GLUER integrative analysis of single-cell omics and imaging data by deep neural network.pdf

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GLUER: integrative analysis of single-cell omics and imaging data by deep neural
network
Tao Peng1,2
, Gregory M. Chen3
, Kai Tan1,2,4
1
Center for Childhood Cancer Research, The Children’s Hospital of Philadelphia,
Philadelphia, PA 19104, USA
2
Department of Biomedical and Health Informatics, The Children’s Hospital of
Philadelphia, Philadelphia, PA 19104, USA
3
Graduate Group in Genomics and Computational Biology, University of Pennsylvania,
Philadelphia, PA 19104, USA
4
Department of Pediatrics, University of Pennsylvania, Philadelphia, PA 19104, USA
Correspondence to: Kai Tan, tank1@email.chop.edu
Keywords: single cell; transcriptomics; epigenomics; multi-omics; molecular imaging;
CODEX; SeqFISH; MERFISH; data integration; joint nonnegative matrix factorization;
deep neural network
ABSTRACT
Single-cell omics assays have become essential tools for identifying and characterizing
cell types and states of complex tissues. While each single-modality assay reveals
distinctive features about the sequenced cells, true multi-omics assays are still in early
stage of development. This notion signifies the importance of computationally
integrating single-cell omics data that are conducted on various samples across various
modalities. In addition, the advent of multiplexed molecular imaging assays has given
rise to a need for computational methods for integrative analysis of single-cell imaging
and omics data. Here, we present GLUER (inteGrative anaLysis of mUlti-omics at
single-cEll Resolution), a flexible tool for integration of single-cell multi-omics data and
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imaging data. Using multiple true multi-omics data sets as the ground truth, we
demonstrate that GLUER achieved significant improvement over existing methods in
terms of the accuracy of matching cells across different data modalities resulting in
ameliorating downstream analyses such as clustering and trajectory inference. We
further demonstrate the broad utility of GLUER for integrating single-cell transcriptomics
data with imaging-based spatial proteomics and transcriptomics data. Finally, we extend
GLUER to leverage true cell-pair labels when available in true multi-omics data, and
show that this approach improves co-embedding and clustering results. With the rapid
accumulation of single-cell multi-omics and imaging data, integrated data holds the
promise of furthering our understanding of the role of heterogeneity in development and
disease.
INTRODUCTION
A number of single-cell omics assays have been developed for robust profiling of
transcriptome, epigenome and 3-dimensional chromosomal organization. Similarly,
multiplexed molecular imaging assays have been developed for simultaneous profiling
of a large number of proteins 1, 2
and transcripts 3-5
at single-cell resolution. Collectively,
these assays provide powerful means to characterize molecular heterogeneity.
However, each omics and imaging assay has its own strengths and weaknesses, which
results in a partial picture of the biological systems. For example, single-cell omics
assays are unable to capture the spatial distribution of measured molecules. On the
other hand, imaging assays such as CODEX (co-detection by indexing) 1
and MERFISH
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can capture spatial expression patterns of proteins and transcripts within the intricate
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tissue architecture. However, their coverage is much lower than single-cell omics
assays and therefore lack the power to resolve cell types/states 6
.
Recently, single-cell assays have been developed to jointly measure two or more
of molecular modalities in the same cells. For example, sci-CAR 7
and SNARE-Seq 8
allow simultaneous profiling of open chromatin and gene expression. Methyl-HiC 9
and
single-nucleus methyl-3C 10
have been developed to profile chromatin interaction and
DNA methylation simultaneously. Although in theory dual-modality measure makes data
integration easier, in practice, data integration remains a challenge due to differences in
coverage and data modality-specific characteristics.
Computational tools that can flexibly and robustly integrate individual single-cell
data sets offer many exciting opportunities for discovery. To date, the most widely used
data integration methods are Seurat (v3) 11
and LIGER 12
. Seurat seeks to map data
sets into a shared latent space using dimensions of maximum correlations and
subsequently maximizes correlated latent factor space which is determined by
maximize the correlations. By doing so, it may miss true biological variations across the
data sets that may be important. LIGER uses nonnegative matrix factorization and
computes the joint clustering using the loading matrices. However, it only considers cell
pairs with the smallest distance across the data sets and thus ignore one-to-many and
many-to-many pairs, which are biologically meaningful.
Here, we describe GLUER (inteGrative anaLysis of mUlti-omics at single-cEll
Resolution by deep neural network). A flexible method for integrating single-cell omics
and molecular imaging data. It employs three computational techniques, joint
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nonnegative matrix factorization, mutual nearest neighbor algorithm, and deep learning
neural network. Joint nonnegative matrix factorization of the data sets maintains
biological differences across the data sets while allowing identification of common
factors shared across the data sets. Mutual nearest neighbor algorithm enables
mapping of many-to-many relationships among cells across the data sets. Deep
learning neural networks can capture nonlinear relationships between the data sets. In
comparison, only linear functions were used in previous methods. Using multiple true
multi-omics data sets as the ground truth, we show that GLUER achieved significant
improvement in data integration accuracy. We implemented GLUER in Python and also
provided a graphical user interface (GUI) for users to explore the integration results.
RESULTS
Overview of the GLUER algorithm
GLUER combines joint nonnegative matrix factorization (NMF), mutual nearest neighbor
algorithm, and deep neural network to integrate data of different modalities (Figure 1).
The purpose of joint NMF is to identify shared components across data sets of different
modalities. The result of this step are dimension-reduced matrices (factor loading
matrices) for each data modality. The factor loading matrix from one data modality is
defined as the reference matrix and the rest as the query matrices. These matrices are
used to calculate the cell distance and subsequently determine putative cell pairs
between the reference data set and the query data sets. Under the guidance of the
putative cell pairs, a deep neural network is used to learn map functions between factor
loading matrices of query data sets to the reference factor loading matrix. Using the
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learnt functions, co-embedded data is then computed by combining the reference factor
loading matrix and query factor loading matrices. GLUER is freely available as a Python
package at https://github.com/tanlabcode/GLUER.
