key: cord-0968588-mlht1frb
authors: Armingol, Erick; Baghdassarian, Hratch M.; Martino, Cameron; Perez-Lopez, Araceli; Knight, Rob; Lewis, Nathan E.
title: Context-aware deconvolution of cell-cell communication with Tensor-cell2cell
date: 2021-09-23
journal: bioRxiv
DOI: 10.1101/2021.09.20.461129
sha: c8ceef1774da1207a425dcb3951cd2989ac0a59d
doc_id: 968588
cord_uid: mlht1frb

Cell interactions determine phenotypes, and intercellular communication is shaped by cellular contexts such as disease state, organismal life stage, and tissue microenvironment. Single-cell technologies measure the molecules mediating cell-cell communication, and emerging computational tools can exploit these data to decipher intercellular communication. However, current methods either disregard cellular context or rely on simple pairwise comparisons between samples, thus limiting the ability to decipher complex cell-cell communication across multiple time points, levels of disease severity, or spatial contexts. Here we present Tensor-cell2cell, an unsupervised method using tensor decomposition, which is the first strategy to decipher context-driven intercellular communication by simultaneously accounting for multiple stages, states, or locations of the cells. To do so, Tensor-cell2cell uncovers context-driven patterns of communication associated with different phenotypic states and determined by unique combinations of cell types and ligand-receptor pairs. We show Tensor-cell2cell can identify multiple modules associated with distinct communication processes (e.g., participating cell-cell and ligand receptor pairs) linked to COVID-19 severities. Thus, we introduce an effective and easy-to-use strategy for understanding complex communication patterns across diverse conditions.

Organismal phenotypes arise as cells adapt and coordinate their functions through cell-cell interactions within their microenvironments 1 . Variations in these these interactions and the resulting phenotypes can occur because of genotypic differences (e.g. different subjects) or the transition from one biological state or condition to another 2 (e.g. from one life stage into another, migration from one location into another, and transition from health to disease states). These interactions are mediated by changes in the production of signals and receptors by the cells, causing changes in cell-cell communication (CCC).

Thus, CCC is dependent on temporal, spatial and condition-specific contexts 3 , which we refer to here as cellular contexts. That is, "cellular contexts" refer to variation in genotype, biological state or condition that can shape the microenvironment of a cell and therefore its CCC. Under this idea, CCC can be seen as a function of a context variable that is not necessarily binary and can encompass multiple levels (e.g. multiple time points, gradient of disease severities, different subjects, distinct tissues, etc.). Consequently, varying contexts trigger distinct strength and/or signaling activity 1,4-6 of communication, leading into complex dynamics of CCC (e.g. increasing, decreasing, pulsatile and oscillatory communication activities across contexts). Importantly, unique combinations of cell-cell and ligand-receptor (LR) pairs can follow different context-dependent dynamics, making CCC hard to decipher across multiple contexts.

Single-cell omics assays provide the necessary resolution to measure these cell-cell interactions and the ligand-receptor pairs mediating the CCC. While computational methods for inferring CCC have been invaluable for discovering the cellular and molecular interactions underlying many biological processes, including organismal development and disease pathogenesis 5 , current approaches cannot account for high variability in contexts (e.g., multiple time points or phenotypic states) simultaneously.

Existing methods lose the correlation structure across contexts since they usually involve repeating analysis for each context separately, disregarding informative variation across such factors as disease severities, time points, subjects or cellular locations 7 . Additional analysis steps are required to compare and compile results from pairwise comparisons [8] [9] [10] [11] , reducing the statistical power and hindering efforts to link phenotypes to the interacting cells and their associated CCC. Moreover, this roundabout process is computationally expensive, making analysis of large sample cohorts intractable. Thus, new methods are needed that analyze CCC while accounting for the correlation structure across multiple contexts simultaneously.

