignment of such scRNA-seq cell to a scDNA-seq cell is considered correct if the predicted scDNA-seq cell is the true corresponding scDNA-seq cell or if both the predicted and true scDNA-seq cells belong to the same clone according to the results of the clustering algorithm.Predictive accuracy for clonal prevalences: According to the ground truth information and the clonal assignment of the scDNA-seq cells , one can count the number of the scRNA-seq cells that are assigned to each of the scDNA-seq clones. While such counts can serve as the true clonal prevalences in the scRNA-seq data, we can obtain the predicted clonal prevalences by counting the number of the scRNA-seq cells that are assigned to the scDNA-seq clones by a method. In particular, we are interested in understanding the correlation between the true and predicted clonal prevalences for each clone.In the following, we will describe the experiments we conducted on MaCroDNA, Seurat, and clonealign. Through these experiments, we sought to answer the two following questions:It is to be noted that answering the above questions reveals two distinct characteristics of a method’s performance. A method could be very inaccurate in mapping the scRNA-seq cells to the scDNA-seq clones while being faithful to the proportion of clones in the scRNA-seq data or vice versa.40 and agglomerative clustering. Testing the integration methods under different clustering results leads to a better understanding of the robustness of the methods’ performance to the choice of clustering algorithm.We first inferred the scDNA-seq clones to measure both the cell-to-clone assignment accuracy and the predictive accuracy for clonal prevalences. Here, we chose two different clustering techniques, namely intNMF45. We transformed the data using x is the original copy number value and In addition to the clustering algorithm, data transformation is another contributing factor in clonal inference. The original copy number values in the scDNA-seq datasets are in the form of non-negative integers. Along with the original copy number values, we used the log-transformed copy number values for the clonal inference as well. Log transformation is a commonly used transformation for the genomic dataGiven the original and log-transformed data, we performed intNMF and agglomerative clustering techniques on each patient’s scDNA-seq data separately. intNMF’s clustering algorithm provides the optimal number of clusters along with the clonal assignments for the single cells . intNMF identified two clusters in each of the patients, CRC04, CRC10, and CRC11, using the original copy number values as input. Here, in both patients, CRC10 and CRC11, the largest clone contained more than half of the patient’s cells, while CRC04 had relatively balanced clusters . By doing so, we obtained the clonal assignments at different resolutions, ranging from six to 12 clusters in total.After inferring the clusters under different configurations of the clustering method and data transformation, we assessed the performance of MaCroDNA, clonealign, and Seurat for the cell-to-clone assignment and predicting the clonal prevalences. Although Seurat was introduced for the data integration between different scRNA-seq assays or between scRNA-seq and scATAC-seq datasets, we decided to incorporate it into this study as the exemplar of the commonly used methods in SCS multi-omic analyses. For CCNMF, we decided to assess its performance separately since it did not fit into our evaluation scheme (due to not accepting the predefined clones as its input). Even on this basis, its performance was poor, therefore we excluded its results from our main analysis and included them in Supplementary Figs. Prior to running each method for integrating the scDNA-seq and scRNA-seq data, we preprocessed the CRC patients’ data according to the requirements of each method as well as the preprocessing strategies that we considered . Since clonealign requires the clone-specific copy number profiles as input, we provided the median of all copy number profiles in a cluster as the clone-specific profile to clonealign. We ran Seurat and clonealign with their default parameters. Note that MaCroDNA does not require any user-specified parameters as the input. In all experiments related to cell-to-clone assignment and prediction of clonal prevalences  for the cell-to-clone assignment are shown in Fig. x-axis and the proportion of the same clone predicted by a method on the y-axis. Here, again, we have used the results of agglomerative clustering at the highest-resolution setting, i.e., four clusters per patient . In