Performance evaluation using transcriptomics and chromatin accessibility dual-
omics data on mixtures of cell lines
We first evaluated the performance of GLUER using true single-cell dual-omics data
where the ground truth of cell pairing is known. These data sets were generated using
state-of-the-art assays that simultaneously profile mRNA expression and chromatin
accessibility, including sci-CAR 7
, SNARE-Seq 8
, and scCAT-seq 13
. sci-CAR and
SNARE-Seq process thousands to millions of cells together by using droplet platforms
or combinatorial DNA barcoding strategies with high scalability and cost effectiveness.
scCAT-seq processes hundreds of single cells in individual wells of microwell plates.
Three data sets on mixtures of human cell lines were used (Supplementary Table 1).
Data Set 1 was generated using the SNARE-Seq assay 8
and a mixture of four human
cell lines, BJ, H1, K562, and GM12878. Data Set 2 was generated using the scCAT-seq
assay 13
and a mixture of 5 human cell lines, including K562, HeLa-S3, HCT116, cells of
patient-derived xenograft (PDX) samples of a moderately differentiated squamous cell
carcinoma patient (PDX1) and a large-cell lung carcinoma patient (PDX2). Data Set 3
was generated using the sci-CAR assay 7
and human lung adenocarcinoma-derived
A549 cells after 0,1, and 3 hours of treatment of 100nM dexamethasone (DEX).
We compared three integration methods, Seurat, LIGER, and GLUER using
these three data sets, ensuring that each method was blinded to the true cell-pair
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labels. Thus, this analysis simulated a situation in which single-cell RNA-Seq and
ATAC-Seq assays were performed independently on separate batches of cells. We
inspected the Uniform Manifold Approximation and Projection (UMAP) plots of the
integration results (co-embedded data) and evaluated the results quantitatively using
the integration accuracy metric (see Online Methods for details). Since human cell lines
were used for generating the ground truth data sets, the true biological identity of the
cells is known. Hence, a proper integration should result in retaining the known
biological clusters after integrating the data sets.
Figure 2 shows the integration results of Data Set 1 by Seurat, LIGER, and
GLUER. A good integration method should generate well-mixed cells identified with
different data modalities. Visual inspection of the UMAP plots revealed that the degree
of mixing of transcriptome and chromatin accessibility data was the highest in the
GLUER result and lowest in the LIGER result (Figure 2a-c). The same trend was also
observed in Data Sets 2 and 3 (Supplementary Figures 1a-c, 2a-c). By design, the cell
line mixture data provides the ground truth for the number of cell clusters we should
expect in the integrated data. For Data Set 1, LIGER result produced 10 cell clusters,
which is not consistent with the fact that only four cell lines were used for generating the
SNARE-Seq data set 5
(Figure 2b). Similar result was also observed with Data Set 2
where LIGER result yielded more than 5 cell clusters which was the number of cell lines
used to generated the scCAT-Seq data set 3
(Supplementary Figure 1b). Seurat result
yielded the correct number of clusters (four) on Data Set 1 although separation between
two of the clusters was less clear (Figure 2d). Only GLUER result yielded four cell
clusters that were well separated and represented the four cell lines in the mixture
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sample (Figure 2f). For Data Set 3, only GLUER result can separate DEX untreated and
treated A549 cells (Supplementary Figure 2d-f). Finally, the expression patterns of
known marker genes for the cell lines confirm their identities (Figure 2i, Supplementary
Figure 1h).
To quantitatively evaluate the performance of the methods, we devised a metric
called integration accuracy that is the percentile of the true cell pairs among the
predicted neighbors of a cell. It is calculated based on the dimension-reduced matrices
of the co-embedded data (see Online Methods for details). This metric ranges from 0 to
1 and is high when the true cell pairs across the data sets share a high percentage of
the same neighbors. Our analysis indicates that GLUER had significantly higher
integration accuracy compared to Seurat and LIGER for all three data sets (p < 0.05,
paired Student’s t-test; Figure 2g, Supplementary Figures 1g, 2g).
Performance evaluation using transcriptomics and chromatin accessibility dual-
omics data on primary tissues
To further evaluate the performance of GLUER on data of complex tissues, we used
three true dual-omics data sets of primary tissue samples generated using SNARE-Seq
and sci-CAR assays (Supplementary Table 1). Data Sets 1 and 2 8
were generated
using SNARE-Seq and neonatal mouse cerebral cortex and adult mouse cerebral
cortex samples, respectively. Data Set 3 7
was generated using sci-CAR and mouse
kidney sample.
Figure 3 shows integration results of Data Set 1 by Seurat, LIGER, and GLUER.