Tensor-based approaches such as Tensor Component Analysis 12 Embedding (t-SNE) can extract low-dimensional structures from the data and reflect important molecular signals 13, 14 , TCA is better suited to analyze multidimensional datasets obtained from multiple biological contexts or conditions 7 (e.g. time points, study subjects and body sites). Indeed, TCA outperforms matrix-based dimensionality reduction methods when recovering ground truth patterns associated with, for example, dynamic changes in microbial composition across multiple patients 15 and neuronal firing dynamics across multiple experimental trials 12 . TCA's superior performance resides in that it does not require the aggregation of datasets across varying contexts into a single matrix. It instead organizes the data as a tensor, the higher order generalization of matrices, which better preserves the underlying context-driven correlation structure by retaining mathematical features that matrices lack 16, 17 . Thus, with the correlation structure retained, the use of TCA with expression data across many contexts allows one to gain a detailed understanding of how context shapes communication, as well as the specific molecules and cells mediating these processes.

Here, we introduce Tensor-cell2cell, a TCA-based strategy that deconvolves intercellular communication across multiple contexts and uncovers modules or latent patterns of CCC. These context-driven latent patterns of intercellular communication in an unsupervised manner. Briefly, Tensor-cell2cell first generates a 4D-communication tensor that contains non-negative scores to represent cell-cell communication across different conditions (Figures 1a-c) . Then, a non-negative TCA 19 is applied to deconvolve the latent CCC structure of this tensor into low-dimensional components or factors (Figures 1d-e) . Thus, each of these factors can be interpreted as a module or pattern of communication whose dynamics across contexts is indicated by the loadings in the context dimension Our simulation-based analysis further demonstrates that Tensor-cell2cell accurately detects context-dependent changes of communication, and identifies which LR pairs, sender cells, and receiver cells are important (Figure 2g ). In particular, the context loadings of the TCA on the simulated tensor accurately recapitulate the introduced patterns (Figures 2f-g) , while ligand-receptor and cell loadings properly capture the ligand-receptor pairs, sender cells and receiver cells assigned as participants of the cognate pattern ( Figure 2g ). Indeed, we observed a concordance between the "ground truth" LR pairs assigned to a pattern and their respective factor loadings through Jaccard index and Pearson correlation metrics (Supplementary Tables S1-S2) . Moreover, Tensor-cell2cell robustly recovered communication patterns when we added noise to the simulated tensor (Supplementary Figure S2 and Supplementary Notes).

Tensor-cell2cell is the first method for interpreting CCC across multiple conditions or contexts simultaneously, enabling a wealth of analyses and conclusions inaccessible to any other tools. Most available tools for inferring intercellular communication are designed to analyze one context at the time, while a few also allow pairwise comparisons between contexts (Table 1) . However, pairwise comparisons will likely miss insights about changes of intercellular communication across multiple contexts.