such a plot, the less deviated a method’s results are from the diagonal line, the more correlated the true and predicted clonal prevalences are. As shown in Fig. Next, we assessed the performance of the methods in predicting the clonal prevalences. Figure This experiment emphasized the importance of respecting the same underlying clonal abundance in the two modalities as a determining factor in the methods’ performance. Moreover, the performance of the random baseline in the two above experiments showed that a method could be accurate in predicting the clonal prevalence while inaccurate in the cell-to-clone assignment.While assuming similar clonal abundance across modalities favors MaCroDNA over existing methods, significant deviations from this assumption can impact its accuracy. We conducted a comprehensive study to determine the conditions and the extent to which discrepancies in the clonal proportions between the two modalities affect MaCroDNA’s accuracy  and gastric cardia (CARD) tissues. After filtering and normalizing DNA and RNA datasets, we created separate DNA and RNA read count tables for genes with mapped RNA reads, which also overlapped bins with mapped DNA reads Table . We thenK* statistic of phylogenetic signal, which quantifies correlations between a continuous trait and a phylogenetic tree49. For our analysis, the trait was the normalized read count for a particular gene. The phylogenetic tree, which was estimated from normalized binned DNA read counts as a proxy for copy number profiles and encoded cell lineage information. Using a phylogenetic tree to model cell lineages is natural, given the bifurcating nature shared by such trees and by the cell cycle, and correlations between cell transcriptome and lineage will result from mutations or environmental factors that are both specific to sub-lineages of cells within a biopsy and have some effect on the transcriptome. K* has an expected value of 1 when traits evolve along the tree following a Brownian motion (BM) model, where the variance of a trait increases linearly with time, so a K* of 1 would represent a very strong correlation between cell transcriptome and lineage. K* < 1 or K* > 1 when the correlation is weaker or stronger, respectively, than expected under BM49.To measure the contribution of genomic mutations to transcriptomic changes, we used the K* values for all post-filtering genes within each biopsy revealed that the bulk of gene expression patterns exhibit correlations with the cell lineage phylogeny below what would be expected under BM, regardless of tissue type or BE staging  relative to the amount of change toward the tipsK* test49, we identified hundreds of genes with inferred K* > 1 in every HGD and EAC biopsy. In biopsies of lower-grade or healthy tissue, far fewer genes were identified following the same criteria  were used as the preprocessed data for MaCroDNA, resulting in two versions: MaCroDNA_2000 and MaCroDNA.We evaluated the computational cost of each method by measuring its runtime and peak memory usage when applied to clusters inferred by intNMF. To investigate how input size affects computational cost, we created different-sized datasets for each patient by sampling cells with replacement. For each method, we randomly sampled a proportion The simulation was run on Ubuntu 20.04.4 using one core of an Intel Core i9-10900K CPU. To measure the runtime of a method, first, we calculated the method’s average runtime for each patient across 10 replications, next, we reported the sum of the average running times across all patients. As shown in Fig. R2 values in both cases were greater than 0.96. Based on the fitted line, we can extrapolate the runtime of MaCroDNA to be around 10 min for 20,000 cells.To estimate the runtime of MaCroDNA for larger samples outside of the observed range, we fitted a linear regression between MaCroDNA’s running time measures and the input sizes for the original and log-transformed data separately Fig. a, b. TheFor memory usage of each method, we reported its peak of memory usage across all patients and all replications per sampling rate. The peak memory usage of each method is presented in Fig. 54. In this work, we developed a method for mapping the single cells with only gene expression measurements to single cells with only copy number values from the high-throughput scRNA-seq and scDNA-seq data. Our method, named MaCroDNA, finds the correspondence between the scRNA-seq and scDNA-seq cells by maximizing the sum of the Pearson correlation coefficients between the paired cells. We also pose a restriction on this correspondence: The number of scRNA-seq