Visual inspection of the UMAP plots revealed that the degree of mixing of transcriptome
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and chromatin accessibility data was the highest in the GLUER result and lowest in the
Seurat result (Figure 3a-c). The same trend was also observed in Data Sets 2 and 3
(Supplementary Figures 3a-c, 4a-c). Clustering analysis using the Leiden method 14
revealed more cell clusters in GLUER result versus results of the other two methods,
which is consistent with fact of large numbers of cell types in these tissues (Figure 3e,
Supplementary Figures 3e and 4e). For instance, in Data Set 1, integrated data by
GLUER revealed 14 cell clusters, representing excitatory neurons in Layer 2/3 (EL-2/3-
Rasgrf2), Layer 3/4 (Ex-L3/4-Rorb), Layer 4/5 (Ex-L4/5-Il1rapl2 and Ex-L4/5-Epha4),
Layer 5 (Ex-L5-Klhl29 and Ex-L5-Parm1), Layer 5/6 (Ex-L5/6-Tshz2 and Ex-L5/6-Sulf1),
and Layer 6 (Ex-L6-Foxp2), inhibitory neurons (In-Npy, In-Sst, and In-Pvalb), claustrum,
and astrocytes/oligodendrocytes (Ast/Oli) (Figure 3e). Interestingly, the different types of
excitatory neurons were closer to each other in the UMAP, reminiscent of their adjacent
physical locations in the mouse cerebral cortex. The identification of each cell cluster
was determined based on gene expression and gene activity profiles of known cell-type
markers, which was calculated using the co-embedded transcriptome and chromatin
accessibility data. The marker gene expression and activity profiles clearly demonstrate
cell type specificity (Figure 3f and 3g). More cell clusters were also identified in Data
Sets 2 (adult mouse cerebral cortex, Supplementary Figure 3e-g) and 3 (mouse kidney,
Supplementary Figure 4e-g) integrated by GLUER.
Using the integration accuracy metric, we quantified the performance and found
that GLUER has the highest accuracy in all three data sets (p < 0.05, paired Student’s t-
test; Figure 3d and Supplementary Figures 3d and 4d).
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In summary, using both cell line mixture and primary tissue data where the
ground truth of cell-pairs is known, we demonstrate that GLUER achieved significant
improvement in integrating single-cell transcriptomic and chromatin accessibility data.
Use case 1: Integrating spatial proteomics data with scRNA-Seq data
Co-detection by indexing (CODEX), a multiplexed cytometric imaging method, can
simultaneously profile the expression levels of several dozens of proteins in a tissue
section with single-cell resolution 6
. However, the ability of the method to resolve cell
types/states is limited due to the small number of features (proteins) in a typical data
set. On the other hand, scRNA-Seq assays can profile the expression levels of
thousands of genes in each cell, which enables much finer classification of cell types
and states. To demonstrate the utility of GLUER for integrating spatial proteomics data
and single-cell omics data, we applied it to a matched data set of murine spleen cells
that consists of 7,097 cells profiled by scRNA-Seq 15
and 9,186 cells profiled by CODEX
6
(Supplementary Table 1). A 30-antibody panel was used in the CODEX experiment to
identify splenic-resident cell types.
Inspecting the UMAP plots of the original scRNA-Seq data and CODEX data,
multiple cell clusters are readily evident in the scRNA-Seq data whereas cluster
structure is not clear in the CODEX data (Figure 4a). After data integration and
clustering of the co-embedded data using the Leiden method, cluster structures in the
UMAP plots are more evident in the Seurat and GLUER results than that of the LIGER
result (Figure 4a). 17, 20, and 18 clusters were identified based on the integrated
results by Seurat, LIGER and GLUER respectively (Figure 4b). Using known cell-type
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marker genes, we annotated the clusters based on GLUER integration result (Figure 4c
and Supplementary Figure 5). GLUER identified NK cells, red pulp macrophages,
neutrophils, monocytes, pDCs, plasma cells, erythrocytes/erythroblasts, B cells, and T
cells (Figure 4c). Integrated result by GLUER can effectively separate distinct cell types,
for instance NK cells and red pulp macrophages. The latter are distinct from monocytes
and monocyte-derived macrophages. Natural cytotoxicity triggering receptor (Ncr1) 16
and vascular cell adhesion molecule 1 (Vcam1) 17
are specific markers for these two cell
types, respectively. In the original data, Vcam1 transcript expression was restricted to a
cluster of cells in the scRNA-Seq UMAP but VCAM1 protein expression was more
scattered in the CODEX UMAP. In the integrated data, both transcript and protein
expression were mostly restricted in one cluster in the GLUER result (cluster 12)
compared to more scattered expression in Seurat (centered around clusters 6 and 12)
and LIGER (centered around clusters 1 and 18) results (Figure 4d and 4f). Similar to
Vcam1/VCAM1, Ncr1/NCR1 expression was restricted to a cluster of cells in the
scRNA-Seq UMAP but more scattered in the CODEX UMAP. In the integrated data,
both transcript and protein expression were mostly restricted in one cluster in the
GLUER result (cluster 16) compared to Seurat (centered around clusters 6 and 12) and
LIGER (centered around clusters 1 and 17) results (Figure 4e and 4g). In summary, we
show that by integrating with scRNA-Seq data, cell types that are hard to distinguish in
the original CODEX data can be readily identified. Using the co-embedded data, spatial
distribution of additional genes that are not covered in the CODEX panel can then be
studied.
Use case 2: Integrating spatial transcriptomics data and scRNA-Seq data
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Highly multiplexed single-molecule fluorescence in situ hybridization (smFISH) assays
such as sequential fluorescence in situ hybridization (SeqFISH+) 3
and multiplexed
error-robust fluorescence in situ hybridization (MERFISH) 4
enable spatial profiling of
hundreds to thousands of transcripts at single-cell resolution. Here we demonstrate the
utility of GLUER for integrating scRNA-Seq data with SeqFISH+ data. We used
matched data sets on mouse visual cortex and olfactory bulb 3, 18
, respectively
(Supplementary Table 1). The scRNA-Seq data set consists of 1344 and 17709 cells for
the two tissue types and the SeqFISH+ data set consists of 523 and 2050 cells for the
two tissue types. Similar to CODEX data, due to the smaller number of features in the
SeqFISH+ data, UMAP plot of the original data does not reveal clear clusters (Figure
5c,d and 5g,h). After applying GLUER, UMAP plots show that cells identified by both
assays are well mixed. Clustering of the co-embedded data revealed 5 major clusters
representing oligodendrocytes, endothelial cells, astrocytes, GABAergic neurons, and
glutamatergic neurons (Figure 5a and 5b). In general, the same cell types labeled by
both data modalities clustered together. For instance, oligodendrocytes, endothelial
cells, and astrocytes from SeqFISH+ data and scRNA-Seq data clustered together. L5a,
L5b, L2/3, L6a, L4_Ctxn3/Scnn1a neurons from SeqFISH+ data and glutamatergic
neurons from scRNA-Seq data clustered together. Pvalb, L6b, Sst, Lgtp/Smad3
neurons from SeqFISH+ data and GABAergic neurons from scRNA-Seq clustered
together. Using a second data set on mouse olfactory bulb 3, 19
, we show that GLUER
yielded similar result (Figure 5e-h). Again, UMAP plot of the original SeqFISH+ data did
not reveal clear clusters in the SeqFISH+ data (Figure 5h). After data integration, many
cell types labeled by both modalities were clustered together, such as astrocytes,
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microglia cells and macrophages, and endothelial cells. In summary, our result
demonstrates that GLUER is able to accurately integrate multiplexed RNA FISH data
with scRNA-Seq data.
