E NHANCING EXPERIMENTAL SIGNALS IN SINGLECELL RNA- SEQUENCING DATA USING GRAPH SIGNAL PROCESSING
A BSTRACT
Single-cell RNA-sequencing (scRNA-seq) is a powerful tool for analyzing biological systems.
However, due to biological and technical noise, quantifying the effects of multiple experimental conditions presents an analytical challenge.
To overcome this challenge, we developed MELD:
Manifold Enhancement of Latent
Dimensions.
MELD leverages tools from graph signal processing to learn a latent dimension within the data, which scores the prototypicality of each datapoint with respect to experimental or control conditions.
We call this dimension the Enhanced Experimental Signal (EES).
MELD learns the EES by ﬁltering the noisy categorical experimental label in the graph frequency domain to recover a smooth signal with continuous values.
This method can be used to identify signature genes that vary between conditions and identify which cell types are most affected by a given perturbation.
We demonstrate the advantages of MELD analysis in two biological datasets, including T-cell activation in response to antibody-coated beads and treatment of human pancreatic islet cells with interferon gamma.
I NTRODUCTION
As single-cell RNA-sequencing (scRNA-seq) has become more accessible, design of single cell experiments has become increasingly complex.
However, quantifying the differences between single cell data sets collected from different conditions presents an analytical challenge.
There is often a large overlap between single-cell proﬁles across conditions and single cell data sets are prone to biological and technical noise.
As a result, the signal of an experimental perturbation is small with respect to the biological and technical variation in an experiment ( Fig. 1 ).
To quantify the differences between experimental conditions, it would be helpful to ﬁnd groups of cells that are prototypical of experimental or control conditions.
Thus, we effectively want a quantiﬁcation ( i.e. a score) of how prototypical each cell is of the control or experimental condition.
Such a score would identify the cells and populations that are the most or least affected by an experimental perturbation.
We term this score the Enhanced Experimental Signal (EES).
For example, in a simple experiment with one experimental condition and one control condition, we would like the
EES to be +1 or -1 for cells that are most likely to arise in the experimental or control condition, respectively, and 0 for cells equally likely to arise in either condition.
To derive this score, we developed MELD (Manifold Enhancement of Latent Dimensions).
MELD is based on methods from graph signal processing (GSP) that, despite their proven strength in other domains, have not often been used in biomedical data analysis (Shuman et al.,
2013).The key advantage of GSP is the access to a set of tools for processing graph signals , which are functions deﬁned over the nodes in a graph.
MELD models the condition label indicating from which condition each cell was sampled as a graph signal that we call the Raw Experimental Signal .
In a two-sample experiment, the RES would be deﬁned as -1 for cells from the control condition and +1 for cells in the experimental condition.
To remove high-frequency noise from the RES, MELD applies a novel ﬁlter over the graph frequency domain of the RES to infer the EES.
Finally, we incorporate information from the RES and EES into Vertex Frequency Clustering (VFC), a novel clustering algorithm that identiﬁes cell types most or least affected by the experimental perturbation.
MELD has wide applicability in the analysis of high dimensional single cell data.
Here, we describe the algorithms for MELD and VFC and demonstrate the methods on two scRNA-seq datasets.
More results can be found in Burkhardt et al.
T HE MELD ALGORITHM
The goal of the MELD algorithm is to use a manifold model of cellular states across experimental conditions to learn an Enhanced Experimental Signal (EES) that quantiﬁes how prototypical each cell is of each experimental condition.
The MELD algorithm computes the EES in the following steps:
A cell similarity graph is constructed over the data.
The experimental label that indicates the sample origin of the cell is modeled over the graph as a discrete signal called the Raw Experimental Signal (RES) .
MELD ﬁlters biological and technical noise from the RES to infer the EES, which reﬂects how prototypical each cell is of each condition.
The EES and Fourier transform of the RES are used to identify cell populations that are prototypical of each condition and to infer gene trends of the experimental perturbation.
The cell similarity graph in step one is constructed using a variant of the radial basis kernel called the α -decay kernel, ﬁrst proposed by Moon et al.