cells assigned to a scDNA-seq cell should be limited as much as possible to avoid trivial solutions (see “MaCroDNA” for more details).High-throughput scRNA-seq and scDNA-seq can measure either the genomic or transcriptomic contents of the cells. Such abundant scDNA-seq and scRNA-seq datasets, if integrated precisely, would provide an unprecedented opportunity for studying the transcriptomic effects of genomic alterations. Ensuring this precise integration is not an easy task as the integration of the single-cell data across different measurements and samples—in a broader perspective—has been identified as one of the eleven grand challenges in single-cell data science21—as the state-of-the-art method for integrating the scRNA-seq and scDNA-seq data—and Seurat19—as the representative of the commonly used methods in the single-cell multi-omic studies—through their application to a CRC dataset31. This dataset contains the cells measured for both gene expression and copy number data. We exploited such cells’ information as the ground truth and used it for evaluation purposes. While simulation studies based on synthetic single-cell gene expression and copy number data can be very insightful for the evaluation of integration tools, such a task would be very challenging as our knowledge of the DNA-to-RNA process is too limited to produce realistic simulations.We assessed MaCroDNA’s performance against clonealignWe evaluated the accuracy of the methods for two inference tasks, namely the cell-to-clone assignment and prediction of the clonal prevalences. MaCroDNA outperformed clonealign and Seurat in both tasks. We hypothesize that the key to the better performance of MaCroDNA is restricting the number of the scRNA-seq cells being assigned to each scDNA-seq cell. This restriction helped MaCroDNA implicitly assume the same underlying clonal prevalences in the two modalities, whereas clonealign and Seurat do not—either explicitly or implicitly—account for such an assumption.21. Since the Pearson correlation—which we used as our dosage function—was not restricted or capped, we speculate that limiting the linearity between copy number and gene expression values in clonealign has had a negative impact on its performance.Among the three methods, clonealign showed the poorest performance. It is worth noticing that the only clonal inputs to clonealign are the clone-specific copy numbers (a CNA profile for each clone). Therefore, clonealign is oblivious to the distribution of the clones in the tumor. Another contributing factor that may have degraded the performance of clonealign could be its dosage function. Although MaCroDNA and clonealign are both based on the assumption that an increase (decrease) in the copy number of a gene can increase (decrease) the corresponding gene expression value at that gene, the linear dosage function of clonealign that maps the copy number of a gene to its expression is capped at an upper limitAdditionally, we made efforts to investigate the behavior of clonealign as thoroughly as possible using the CRC dataset. We observed that in the first iteration of its optimization process, clonealign assigns all or most of the scRNA-seq cells to the clone(s) where every gene has the same copy number or the proportion of the clone’s most common copy number is high. The lack of a detailed description of Evidence Lower Bound (ELBO) for the variational approximation hindered our ability to further determine the root cause of this behavior  studies.31. To generate this dataset, the authors used the single-cell triple omics sequencing2 (scTrio-seq2) sequencing technique. This sequencing technology provides the joint measurement of somatic copy number variations, DNA methylation, and gene expression read counts from the same cell. In the original study, for six patients, namely CRC01, CRC02, CRC04, CRC09, CRC10, and CRC11, the joint copy number and gene expression measurements were provided. Note that not all the cells in these patients have both scRNA-seq and scDNA-seq data. The sequenced cells with joint copy numbers and gene expression values from these patients are valuable for evaluation purposes. However, we did not include all patients’ datasets in our analysis.To assess the performance of the integration methods, we used a colorectal cancer (CRC) dataset introduced by Bian et al.57 for transcriptome sequencing library preparation of CRC01 and CRC02, while for the other patients, multiplexed scRNA-seq method58 was used. To maintain consistency across our experiments, we did not consider CRC01 and CRC02 in our analysis. Besides, the data of the patient CRC09 