Use case 3: Improving integration of true transcriptomics and epigenomics dual-
omics data
True dual/multi-omics protocols have started to emerge recently. Although the different
modalities are measured in the same cells, integration of such data remains a challenge
due to differences in coverage and data modality-specific characteristics. For instance,
transcriptomic data in dual scRNA-Seq and scATAC-Seq data typically reveals more
granular structure in the data, as demonstrated using a SNARE-Seq data set on adult
mouse cerebral cortex (Figure 6a, 6b) (Supplementary Table 1). Here, we illustrate the
ability of GLUER to improve integration of true dual/multi-omics data. One of the key
steps of GLUER is inference of cell pairs among different data modalities using mutual
nearest neighbor algorithm (Figure 1b). With true dual/multi-omics data, instead of
inferring cell pairs using the mutual nearest neighbor algorithm, GLUER can take
advantage of the true cell-pair information to perform joint dimensionality reduction and
co-embedding. After integration of the mouse cerebral cortex SNARE-Seq data set,
cells labeled by the two data modalities were well mixed (Figure 6c). Clustering
analysis of the integrated data uncovered 15 clusters (Figure 6e) that can be annotated
to known cerebral cortex cell types based on known marker genes. Importantly, based
on the co-embedded data, expression profiles of marker genes across cell types are
consistent with gene activity profiles across cell types (Figure 6f and 6g), confirming the
high degree of mixing of cells identified by these two data modalities in the UMAP plot.
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Compared to Seurat and LIGER, the integration accuracy of GLUER is significantly
higher (p < 0.05, paired Student’s t-test; Figure 6d).
DISCUSSION
An accurate definition of cell type/state and underlying gene regulatory mechanisms
requires integration of multiple measurement modalities at the single cell resolution.
GLUER was designed as a general framework for single-cell data integration.
Integration can be performed for multiple single-modality omics data sets, single-
modality omics data and multiplexed molecular imaging data, and different
measurement modalities of true multi-omics data. Each of the three major steps of
GLUER addresses a specific challenge in data integration. The joint nonnegative matrix
factorization addresses the high dimensionality of single-cell omics data. The mutual
nearest neighbor algorithm can capture many-versus-many relationships among cells
and thus further reduce the search space for cells of matched data modalities. The deep
neural network can capture non-linear functional relationships between different data
modalities. The combination of these three critical steps enables robust integration of
high-dimensional and multi-modality data. Using diverse single-cell data sets generated
with different protocols and tissue types, we demonstrated that GLUER achieved
significantly higher integration accuracy over existing methods.
The GLUER software offers additional technical benefits. First, the software is
high scalable due to its implementation of parallel computing using CPUs and GPUs. It
takes <5 minutes to integrate ~10,000 cells with multi-omics data. Second, GLUER is
built on the AnnData object which supports preprocessing and plotting functions in
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SCANPY 20
. Third, the graphical user interface (GUI) allows interactive exploration of
the integration results.
Here, in order to conduct joint NMF of transcriptomic/proteomic data and
epigenomic data, we summarized the epigenomic data (chromatin accessibility data in
this case) as a gene activity matrix. For each gene, its activity score is the sum of reads
in its promoter region and gene body regions. Novel approaches for computing gene
activity matrices that take into account additional information located in distal regulatory
regions in the genome may help to improve integration accuracy. Compared to
chromatin accessibility, the relationship between DNA methylation and gene expression
is more complicated. More sophisticated functions other than summation are needed to
accurately and comprehensively capture the relationship of DNA methylation and gene
expression to construct a gene activity matrix.
In summary, GLUER is a much-needed tool for integrating single-cell data across
measurement modalities and/or samples. With the rapid accumulation of single-cell
multi-omics and imaging data, integrated data holds the promise of furthering our
understanding of the role of heterogeneity in development and disease.
ONLINE METHODS
Overview of GLUER
GLUER integrates single-cell omics and molecular imaging data using three major
computational techniques: joint nonnegative matrix factorization, mutual nearest
neighbors, and convolutional deep neural network. Specifically, it consists of the
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following steps (Figure 1): (a) normalize data for each data modality; (b) perform joint
nonnegative matrix factorization of the different data sets and identify cell pairs using
the mutual nearest neighbor algorithm; (c) learn a nonlinear mapping function between
the factor loadings of a pair of data modalities using convolutional deep neural network;
(d) generate a co-embedding matrix and jointly visualize the cells using UMAP or t-SNE
with the option of performing imputation on the co-embedded data.