To quantify computational efficiency and accuracy of Tensor-cell2cell, we compared our method to CellChat 10 , the only tool that summarizes multiple pairwise comparisons in an automated manner (Table   1 ). While CellChat cannot extract patterns of CCC across multiple contexts, we instead use the output of its joint manifold learning on pairwise-based changes in signaling pathways as a comparable proxy to the output of Tensor-cell2cell. Crucially, Tensor-cell2cell reports behaviors of communication modules across all contexts simultaneously and associates these modules with specific molecular and cellular mechanisms, information that CellChat is limited to reporting when comparing just two contexts. Thus, our comparison of tools is intended to assess running time and memory demand, and each tool's ability to identify signals that could separate contexts by measuring the accuracy of a context classifier trained from each tool output. are computed from the expression of the ligand and the receptor in a LR pair (k-th pair among K pairs) for a specific sender-receiver cell pair (i-th and j-th cells among I and J cells, respectively). This results in a communication matrix containing all pairs of sender-receiver cells for that LR pair (a). The same process is repeated for every single LR pair in the input list of ligand-receptor interactions, resulting in a set of communication matrices that generate a 3D-communication tensor (b). 3D-communication tensors are built for all contexts and are used to generate a 4D-communication tensor wherein each dimension represents the contexts (colored lines), ligand-receptor pairs, sender cells and receiver cells (c). A non-negative TCA model approximates this tensor by a lower-rank tensor equivalent to the sum of multiple factors of rank-one (R factors in total) (d). Each component or factor (r-th factor) is built by the outer product of interconnected descriptors (vectors) that contain the loadings for describing the relative contribution that contexts, ligand-receptor pairs, sender cells and receiver cells have in the factor (e). For interpretability, the behavior that context loadings follow represent a communication pattern across contexts. Hence, the communication captured by a factor is more relevant or more likely to be occurring in contexts with higher loadings. Similarly, ligand-receptor pairs with higher loadings are the main mediators of that communication pattern. By constructing the tensor to account for directional interactions (panels a-b), ligands and receptors in LR pairs with high loadings are mainly produced by sender and receiver cells with high loadings, respectively. Individual LR pairs and cell pairs were categorized into groups of signalling pathways and cell types, respectively. In this simulation, signaling pathways did not overlap in their LR pairs, and each pathway was assigned 100 different LR pairs. (d) Distinct combinations of signaling pathways with sender-receiver cell type pairs were generated (LR-CC combinations). LR-CC combinations that were assigned the same signaling pathway overlap in the LR pairs but not in the interacting cell types. (e) A simulated 4D-communication tensor was built from each time point's 3D-communication tensor. Here, a communication score was assigned to each ligand-receptor and cell-cell member of a LR-CC combination. Each communication score varied across time points according to a specific pattern. (f) Four different patterns of communication scores were introduced to the simulated tensor by assigning a unique pattern to a specific LR-CC combination. From top to bottom, these patterns were an oscillation, a pulse, an exponential decay and a linear decrease. The average communication score (y-axis) is shown across time points (x-axis). This average was computed from the scores assigned to every ligand-receptor and cell-cell pair in the same LR-CC combination. (g) Results of running Tensor-cell2cell on the simulated tensor. Each row represents a factor, and each column a tensor dimension, wherein each bar represents an element of that dimension (e.g. a time point, a ligand-receptor pair, a sender cell or a receiver cell). Factor loadings (y-axis) are displayed for each element of a given dimension. Here, the factors were visually matched to the corresponding latent pattern in the tensor. 26 We ran Tensor-cell2cell and CellChat on a single-cell transcriptome atlas of peripheral blood mononuclear cells (PBMCs) from COVID-19 patients with varying severity 27 28 . We next measured their accuracy with the area under the receiver operating characteristic curve (AUC). Tensor-cell2cell outperformed CellChat when classifying PBMC samples by severity (Figure 3e ), and performed similarly when classifying samples by disease state (Figure 3g ). Moreover, Tensor-cell2cell performed better than CellChat in all classification tasks associated with BALF samples (Figures 3f,h) . Surprisingly, all methods performed better (highest AUC) when classifying BALF samples than when classifying PBMC samples, possibly due to a more evident severity-driven variation of the immune response in the infection site rather than in the periphery. Thus, these results show that Tensor-cell2cell can successfully find signatures of CCC that differentiate between contexts in a computationally efficient manner. 

Great strides have been made to unravel molecular and cellular mechanisms associated with SARS-CoV-2 infection and COVID-19 pathogenesis. Thus, we tested our method on a single-cell dataset of BALF samples from COVID-19 patients 28 Table S3 ). SDC4 and F11R (Figure 4b ), which were determined important for tissue repair and inflammation during lung injury previously [40] [41] [42] . Remarkably, a new technology for tracing experimentally CCC revealed that SEMA4D-PLXNB2 interaction promotes inflammation in a diseased central nervous system 43 ; a role consistent with the pattern in factor 2, which captured this interaction as the top-ranked LR pair correlating with COVID-19 severity (Figures 4a,b) . 