contained only 13 cells with both scRNA-seq and scDNA-seq data, which was insufficient for a statistical method such as clonealign. Finally, only the data from patients CRC04, CRC10, and CRC11 were used to evaluate MaCroDNA and the other integration methods.The authors used Tang protocolFirst, we filtered out the non-informative genes from the scRNA-seq gene expression data by keeping only genes that were expressed as non-zero in more than 1% of cells. The genes obtained from filtering are used for further preprocessing in the integration methods and the clustering techniques. In the following, we will describe our data preparation procedures for the integration methods and the clustering methods. Specifically, data preparation for each of the existing methods is based on the instructions in their original studies.clonealign requires removing the X-chromosome genes prior to the analysis since the presence of the X-chromosome in the data will violate the method’s assumption about the relationship between the copy number and gene expression values. Additionally, as recommended in the original clonealign study, genes with zero variance in copy number for each patient and those with zero copy number in at least one cell were also removed. In addition to removing genes with zero variance, we assessed the impact of adding a pseudocount value of 1 to all absolute copy number values before inputting data into clonealign and then compared the two approaches .Seurat requires different preprocessing procedures. We followed the same procedures in the original paper. First, all cells were log-transformed using a size factor of 10,000 molecules for each cell. Then, z-score normalization was applied to the log-transformed data. Next, a feature selection was done to scRNA-seq data and scDNA-seq data separately, using FindVariableFeatures function in Seurat v3. Following the feature selection on the single measurements, feature selection for integrated analysis was applied to scRNA-seq data and scDNA-seq data together using SelectIntegrationFeatures function in Seurat v3. Finally, the top 2000 genes were selected.In addition to Seurat’s and clonealign’s preprocessing procedures, we considered two other preprocessing strategies for MaCroDNA, resulting in four strategies in total. The first strategy is Seurat’s preprocessing, named as 2000_genes_log in the figure legends in the Supplementary Information. This includes log transformation of the data, z-score normalization with 10,000-factor size, feature selection, and the selection of the top 2000 genes. All these steps were applied sequentially to the input. The second one includes the log transformation and z-score normalization , but all genes were kept. This preprocessing is named as all_genes_log in the supplementary figures. The third one is the clonealign’s preprocessing, tagged with noX_genes_raw. Finally, the last strategy is all_genes_raw, where all genes were used, and the data were kept in the original scale. In Figs. x is the original copy number. Through all experiments, both data scaling strategies were used for clustering and clonal inference.Apart from data preprocessing for the integration methods analyses, the CNA data used for obtaining clusters was also preprocessed. Here, we use two strategies: clustering on the original CNA data and clustering on the log-transformed CNAs. The CNA data can have a right-skewed distribution. Thus, 32. For numerical stability of our calculations, we added a pseudocount of 1 to all entries of the scRNA-seq count tables which is a common practice in gene expression analysis59. To circumvent the effect of unequal sequencing depth, we performed RPM (reads per million mapped reads) normalization by first dividing each gene’s expression value by the total number of reads in the cell and then scaling this ratio by one million. Finally, we log-normalized the gene expression values by applying x is the gene expression value and For scRNA-seq data of each biopsy, first, we filtered out the single cells with less than 3000 transcripts from the data, and next, we kept the genes that were expressed by at least three transcripts in at least one cell, according to the filtering procedure in ref. 32, we divided the copy number bin counts by their median and then multiplied by 2 to obtain a rough estimation of the copy number values. In the next step, we log-normalized the copy number values using The scDNA-seq data was provided to us as the binned genomes containing the number of mapped reads in each copy number bin. Similar to scRNA-seq data, we filtered out the scDNA-seq cells with less than 