Normalization of data of different modalities
For transcriptomic data, we used a cell-by-gene matrix of unique molecular identifier
(UMI) counts as the input for each algorithm. For chromatin accessibility data, we
generated a gene activity matrix by aggregating UMI counts in the 2.5 kb upstream
region of transcription start site and the gene body of each gene. For other types of
omics data, we could use the commonly used approaches to generate the gene activity
matrix. We employed the same standard pre-processing procedures to generate gene
expression matrices and gene activity matrices from all data sets used in this paper. We
applied a log-normalization of the gene expression matrices or gene activity matrices of
all data sets using a size factor of 10,000 molecules for each cell. We removed low-
quality cells before normalization. For CODEX data, single-cell protein expression levels
were calculated using the average intensity of the pixels constituting each single cell.
We first removed cells smaller than 1,000 or larger than 25,000 voxels (the default
settings of STvEA 15
). Then we removed noise in the CODEX data by fitting a Gaussian
mixture model to the expression levels of each protein 9
followed by normalizing the
data by the total levels of protein markers in each cell. The output of the normalization
step of GLUER are normalized gene expression, gene activity, and protein expression
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matrices denoted as 𝑋0, 𝑋1, . . . , 𝑋!, where 𝑋0 is the reference data set. For each 𝑋" (𝑖 =
0, . . . , 𝑁), rows are genes/proteins and columns are individual cells. All 𝑋" (𝑖 =
0, 1, . . . , 𝑁) have the same features (gene/protein) and we use 𝑔 to denote the number
of features and 𝑚0, 𝑚1, . . . , 𝑚! to denote the number of the cells in 𝑋" (𝑖 =
0, 1, . . . , 𝑁) respectively.
Joint nonnegative matrix factorization of multiple datasets
We use the following model to compute the joint non-negative matrix factorization
(NMF) of the multiple data sets. Given normalized data matrices 𝑋", 𝑖 = 0, … , 𝑁, we can
compute the factor loadings matrices 𝐻0, 𝐻1, . . . , 𝐻! for each data set by minimizing the
following cost function:
𝐽(𝐺, 𝐻") = 0 12𝑋" − 𝐺𝐻"
#
2$
%
+ 𝛼2𝐻"
#
𝐻" − 𝐼2$
%
7
!
"&'
where 𝐺 ∈ 𝑅(
)×+
, 𝐻" ∈ 𝑅(
,!×+
(𝑘 is the number of factors in the joint NMF) and 𝐼 is the
identity matrix. The first term in the sum represents approximation error and the second
term the orthogonality of column vectors in 𝐻", where the trade-off is controlled by the
hyperparameter 𝛼. The optimization problem is non-convex, which means no global
optimal solution for the problem. However, it can be solved by the following iterative
scheme to reach its local minimum. The algorithm starts by initializing the values in 𝐺
and 𝐻" randomly and uniformly distributed on [0,1], and updating them with the following
rules until convergence.
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𝐺 = 𝐺 ∘ >
∑ 𝑋"𝐺"
"
∑ 𝑋"𝐺"
#
𝐺"
"
𝐻 = 𝐻 ∘ >
𝑋"
#
𝐺 + 𝛼𝐻"
𝐻"𝑊#𝑊 + 2𝛼𝐻"𝐻"
#
𝐻"
where ∘ represents the element-wise (Hadamard) product 21
. The mathematical proof of
the iterative procedure and its convergence to the stationary points have been shown in
previous literature 21, 22
.
Identification of candidate cell pairs using mutual nearest neighbor algorithm
We identify candidate cell pairs between the reference data (𝐻0) and query data
(𝐻1, . . . . , 𝐻!) using the mutual nearest neighbor (MNN) algorithm where cell distance is
determined by the cosine distance between 𝐻0 and 𝐻1, . . . . , 𝐻!. Given that scRNA-Seq
data has highest coverage among the data modalities and the central role of
transcription linking epigenomic and protein information, by default, scRNA-Seq is
chosen as the reference data modality. The MNN algorithm was first introduced for
removing batch effects and it is also implemented by Seurat 11, 23
. Some cells may
appear in a large number of cell pairs. These dominant cells are more likely to appear in
the integrated data. Furthermore, we found that the number of dominant cells is highly
context- and sample-dependent. Here we employ the following steps to reduce the bias
due to the dominant cells while identifying cell pairs. We use introduce two tunable
parameters for identifying dominant cells. First, we check if cells of a candidate cell pair
are also mutual nearest neighbors in the high dimensional space whose distance is
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calculated directly from the normalized data. The distance calculation can be tuned by
using the joint_rank parameter, which is the number of shared factors in the joint non-
negative matrix factorization step. Second, for each cell, we keep its top K nearest
neighbors in the pairs. Hence, the algorithm is seeking K mutual nearest neighbors.
Finding nonlinear mappings among the factor loadings of different datasets using
a deep neural network
In order to project data from different biological assays onto a common feature space,
we investigated functions 𝐹", 𝑖 ∈ {1, . . . . 𝑁} to map the factor loadings 𝐻1, . . . . , 𝐻! onto the
feature space of 𝐻0. Previous methods such as Seurat uses a linear function. In
contrast, we use a convolutional deep neural network to capture nonlinear relationships
among the factor loading matrices of different modalities (𝐻" and 𝐻0) based on the
identified cell pairs 𝑃". 𝑃" is a matrix consisting of two columns, the first column is the
cell index in the reference data set and the second column is the cell index in the i-th
data set. Each row of 𝑃" corresponds to one cell pair whose indices in the data sets
constitutes the elements of 𝑃".