Next, MELD uses the input experimental label to create the RES on the graph.
For simple two-sample experimental cases, cells from the control condition are assigned a value of -1 and cells from the experimental signal are assigned + ( Fig. 1a ).
For more complex cases, such as in a time course or a series of drug titrations, the raw signal can be deﬁned ordinally as the stage or timepoint of collection or dosage of a drug.
The goal of MELD is to remove biological and technical noise from the RES using a low-pass ﬁlter.
The MELD ﬁlter is inspired by Laplacian regularization (Ando & Zhang, 2007), which is expressed as the optimization
[Equation]
Here, the regularization maximizes (a) reconstruction, and (b) smoothness of z quantiﬁed using the graph Laplacian L .
However, low-pass ﬁlters are not a panacea.
Indeed, low frequency noise (such as background noise) is common and will be exacerbated by low-pass ﬁltering.
In MELD we propose a new class of graph ﬁlters, of which Laplacian regularization is a subﬁlter, that is adaptable to graph and signal noise context, given by the following equation:
[Equation]
where
[Equation]
Here, x corresponds to an input RES, y is an EES, and each of α, β, and ρ are parameters that control the spectral translation, reconstruction penalty, and ﬁlter order, respectively.
MELD solves the problem of learning y using a Chebyshev polynomial approximation.
In contrast to previous works using Laplacian ﬁlters, these parameters allow analysis of signals that are contaminated by noise across the frequency spectrum, which is explored in Burkhardt et al.
Next, to identify populations of cells most or least affect by a given perturbation, we introduce a novel clustering algorithm called Vertex Frequency Clustering (VFC, Fig. 1b ).
VFC combines information about graph structure, RES signal frequency content, and EES signal magnitude at each node to identify clusters of cells that are both transcriptionally similar and affected similarly by the experimental perturbation.
The implementation of VFC is described thoroughly in Burkhardt et al.
At a high level, a series of varying-scale Windowed Graph Fourier Transforms are applied to the graph localized at each node to learn a spectrogram of the RES (Shuman et al., 2016).
This matrix is concatenated with the EES to capture information about signal magnitude and used as input to k-means.
As shown in Section 3.2, this approach can distinguish between intermediate cells between two extreme phenotypes and cells unaffected by an experimental perturbation (discussed in
Section 3.2).
Once the EES and VFC clusters have been inferred, this information can be used to identify gene signatures on an experimental perturbation ( Fig. 1c ) and characterize cells types with varying response to perturbation ( Fig. 1d ).
In the following section, we present application of both strategies on two single cell datasets.
R ESULTS 3. MELD IDENTIFIES A BIOLOGICALLY RELEVANT SIGNATURE OF T CELL ACTIVATION
To demonstrate the ability of MELD to identify a biologically relevant EES, we applied the algorithm to 5740 Jurkat T cells cultured for 10 days with and without anti-CD3/anti-CD28 antibodies published by Datlinger et al.
The goal of the experiment was to characterize the transcriptional signature of T cell Receptor (TCR) activation.
We selected this data because it relatively simple: the experiment proﬁles a single cell type, yet exhibits a heterogeneous continuum of experimental responses.
We visualized the data using PHATE, a visualization and dimensionality reduction tool we developed for single-cell RNA-seq data ( Fig.
2a ; Moon et al.
We observed a large degree of overlap in cell states between the experimental and control conditions, as noted in the original study (Datlinger et al., 2017).
This noise is both technical and biological.
Approximately 76% of the cells were transfected with gRNAs targeting proteins in the TCR pathway, leading to some cells in the stimulated condition lacking key effectors of activation.
The expectation for these cells is to appear transcriptionally unactivated despite originating from the stimulated experimental condition.
In other words, although the RES for these cells is +1 (originating from the stimulated condition), the EES of these cells is expected to be closer to -1 (prototypical of the unstimulated condition).
To obtain a signature of T cell activation, Datlinger et al.