3000 mapped reads. Next, we added the pseudocount of 1 to the number of mapped reads in each bin. Following the instructions from the original study60 annotation file for GRCh37 assembly, Human Release 19 (GRCh37.p13), and extracted the names and coordinates of all known protein-coding genes. Next, for each copy number bin, we annotated it with all the genes whose starting and ending points were within the bin. For each gene, we considered the copy number of the corresponding bin as that gene’s copy number value. Lastly, for each biopsy, we found the genes shared between the scRNA-seq and scDNA-seq datasets and performed MaCroDNA on this set of genes.Running MaCroDNA on the scDNA-seq and scRNA-seq data requires the count tables from the two modality with the same set of genes. As mentioned above, the given data was the binned copy number data. Therefore, we first annotated the copy number bins by searching for the genes whose genomic coordinates lie within the bins. We downloaded the GENCODE61. intNMF is able to identify the optimal number of clusters for each data type in a multi-omic dataset. Its clustering algorithm can also be applied to datasets with single data types (such as scDNA-seq data in CRC dataset). In intNMF, the cluster prediction index (CPI) can evaluate the goodness of a particular number of clusters by measuring the adjusted rand indices62 among the clustering assignments . The optimal number of clusters is the one that yields the maximum CPI value.intNMF is a clustering method based on non-negative matrix factorizationWe applied intNMF to the scDNA-seq cells of each patient to infer the clusters. First, we ran the function nmf.opt.k from the R package of intNMF v1.2.0 to identify the optimal number of clusters in each patient. Next, to perform clustering on the scDNA-seq cells and acquire the clustering membership assignments, we ran the function nmf.mnnals with the optimal number of clusters obtained from the previous step as the input. Given the original data, intNMF detected two clusters in each of the patients, CRC04, CRC10 and CRC11. These patient-specific clusters are denoted by crc04_clone0, crc04_clone1, crc10_clone0, crc10_clone1, crc11_clone0, and crc11_clone1 in Supplementary Fig. For each patient having more than two clusters, calculate all pairwise distances between the clusters within the patient. The distance between two clusters is the Euclidean distance between the averaged copy number profiles representing the clusters.Among all pairwise distance values, identify the pair of clusters (within the same patient) with the minimum distance and merge them into a single cluster.Repeat steps 1 and 2 until only two clusters remain for each patient.In addition to intNMF, we applied agglomerative clustering to obtain scDNA-seq clones from each patient’s cells. The Python implementation of agglomerative clustering provided in sklearn package v0.23.2 was directly applied for obtaining 4 clusters in each patient. We used Euclidean distance as the distance metric and average as the linkage criterion. By obtaining 4 clusters for each patient, we inferred 12 clusters in total across all patients. Since we sought to investigate the effect of varying clustering resolution on the methods’ accuracy, we applied the following procedure to decrement the number of clusters:This way, we varied the resolution of the clusters obtained from all patients, ranging from 6 clusters to 12 clusters in total. The patient-specific clones for different resolutions are tagged in Supplementary Figs. i, the expected number of scRNA-seq cells (whose true clone id is ctrue according to the ground truth information and the current clustering assignment) that are being assigned to the scDNA-seq cells with clone id cpredicted. Let ntrue,predicted denote the above-expected number. Then we have:ctrue in patient i, cpredicted in patient i, and i. This expected number gives us a measurement for the accuracy of the baseline method.To evaluate the performance of MaCroDNA and other methods, we established a random baseline. In this random baseline, each scRNA-seq cell is assigned to a scDNA-seq cell. This scDNA-seq cell is selected by random sampling from all scDNA-seq cells in the same patient with replacement. Following this random method for assignment, we can calculate for each patient 63 to infer the UPGMA tree. As mentioned earlier, we used the copy number values of the genes shared between the two modalities to perform MaCroDNA. Here, however, for phylogenetic inference, we used the complete set of copy number bin counts in order to take advantage of all the available