Let us denote the nonlinear relationship as a function 𝐹" that maps from 𝑅+
to
𝑅+
, where 𝑘 is the number of the factors in the joint NMF. The input layer of our neural
network has a dimension equal to the number of factors 𝑘. The dimensions of seven
internal layers are 200, 100, 50, 25, 50, 100, and 200 respectively. These seven layers
are designed to learn and encode features that are shared across factors. Since in most
data sets, the number of common factors after joint NMF is fewer than 200, we set the
largest number of neurons to 200. All layers are fully connected with a rectified linear
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unit (ReLU) activation function, while the last layer is a fully connected layer for output
24
. We found in practice that results were robust with respect to the chosen number of
layers and numbers of neurons in each layer (Supplementary Figure 6). Throughout this
study the same network architecture was utilized to analyze all data sets. The objective
function of our neural network is
𝑎𝑟𝑔𝑚𝑖𝑛$!
||𝑌" − 𝐹"(𝑆")||$
2
where 𝑌" ∈ 𝑅(
-!×+
and 𝑆" ∈ 𝑅(
-!×+
are obtained from 𝐻' and 𝐻" using the cell pair
information reflected in 𝑃". 𝑌" is formed by the order of the index in the first column of 𝑃"
from the original loading matrix 𝐻'. 𝑆" is formed by the order of the index in the second
column of 𝑃" from the original loading matrix 𝐻". The loss function is a Frobenius norm
function. The objective function is optimized stochastically using Adaptive Moment
Estimation with the learning rate set to 10e–5 for 500 epochs (cross-validation) 24
.
Co-embedding and downstream analyses
We apply UMAP or t-SNE to obtain the co-embedding plots with the inputs of combining
𝑯𝟎, 𝑭𝟏(𝑯𝟏), 𝑭𝟐(𝑯𝟐), …, 𝑭𝑵(𝑯𝑵)25, 26
. Naturally, we could use the distance 𝑫𝒊 (𝒊 =
𝟎, 𝟏, . . . , 𝑵) between cells from all data sets to impute the data, which is calculated as
𝑫𝒊𝑿𝒊 (𝒊 = 𝟏, 𝟐, . . . , 𝑵). These imputed data sets could be used to perform downstream
analyses such as joint trajectory inference and finding the regulatory relationship
between the cis-regulatory DNA sequences and gene promoters.
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Integration accuracy
Taking advantage of data sets that jointly profile RNA and chromatin accessibility in the
same cells7, 8, 13
, we devise a distance metric to quantify the integration accuracy of the
algorithms. First, we compute the co-embedded data 𝐶345678, 𝐶9")46, 𝐶:;546 using each
method. We use the first 50 principal components from principal component analysis in
Seurat and the factor loading matrices in LIGER and GLUER. Next, we construct
pairwise Euclidean distance matrices among all cells ,𝐸345678, 𝐸9")46, 𝐸:;546 based on co-
embedded data, 𝐶345678, 𝐶9")46, 𝐶:;546. For each cell a, we calculate the integrating
accuracy, 1 − 𝐼𝐷(𝑎, 𝑎′), as the percentile of its true paired cell in its neighborhood
defined using the co-embedded data, that is, 𝐼𝐷(𝑎, 𝑎′) = %(𝑎′, 𝐸"(𝑎)), where
%(𝑎′, 𝐸"(𝑎))) is the percentile ranking of a’ in the neighborhood of cell 𝑎. 𝐸"(𝑎) is the
ranked distance vector of cell 𝑎 to the rest of cells in the combined reference and query
data sets. The greater the integrating accuracy, the better the integration result.
DATA AND SOFTWARE AVAILABILITY
GLUER is freely available as a Python package: https://github.com/tanlabcode/GLUER.
Sources of public data sets used in this paper are summarized in Supplementary Table
1.
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FIGURES AND FIGURE LEGENDS
Figure 1. Schematic overview of the GLUER algorithm. (a) Representation of single-cell
omics and imaging data sets, one of them is the reference modality and the rest are the
query modalities. The omics and imaging data sets are processed to generate either
gene/protein expression (transcriptomic and imaging data) or gene activity (epigenomic
data) data matrices. (b) Joint nonnegative matrix factorization to project the normalized
data of all modalities into a subspace defined by shared structure across the data sets.
Candidate cell pairs between the reference and the query data sets are identified using
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the mutual nearest neighbor algorithm. (c) Deep neural network is employed to
determine the nonlinear mapping functions 𝐹1, 𝐹2, … , 𝐹! from the query data to the
reference data based on the cell pairs identified in the previous step. (d) The co-
embedded data matrix is computed using the nonlinear mapping functions. (e)
Downstream analyses using the co-embedded data, including dimensionality reduction,
imputation, cell type identification, and inference of transcriptional regulatory network.
Figure 2. Performance evaluation using data on a mixture of 1047 human BJ, H1, K562
and GM12878 cells profiled using SNARE-Seq. (a-c) UMAP plots of integrated
datasets, color-coded by data modality. (d-f) UMAP plots of integrated datasets, color-
coded by cell line. (g) Integration accuracy of the three methods. P-values were
computed using paired Student’s t-test with Bonferroni correction. (i) Distributions of
gene expressing levels in the original scRNA-Seq data and data computed by the
integration methods. Y-axis, normalized gene expression level. EPCAM, COL1A2,
PRAME, and HLA-DPA1 are the marker genes for BJ, H1, K562, and GM12878 cell
lines, respectively.
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Figure 3. Performance evaluation using data on adult mouse cerebral cortex. 7,892
cells were profiled using SNARE-Seq. (a-c) UMAP plots of integrated datasets, color
coded by data modality. (d) Integration accuracy of the three methods. P-values were
computed using paired Student’s t-test with Bonferroni correction. (e) UMAP plot of
integrated data by GLUER with cell type annotation. Ex-L2/3, excitatory neurons in
Layer 2/3, the same for the rest of excitatory neuron abbreviation; In, inhibitory neurons;
Ast, astrocytes; Oli: Oligodendrocytes. (f) Marker gene expression profiles of the cell
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types identified in panel e. (g) Marker gene activity profiles of the cell types identified in
panel e. Y-axis, cell types, X-axis, marker genes. Color of the dots represents
normalized gene expression (for RNA-Seq) or gene activity (for ATAC-Seq). Size of the
dots represents the percentage of cells with nonzero expression or activity of the gene.