Here we present Tensor-cell2cell, a novel computational approach that finds modules or patterns of cell-cell communication and their changes across contexts (e.g., across subjects with different disease severity, multiple time points, different tissues, etc.). We show the power of Tensor-cell2cell with both simulated and real datasets to extract complex patterns of intercellular communication in an unsupervised fashion. Crucially, our approach can rank LR pairs based on their importance in each module of communication, and it connects these signals with variations in phenotype (e.g., increasing use of LR pairs with COVID-19 severity, as shown in factors 1,2 and 8 in Figure 4a ). These features distinguish Tensor-cell2cell as a novel tool in contrast to state-of-the-art tools that are either unaware of the context driving CCC 5, 20, 23, 56 or require analysis of each context separately and perform pairwise comparisons in posterior steps 10, 11 . Thus, Tensor-cell2cell is the first tool that facilitates the study of CCC in a context-aware manner, simultaneously integrating any number of samples, and helping generate testable hypotheses about the biological role of molecules across multiple conditions.

Tensor-cell2cell is fast for analyzing multiple contexts simultaneously, providing up to 790-fold improvement in running time and reduced memory requirements with respect to analyses involving multiple pairwise comparisons (Figures 3a-d) . It is also more accurate, resulting in a marked 10-20%

higher classification accuracy of subjects with COVID-19 when compared to CellChat (Figures 3e-h) , the only available tool that summarizes multiple pairwise comparisons of contexts. However, it is important to consider that benchmarking tools for predicting CCC is challenging due to the lack of a ground truth 5 , and it is hard to compare and evaluate tools because of the diversity of scoring approaches 57 . Indeed, the outputs and details offered by CellChat and Tensor-cell2cell differ. CellChat reports context-associated UMAP embeddings of signaling pathways, while Tensor-cell2cell outputs TCA embeddings for contexts, ligand-receptor pairs, and interconnected sender and receiver cells. By training classifiers that accept these differing outputs, in most cases, Tensor-cell2cell greatly outperformed CellChat (Figures 3e,f,h) . While in a few scenarios we observed qualitatively comparable performance (Figure 3g , Tensor-cell2cell and the functional method of CellChat), Tensor-cell2cell always performed better quantitatively. Although context classification is a useful approach for comparison, this strategy cannot evaluate how well these methods infer CCC due to their distinct scopes and the vast differences in the tools' outputs. In this regard, the outputs of Tensor-cell2cell seem valuable for identifying specific molecular targets and involved cells of a context-dependent module of communication, encompassing information beyond the scope of CellChat, which largely focuses on pair-wise, context-specific differences between signaling pathways.

Meaningful biological roles are easily identifiable from the patterns captured by Tensor-cell2cell. For example, we detected a previously reported correlation between the interactions of the lung epithelium with the immune cells and COVID-19 severity 18 and differences between moderate and severe COVID-19, especially associated with modules of macrophage communication 28 . Tensor-cell2cell recapitulated molecular findings such as the role of SEMA4D-PLXNB2 interaction promoting inflammation 43 , interaction that Tensor-cell2cell revealed to be stronger in cases with more lung inflammation (severe cases) (Figure 4) , and the role of CCL2, CCL3, CCR1 and CCR5 as proinflammatory molecules, which makes them potential therapeutic targets for diminishing COVID-19 severity 18 , proteins that our strategy associated with CCC in severe cases ( Figure 4b ). Additionally, we interacts with PTPRC (CD45) expressed by other cells (Figure 4a-b) . Interestingly, the MRC1-PTPRC interaction mediating macrophage communication can promote immune tolerance 58 , which is consistent with factor 10 being associated with moderate cases, wherein anti-inflammatory macrophages (M2-like phenotype) seem to be characteristic. Another example is a recent GWAS study that reported 13 significant loci associated with SARS-CoV-2 infection 59 , wherein ICAM1 popped up as an involved gene. Remarkably, Tensor-cell2cell assigned a high loading to the ITGB2-ICAM1 interaction in a communication pattern that seems to be associated with antigen presentation (factor 5, Figures 4a-b) , providing further insights of its potential mechanism.