evolutionary information from scDNA-seq data for the phylogenetic tree reconstruction.To prepare the inputs for phylogenetic signal analysis, we first inferred the single-cell CNA phylogenetic tree of each biopsy using the UPGMA method. We computed the Euclidean distances between all pairs of the cells and passed the pairwise distance matrix as the input to upgma function in phangorn R package v2.11.1NG > NC” for more details). An earlier iteration, in this case, means a better correspondence score. Therefore, we selected the scRNA-seq cell that was assigned to the scDNA-seq in the earliest iteration. Here, for each paired scRNA-seq, we passed the gene expression of all genes (rather than only the shared genes with the DNA data) as the traits to phylosignal.In addition to the phylogenetic tree, phylosignal requires a table of traits for each cell. Given the cell-to-cell assignments inferred by MaCroDNA, for each scDNA-seq cell, we provided the vector of gene expression values of the paired scRNA-seq cell as the cell’s traits to phylosignal. Of note, some of the scDNA-seq cells were assigned to multiple scRNA-seq cells by MaCroDNA. In such cases, for one particular scDNA-seq cell, we ranked the assigned scRNA-seq cells according to the iteration number they were assigned to the scDNA-seq cell  of some single cells at a particular set of genes. The other dataset consists of gene expression read counts  belonging to another set of single cells at the same genes as in the CNA dataset.C and G for CNA and gene expression data, respectively. Formally, let NC represents the number of single cells, M denotes the number of genes, and cij is the absolute copy number or its log-transformed value in the ith single cell at the jth gene. Similarly, NG denotes the number of single cells, M denotes the number of genes, and gij is the gene expression read count or its log-transformed value in the ith single cell at the jth gene. Each row in C or G represents the CNA profile or gene expression vector of a single cell. We use ci and gi to denote the ith cell’s CNA profile and gene expression vector, respectively.These two datasets are provided as inputs to MaCroDNA in the form of matrices Iij is 1 if the ith scRNA-seq cell is associated with the jth scDNA-seq cell, otherwise, Iij is 0. Of note, since each scRNA-seq cell has exactly one corresponding scDNA-seq cell, each row of the correspondence matrix has exactly one entry of value 1.Given the above matrices, MaCroDNA associates each cell in gene expression data (scRNA-seq cell) to exactly one cell in CNA data (scDNA-seq cell) according to a criterion described in the following. This correspondence is presented in the form of a binary matrix, NG ≤ NC) and second, our heuristic for datasets where the number of scRNA-seq cells is more than the number of scDNA-seq cells (NG > NC). Finally, we discuss how our solution for the former constitutes the basis for the solution to the latter.In the following, we discuss how MaCroDNA infers the abovementioned correspondence matrix by, first, describing our polynomially solvable algorithm for cases where the number of scRNA-seq cells is less than or equal to the number of scDNA-seq cells  of the selected pairs,ωij is the Pearson correlation coefficient between the ith scRNA-seq cell and the jth scDNA-seq cell. Since each scDNA-seq cell is allowed to be assigned to at most one scRNA-seq cell, at most one of the indicator variables of each scDNA-seq cell can be 1. The following inequality forces this constraint for each scDNA-seq cell:NG ≤ NC, we propose two alternative constraints that yield the same results and can also be used in the cases where NG > NC as well (see Section “MaCroDNA for NG > NC” for more details). First, we force each scRNA-seq cell to have at most one pair in scDNA-seq data by the following inequality:https://www.gurobi.com) and CPLEX . After solving the optimization problem in equation (I = (Iij).Considering the above conditions, we require the solution to be of the highest similarity score between the corresponding pairs. We formulated this optimization problem as an instance of Mixed Integer Linear Programming (MILP). Specifically, we introduce binary indicator variables V vertices and E edges. Here, the vertices represent single cells from scDNA-seq and scRNA-seq. All possible pairs of single cells in scRNA-seq and scDNA-seq are connected by edges that are weighted with the Pearson correlation coefficient between the pair. The goal of the maximum weight perfect matching problem is to find a one-to-one matching between the nodes in the bipartitions such that the sum of the