(2017) devised an ad hoc iterative clustering approach whereby cells were ﬁrst clustered by the gRNA observed in that cell and then further clustered by the gene targeted.
In each cluster, the median gene expression was calculated and the ﬁrst principle component was used as the dimension of activation.
The 165 genes with the highest component loadings were deﬁned as signature genes and used to judge the level of activation in each cell.
We reasoned that MELD would be able to identify an EES of TCR activation without relying on clustering or access to information about the gRNA observed in each cell.
Applying MELD to the data, we observe a continuous spectrum of scores across the data set ( Fig. 2a ).
As expected, the regions enriched for cells from the stimulated condition have higher
EES values representing highly activated cells, and the converse is true for regions enriched for unstimulated cells.
To ensure that the EES represents a biologically relevant dimension of activation, we looked for genes with a high mutual information with the EES using kNN-DREMI (van
Dijk et al., 2018).
To facilitate comparison with the results of Datlinger et al.
(2017), we used EnrichR (Kuleshov et al., 2016) to perform gene set enrichment analysis on the 165 genes with the top kNN-DREMI scores ( Fig. 2b ).
We found comparable enrichment for gene sets related to T cell activation, T cell differentiation, and TCR response ( Fig. 2c ) and identify an overlap of 53 genes between the MELD-inferred and published signatures.
We ﬁnd that in the GO sets of T cell activation, T cell differentiation, and T cell receptor signalling, the MELD signatures includes as many or more genes for each GO term.
Furthermore, our signature includes genes known to be affected by
TCR stimulation but not present in the Datlinger et al.
(2017) signature list, such as down regulation of RAG1 and RAG2 (Turka et al., 1991).
These results show that MELD is capable of identifying a biologically relevant dimension of T cell activation at the resolution of single cells.
3. MELD AND VFC CAPTURE EFFECT OF IFN G STIMULATION IN PACREATIC ISLET CELLS
To demonstrate the ability for VFC to identify biological populations with various responses to perturbation, we analyzed a newly generated scRNA-seq experiment of human pancreatic islets stimulated with interferon-gamma (IFNg).
Human islets from three donors were cultured for 24 hours with or without IFNg before collection for scRNA-seq.
We visualized the data using PHATE and used MELD to infers a cell type speciﬁc response to treatment.
Next, we used VFC to identify clusters of cells with similar response to IFNg.
We calculated a spectrogram from the RES, concatenated the EES, and calculated k-means to obtain 9 VFC clusters (further description in
Burkhardt et al.
Examining the resulting cluster, we identiﬁed alpha, beta, and delta cells ( Fig. 3a ).
In each cell type, we observed that genes strongly correlated with the EES include known downstream targets of IFNg signalling including STAT1, IRF1, and ISG20 (data shown in Burkhardt et al.
Zooming in on the beta cell clusters, we observed four groups of cells: cells enriched in either the stimulated or unstimulated condition, cells intermediate of these groups, and a group of cells with high-frequency RES content suggesting no response to IFNg ( Fig. 3b ).
To conﬁrm these clusters are biologically relevant, we examined expression of STAT1 and found that the cells enriched in the unstimulated condition and non-responsive cells have the lowest expression of this IFNg-induced gene.
This indicates that the non-responsive cluster, despite containing roughly equal number of stimulated and unstimulated cells, exhibits no stimulation phenotype.
We also ﬁnd that the nonresponsive cells are marked by extreme high insulin expression.
Recent studies have described a subpopulation of beta cells marked by high insulin mRNA production that are hypothesized to have functional differences to typical beta cells Farack et al.
The results demonstrate the ability of
MELD and VFC to tease apart subpopulations of cells exhibiting diverse responses to perturbation
C ONCLUSION
MELD introduces a novel and ﬂexible ﬁlter on graph frequency domain to remove noise from the experimental labels indicating from which condition each cell was sampled.
We show that this ﬁlter is capable of recovering unique signals from data with multiple structures.
We also demonstrate the ability of MELD and VFC to identify biologically relevant signals across multiple cell types and biological systems.