One limitation of Tensor-cell2cell is that it is not intended for analyzing the behavior of specific pairs of cells or ligands and receptors of interest across contexts. Instead, Tensor-cell2cell finds data-driven modules of communication, which may result in factors with small loadings for cells and LR pairs of interest. In such a scenario, those cells and LR pairs may not participate in a latent context-dependent module but may still follow certain behavior across contexts; thus, applying Tensor-cell2cell would not be appropriate. Instead, using other tools may be recommended (Table 1) Tensor-cell2cell is therefore a flexible method that can integrate multiple datasets and readily identify patterns of intercellular communication in a context-aware manner, reporting them through interconnected and easily interpretable scores. In addition to single cell data shown here, Tensor-cell2cell also accepts bulk transcriptomics data (an example of a time series bulk dataset of C.

elegans is included in a CodeOcean capsule, see Methods), and it could further be used to analyze proteomic data. We demonstrated the application of Tensor-cell2cell in cases where samples correspond to distinct patients, but it can be applied to many other contexts. For instance, our strategy can be readily applied to time series data by considering time points as the contexts, and to spatial transcriptomic datasets, by previously defining cellular niches or neighborhoods as the contexts.

Moreover, we have also included Tensor-cell2cell as a part of our previously developed tool cell2cell 60 , enabling previous functionalities such as employing any list of LR pairs (even including protein complexes), multiple visualization options, and personalizing the communication scores to account for other signaling effects such as the (in)activation of downstream genes in a signaling pathway 23, 61 , which could lead to different biological interpretations 57 . Lastly, we demonstrated that Tensor-cell2cell stands as a fast, low-memory and accurate method (Figure 3 ), which can be substantially accelerated when a GPU is available (Figure 3a) . Thus, these attributes make Tensor-cell2cell valuable for identifying key cell-cell and LR pairs mediating complex patterns of cellular communication in future studies, especially when considering the response time needed to deal with, for example, the COVID-19 pandemic.

RNA-seq datasets were obtained from publicly available resources. 

A human list of 2,005 ligand-receptor pairs, 48% of which include heteromeric-protein complexes, was obtained from CellChat 10 . We filtered this list by considering the genes expressed in the PBMC and BALF expression datasets and that match the IDs in the list of LR pairs, resulting in a final list of 1639 and 189 LR pairs, respectively.

For building a context-aware communication tensor, three main steps are followed: To build the tensor for both COVID-19 datasets, we computed the communication scores as the mean expression between the ligand in a sender cell type and cognate receptor in a receiver cell type, as previously described 20 . For the LR pairs wherein either the ligand or the receptor is a multimeric protein, we used the minimum value of expression among all subunits of the respective protein to compute the communication score. In both cases we further considered cell types that were present across all samples. Thus, the 4D-communication tensor for the PBMC and BALF datasets resulted in a size of 60

x 1639 x 6 x 6 and 12 x 189 x 6 x 6, respectively (that is, samples x ligand-receptor pairs x sender cell types x receiver cell types).

Briefly, non-negative TCA is a generalization of NMF to higher-order tensors (matrices are tensors of order two). To detail this approach, let represent a C x P x S x T tensor, where C, P, S and T χ correspond to the number of contexts/samples, ligand-receptor pairs, sender cells and receiver cells contained in the tensor, respectively. Similarly, let denote the representative interactions of context χ i, using the LR pair j, between the sender cell k and receiver cell l. Thus, the TCA method underlying Tensor-cell2cell corresponds to CANDECOMP/PARAFAC 65, 66 , which yields the decomposition, factorization or approximation of through a sum of r tensors of rank-1 (Figure 1d) :

Where the notation represents the outer product and are vectors of the factor r that 

In the COVID-19 dataset of BALF samples, we compared the loadings of samples as well as the fraction of macrophages with non-zero expression for a set of ligands and receptors across the categories representing healthy patients and varying severities of COVID-19. To perform these comparisons, we used an independent t-test followed by a Bonferroni's correction to indicate significance of the change (Supplementary Figures S3 and S4 ).