edge weights connecting the pairs is maximized. The well-known Hungarian algorithm67 can solve this problem in polynomial time39. The time complexity of this algorithm is V is the set of nodes in the bipartite graph69.It is worth mentioning that this problem can be viewed as an instance of maximum weight perfect matching on a complete bipartite graph, also known as assignment problem. To reformulate as such, we need to introduce a graph The Hungarian algorithm requires the number of scRNA-seq and scDNA-seq cells to be equal which is not the case necessarily in real applications. However, we can add dummy scRNA-seq cells that are connected to scDNA-seq cells with edges weighted by negative values with large magnitudes. By doing so, the number of cells in both bipartitions will be the same and the Hungarian algorithm is applicable.Initialization: let R(0) be the set of scRNA-seq cells at the initialization step of the algorithm, and R(0). Note that at the initialization step, all the scRNA-seq cells are involved, so NG assignments, we need to infer the best R(0). Name the new set, R(1), and proceed to the next step.equation : insteadequation  becomes:Iteration: let Rk)( denote the set of scRNA-seq cells at iteration k. Perform the optimization in equation (Rk)(. Name the new set Rk+1). Given two cells’ vectors, ci and gj, the Pearson correlation between them is calculated using the following formulaci and gj; cik and gjk are kth elements in vectors ci and gj, respectively.To calculate Pearson correlation coefficients between each RNA-DNA pair of cells, we use the raw read counts in the CNA profile and gene expression vector of the cells (Further information on research design is available in the Supplementary Information filePeer Review FileReporting SummarySource Data


However, the potential role of mitophagy in sepsis remains poorly explored. Here, we studied the role of mitophagy in sepsis and its immune heterogeneity. By performing mitophagy-related typing on 348 sepsis samples, three clusters  were obtained. Cluster A had the highest degree of mitophagy accompanied by lowest disease severity, while cluster C had the lowest degree of mitophagy with the highest disease severity. The three clusters had unique immune characteristics. We further revealed that the expression of PHB1 in these three clusters was significantly different and negatively correlated with the severity of sepsis, suggesting that PHB1 was involved in the development of sepsis. It has been reported that impaired mitophagy leads to the over-activation of inflammasomes, which promotes sepsis development. Further analysis showed that the expressions of NLRP3 inflammasomes core genes in cluster C were significantly up-regulated and negatively correlated with PHB1. Next, we verified whether PHB1 downregulation caused the activation of inflammasomes and found that the PHB1 knockdown increased the levels of mtDNA in the cytoplasm and enhanced the activation of NLRP3 inflammasomes. In addition, mitophagy inhibitor treatment abolished PHB1 knockdown-mediated activation of NLRP3 inflammasomes, suggesting that PHB1 inhibited the activation of inflammasomes through mitophagy. In conclusion, this study reveals that a high degree of mitophagy may predict a good outcome of sepsis, and PHB1 is a key NLRP3 inflammasome regulator  Auto22.1https://www.ncbi.nlm.nih.gov/geo/) by R package “GEOquery”. The whole blood RNA-seq data and clinical data of 392 samples were collected in this cohort, including 348 patients from emergency room (ER) or intensive care unit (ICU) and 44 normal samples. Annotation conversion was performed on the gene probes of the raw data, and the count data was further converted into tpm data for subsequent analysis.R 4.0.3 was used for data mining and analysis. The sepsis-related dataset GSE185263  was obta2.2≥ 0.5 & Module Membership in Greenyellow module ≥ 0.8). In addition, 230 mitophagy-related genes (Relevance score ≥ 1.5) were identified through retrieval “mitophage” from GeneCards (https://www.genecards.org/). Finally, 22 mitophagy genes of top genes in the module were as the signature set related to mitophagy in sepsis.First, in 348 sepsis samples, gene module with a high correlation pattern (excluding grey modules that are not clustered) were identified by using WGCNA  . Accordi2.3https://www.gsea-msigdb.org/gsea/index.jsp). In addition, Metascape (http://metascape.org/)  was used to quantify the score of the mitophagy  signature set for each sample to assess the extent of mitophagy enrichment for different samples. MA score was introduced to quantify mitophagy signature set of each