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Figure 4. Integration of scRNA-Seq and single-cell spatial proteomics data. The dataset
consists of scRNA-Seq and CODEX data on mouse spleen. (a) UMAP plots of the
integrated data and original data. First row, UMAPs based on the scRNA-Seq part of
the co-embedded data; Second row, UMAPs based on the CODEX part of the co-
embedded data; Third row, UMAPs based co-embedded scRNA-Seq and CODEX data.
(b) Cell clusters identified using integrated data by Seurat, LIGER, and GLUER.
Clustering was performed using the Leiden method. (c) Cell type annotation based on
data integrated using GLUER. (d-e) UMAP of marker gene/protein expression for red
pulp macrophages and NK cells. Vcam1, marker gene for red pulp macrophages;
NKp46, marker gene for NK cells. (f-g) Violin plots of Vcam1 and NKp46 expression
levels across cell clusters. Y-axis, normalized expression levels of genes/proteins.
Figure 5. Integration of scRNA-Seq and single-cell spatial transcriptomics data. (a-d)
UMAP plots of mouse visual cortex data. (a) Integrated data annotated by data
modalities, SeqFISH+ and scRNA-Seq. (b) Integrated data annotated by cell types. Cell
type annotation is from original publications. Cell types from scRNA-Seq and SeqFISH+
data are labeled with “ns” and “s”, respectively. Astro, astrocytes; Endo, endothelial
cells; Gaba, GABAergic neurons; Lgtp/Smad3, Interneurons highly expressing
Lgtp/Smad3; Pvalb, Interneuron highly expressing Pvalb; Sst, Interneurons highly
expressing Sst; Vip, Interneuron highly expressing Vip; Ndnf, Interneurons highly
expressing Ndnf; Glut, glutamatergic neurons; L2/3, excitatory neurons in Layer 2/3;
L4_Ctxn3/Scnn1a, excitatory neurons in Layer 4 highly expressing Ctxn3/Scnn1a; L5a,
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excitatory neurons in Layer 5a; L5b, excitatory neurons in Layer 5b; L6a, excitatory
neurons in Layer 6a; L6b, excitatory neurons in Layer 6b; OPC, oligodendrocyte
precursor cells; Oligo, oligodendrocytes; Micro, microglia cells; (c) scRNA-Seq data
alone (d) SeqFISH+ data alone. (e-h) UMAP plots of mouse olfactory bulb data. (e)
Integrated data annotated by data modalities. (f) Integrated data annotated by cell
types. (g) scRNA-Seq data alone. (h) SeqFISH+ data alone. Astro, astrocytes; Endo,
endothelial cells; Micro, microglia cells; Neur, neurons; Myol, myelinating-
oligodendrocytes; Mesen, mesenchymal cells; Mura, mural cells; Mono, monocytes;
Macro, macrophages; Rbcs, red blood cells; Opc, oligodendrocyte progenitor cells; Oec,
olfactory ensheathing cells; Pia, pial cells;
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Figure 6. GLUER improves integration of true single-cell dual-omics data. The data set
consists of 7,892 cells from adult mouse cerebral cortex profiled using SNARE-Seq. (a-
c) UMAP plots of original data and integrated data by GLUER. (d) Integration accuracy
of the three methods. P-values were computed using paired Student’s t-test with
Bonferroni correction. (e) UMAP plot of integrated data by GLUER with cell type
annotation. Ast, astrocytes; Oli, oligodendrocytes; Ex-L2/3-Rasgrf2, excitatory neuron
highly expressing Rasgrf2; In-Npy, inhibitory neuron highly expressing Npy. The same
nomenclature applies to other excitatory and inhibitory neuron subtypes. (f) Marker
gene expression profiles of the cell types identified in panel e. (g) Marker gene activity
profiles of the cell types identified in panel e. Y-axis, cell types, X-axis, marker genes.
Acknowledgements
We thank the Research Information Services at the Children’s Hospital of Philadelphia
for providing computing support. This work was supported by National Institutes of
Health of United States of America grants CA233285, CA243072, and HL156090 (to
K.T.), a grant from the Leona M. and Harry B Helmsley Charitable Trust (2008-04062 to
K.T.) and a grant from the Alex’s Lemonade Stand Foundation (to K.T.)
Author contributions
TP and KT conceived and designed the study. TP and KT designed and TP
implemented the GLUER algorithm. TP performed data analysis. KT supervised the
overall study. TP, GC, and KT wrote the paper.
Competing interests
The authors declare no competing interests.
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12. Welch, J.D. et al. Single-Cell Multi-omic Integration Compares and Contrasts Features of
Brain Cell Identity. Cell 177, 1873-1887 e1817 (2019), PMC6716797
13. Liu, L. et al. Deconvolution of single-cell multi-omics layers reveals regulatory
heterogeneity. Nat Commun 10, 470 (2019), PMC6349937
14. Traag, V.A., Waltman, L. & van Eck, N.J. From Louvain to Leiden: guaranteeing well-
connected communities. Sci Rep 9, 5233 (2019), PMC6435756
15. Govek, K.W., Troisi, E.C., Woodhouse, S. & Camara, P.G. Single-Cell Transcriptomic
Analysis of mIHC Images via Antigen Mapping.
16. Abel, A.M., Yang, C., Thakar, M.S. & Malarkannan, S. Natural Killer Cells: Development,
Maturation, and Clinical Utilization. Front Immunol 9, 1869 (2018), PMC6099181
17. Dutta, P. et al. Macrophages retain hematopoietic stem cells in the spleen via VCAM-1. J
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18. Tasic, B. et al. Adult mouse cortical cell taxonomy revealed by single cell transcriptomics.