We measured the running time and memory demanded by Tensor-cell2cell and CellChat to analyze the COVID-19 dataset containing PBMC samples. Each tool was evaluated in two scenarios: either using each sample individually, or by first combining samples by severity (control, mild/moderate, and severe/critical) by aggregating the expression matrices. The latter was intended to favor CellChat by diminishing the number of pairwise comparisons to always be between three contexts; thus, increases in running time or memory demand in this case are not due to an exponentiation of comparisons (n samples choose 2). CellChat was run by following the procedures outlined in the "Comparison_analysis_of_multiple_datasets" vignette (https://github.com/sqjin/CellChat/tree/master/tutorial). Briefly, signalling pathway communication probabilities were first individually calculated for each sample or context. Next, pairwise comparisons between each sample or context were obtained by computing either a "functional" or a "structural" similarity. The functional approach computes a Jaccard index to compare the signaling pathways that are active in two cellular communication networks, while the structural approach computes a network dissimilarity 70 to compare the topology of two signaling networks (see REF 10 for further details). Finally, CellChat performs a manifold learning approach on sample similarities and returns UMAP embeddings for each signaling pathway in each different context (e.g. if CellChat evaluates 10 signaling pathways in 3 different contexts, it will return embeddings for 30 points) which can be used to rank the similarity of shared signalling pathways between contexts in a pairwise manner.

The analyses of computational efficiency were run on a compute cluster of 2.8GHz x2 Intel(R) Xeon(R) Gold 6242 CPUs with 1.5 TB of RAM (Micron 72ASS8G72LZ-2G6D2) across 32 cores. Each timing task was limited to 128 GB of RAM on one isolated core and one thread independently where no other processes were being performed. To limit channel delay, data was stored on the node where the job was performed, where the within socket latency and bandwidth are 78.9 ns and 46,102 MB/s respectively. For all timing jobs, the same ligand-receptor pairs and cell types were used. Furthermore, to make the timing comparable, all samples in the dataset were subsampled to have 2,000 single cells.

In the case of Tensor-cell2cell, the analysis was also repeated by using a GPU, which corresponded to a Nvidia Tesla V100.

A Random Forests 71 (RF) model was trained to predict disease status based on both COVID-19 status (healthy-control vs. patient with COVID-19) and severity (healthy-control, moderate symptoms, and severe symptoms). The RF model was trained using a Stratified K-Folds cross-validation (CV) with 3-Fold CV splits. On each CV split a RF model with 500 estimators was trained and RF probability-predictions were compared to the test set using the Receiver Operating Characteristic (ROC). The mean and standard deviation from the mean were calculated for the area under the Area Under the Curve (AUC) across the CV splits. This classification was performed on the context loadings of Tensor-cell2cell, and the two UMAP dimensions of the structural and functional joint manifold learning of CellChat, for both the BALF and PBMC COVID-19 datasets. All classification was performed through Scikit-learn (v. 0.23.2) 72 .

Tensor-cell2cell is implemented in our cell2cell suite 60 , which is available in a GitHub repository (https://github.com/earmingol/cell2cell). All the code and input data used for the analyses are available online in a Code Ocean capsule for reproducible runs (https://doi.org/10.24433/CO.0051950.v1). While the code for benchmarking the computational efficiency in a local computer is available in a GitHub repository (https://github.com/LewisLabUCSD/CCC-Benchmark).

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All the described calculations were implemented in Tensor-cell2cell through functions available in Tensorly 68 , a Python library for tensors.

Depending on the number of factors used for approximating the 4D-communication tensor, the reconstruction error calculated in the objective function can vary. To quantify the error with an interpretable value, we used a normalized reconstruction error as previously described 12 . This normalized error is on a scale of zero to one and is analogous to the fraction of unexplained variance used in PCA:

To represent an overall communication state of cells in a factor r, the outer product can be computed between the vectors and , which contains the loadings of sender and receiver cells for that factor, respectively. This outer product represents a joint distribution of cell pair loadings, and each value 

The authors declare no competing interests.