sample by ssGSEA. The enrichment scores of related pathways between different samples were compared by Gene Set Variation Analysis (GSVA) . Gene Sepe.org/)  was also2.4Consensus clustering, an unsupervised clustering method, classifies samples into several clusters based on omics data set, and can compare and analyze different clusters. The R package “ConsensusClusterPlus”  was used2.5https://cn.string-db.org/) (http://metascape.org/) database was used for a further modular analysis of gene interaction network, and Cytoscape (https://cytoscape.org/) (STRING (db.org/)  databasepe.org/)  was used2.6The immune scores of different samples were calculated using different immune algorithms of R package “IOBR”  to quant2.75 cells per well), then transfected with siRNA using Lipofectamine RNAiMAX (Thermo Fisher Scientific) according to the manufacturer’s instructions. The siRNA sequences for mouse PHB1  and the negative control (UUCUCCGAACGUG UCACGUTT) were chemically synthesized by Sangon Biotech Co., Shanghai, China.To obtain mouse primary peritoneal macrophages, mice were injected intraperitoneally with 3% thioglycolate. Three days later, peritoneal exudate cells were harvested and incubated. Two hours later, nonadherent cells were removed and the adherent monolayer cells were used as peritoneal macrophages. For silencing of PHB1, mouse primary peritoneal macrophages were seeded in 12-well (5 × 102.8Cell lysates were prepared using RIPA lysis buffer and protein concentration was determined by the BCA method (Thermo Fisher Scientific). Samples were separated by 12% SDS-PAGE and transferred onto PVDF membranes (Millipore). Antibody to PHB1 (Abcam) was used at 1:1000 dilution. Blots were normalized to GAPDH expression.2.9For NLRP3 inflammasome activation, mouse primary peritoneal macrophages were primed with LPS (100 ng/mL) for 3 h followed by stimulation with 5 mM ATP (30min) or 10 μM Nigericin (1h). For mitophagy inhibition, cells were pre-treated with 5 mM 3-MA (1h). Supernatants were collected for ELISA detection.2.10The level of IL-1b and IL-18 in cell culture supernatant were analyzed using IL-1b ELISA kit (eBioscience) and IL-18 (Abcam) according to the manufacturer’s instructions.2.11mtDNA was isolated from the cytosolic fractions using a DNeasy Blood & Tissue Kit (Qiagen). The relative mtDNA levels were determined by qPCR with the primers of NADH dehydrogenase 6 (ND6) gene. Forward primer (5’-TTAGCATTAAAGCCT TCACC-3’) and reverse primer (5’-TAACAATCACCCAAACAACC-3’) of ND6 were used. Quantitative PCR was performed using SYBR Green (Vazyme Biotech) on a LightCycler 480 (Roche Diagnostics).2.12https://www.phosphosite.org/homeAction) (https://go.drugbank.com/)  (https://vina.scrips.edu/) (https://plip-tool.biotec.tu-dresden.de/plip-web/plip/index)   to predink.com/) . The PHB.ac.uk/) . We furtps.edu/)  and screp/index) .2.13post hoc Bonferroni test for multiple comparisons. Statistical analysis was performed using R 4.0.3 and GraphPad Prism software 8.0. A p value < 0.05 was considered statistically significant for all analyses. *P<0.05, **P<0.01, ***P<0.001, ****P<0.0001.The Wilcoxon test was used to compare non-normally distributed variables between unpaired groups. The Kruskal-Wallis test was used to compare non-normally distributed variables between groups. Pearson method was used for correlation analysis. For all experiments, the number of independent experiments (n) were described in the legend. Two-tailed unpaired Student’s t test was used to compare the differences between two groups. Two-way ANOVA tests were used followed by 33.1To test whether the mitophagy activity of sepsis patients is changed, we first evaluated the enrichment of mitophagy-related pathways in emergency room (ER) or intensive care unit (ICU) samples  that may bind to the ubiquitination site of PHB1 protein to increase the stability of the protein in the batch screened drugs. Among them, we learned that Bemcentinib has been currently studied for the treatment of non-small cell lung cancer, and the analysis results showed that Bemcentinib can bind to multiple ubiquitination sites  of PHB1 with superior affinity (≤ -7). Interestingly, Bemcentinib is also an inhibitor of Spike glycoprotein, this drug was previously reported for the treatment of COVID-19 , which aThe original contributions presented in the study are included in the article/FL conceived the project and designed experiments and wrote the paper. SC analyzed the data and wrote the paper. JM and PY performed the experiments and assisted in data interpretation. All authors contributed to the article and approved the submitted version.