Nat Neurosci 19, 335-346 (2016), PMC4985242
19. Tepe, B. et al. Single-Cell RNA-Seq of Mouse Olfactory Bulb Reveals Cellular
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SUPPLEMENTARY MATERIALS
Supplemental Table 1. Public single-cell sequencing and imaging data sets that
were used in this study.
Experimental
Assays
Data
Modalities
Tissue
Types
References (PMID &
accession #/downloading
link)
SNARE-Seq ● Transcriptome
● Chromatin
accessibility
Mixture of BJ,
GM12878, H1 and
K562 cells
PMID:31611697;
GSE126074
● Chromatin
accessibility
Neonatal mouse
cerebral cortex
PMID:31611697;
GSE126074
● Chromatin
accessibility
Adult mouse cerebral
cortex
PMID:31611697;
GSE126074
scCAT-Seq ● Transcriptome
● Chromatin
accessibility
Mixture of HeLa-S3,
HCT116, K562,
PDX1, PDX2 cells
PMID:30692544;
SRP167062
sci-CAR ● Transcriptome
● Chromatin
accessibility
Mixture of DEX-
treated A549 time
course
PMID:30166440;
GSE117089
sci-CAR ● Transcriptome
● Chromatin
accessibility
Mouse kidney
PMID:30166440;
GSE117089
CITE-Seq ● Transcriptome
● Proteome
Mouse spleen Govek, Kiya W., et al,
BioRxiv, 2019
(https://www.dropbox.com/s
/910hhahxsbd9ofs/gene_m
atrix_all_new.csv?dl=1)
CODEX ● Spatial
proteome
Mouse spleen Goltsev Y et al, Cell, 2018
(https://data.mendeley.com/
datasets/zjnpwh8m5b/1)
SMARTer ● Transcriptome Mouse visual cortex PMID:26727548;
GSE71585
SeqFISH+ ● Spatial Mouse visual cortex PMID:30911168;
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Transcriptome (https://github.com/CaiGrou
p/seqFISH-PLUS)
Droplet-based ● Transcriptome Mouse olfactory bulb PMID:30517858;
GSE121891
SeqFISH+ ● Spatial
Transcriptome
Mouse olfactory bulb PMID:30911168;
(https://github.com/CaiGrou
p/seqFISH-PLUS)
SUPPLEMENTARY FIGURE LEGEND
Supplementary Figure 1. Performance evaluation using data on a mixture of cell types
profiled using the scat-Seq assay. The mixture consists of HeLa-S3 cells, HCT116 cells,
K562 cells, cells derived from a moderately differentiated squamous cell carcinoma
patient (PDX1), and cells derived from a large-cell lung carcinoma patient (PDX2). (a-c)
UMAP plots of integrated data and colored-coded by data modality. (d-f) UMAP plots of
integrated data and color-coded by cell type. (g) Integration accuracy of the three
methods. P-values were computed using paired Student’s t-test with Bonferroni
correction. (h) Distributions of gene expression levels in the original scRNA-Seq data
and data computed by the integration methods. Y-axis, normalized gene expression
level. ESRP1, NPR3, SAMSN1, KRT16, LMO7 are marker genes for HCT116, HeLa-
S3, K562, PDX2, PDX1 cells, respectively.
Supplementary Figure 2. Performance evaluation using data on DEX-treated A549
cells profiled using the sci-CAR assay. Cells were treated at three time points, 0, 1 and
3 hours before profiling. (a-c) UMAP plots of integrated data and color-coded by data
modality. (d-f) UMAP plots of integrated data and color-coded by experimental
condition. (g) Integration accuracy of the three methods. P-values were computed using
paired Student’s t-test with Bonferroni correction.
Supplementary Figure 3. Performance evaluation using data on neonatal mouse
cerebral cortex. 5,081 cells were profiled using the SNARE-Seq assay. (a-c) UMAP
plots of integrated data and color-coded by data modality. (d) Integration accuracy of
the three methods. P-values were computed using paired Student’s t-test with
Bonferroni correction. (e) Cell type annotation using GLUER integration result. (f)
Marker gene expression profiles of cell types identified in panel e. (g) Marker gene
activity profiles of cell types identified in panel e. Y-axis, cell types, x-axis, marker
genes. Shade of the dots is proportional to normalized gene expression (for RNA-Seq
data) or gene activity (for ATAC-Seq data). Size of the dots represents the percentage
of cells with nonzero expression or activity of the gene.
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Supplementary Figure 4. Performance evaluation using data on 5,916 mouse kidney
cells profiled using the sci-CAR assay. (a-c) UMAP plots of integrated data and color-
coded by data modality. (d) Integration accuracy of the three methods. P-values were
computed using paired Student’s t-test with Bonferroni correction. (e) Cell type
annotation using GLUER integration result. (f) Marker gene expression profiles of cell
types identified in panel e. (g) Marker gene activity profiles of cell types identified in
panel e. Y-axis, cell types, x-axis, marker genes. Shade of the dots is proportional to
normalized gene expression (for RNA-Seq data) or gene activity (for ATAC-Seq data).
Size of the dots represents the percentage of cells with nonzero expression or activity of
the gene.
Supplementary Figure 5. Gene/protein expression profiles of cells in mouse spleen.
(a) the gene expression (b) the protein expression. Y-axis, cell type. X-axis,
gene/protein. The color is the normalized expression levels of genes computed by max-
min method. The size of the dot is the percentage of cells with high expression levels of
the gene.
Supplementary Figure 6. Performance robustness against the number of neurons in
each layer of the deep neural network. X-axis, layers of the neural network; Y-axis,
coefficient of variance of integration accuracy. We calculated the integration accuracy
using varying numbers of neurons in each layer, including 40, 40, 20, 10, 20, 40, and 40
different numbers of neurons for layers 1 to 7, respectively.
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