This vignette will demonstrate a full single-cell lineage analysis workflow,
with particular emphasis on the processes of lineage reconstruction and
pseudotime inference. We will make use of the slingshot
package proposed in
(Street et al. 2017) and show how it may be applied in a broad range of settings.
The goal of slingshot
is to use clusters of cells to uncover global structure
and convert this structure into smooth lineages represented by one-dimensional
variables, called “pseudotime.” We provide tools for learning cluster
relationships in an unsupervised or semi-supervised manner and constructing
smooth curves representing each lineage, along with visualization methods for
each step.
The minimal input to slingshot
is a matrix representing the cells in a
reduced-dimensional space and a vector of cluster labels. With these two
inputs, we then:
getLineages
function.getCurves
function.We will work with two simulated datasets in this vignette. The first (referred
to as the “single-trajectory” dataset) is generated below and designed to
represent a single lineage in which one third of the genes are associated with
the transition. This dataset will be contained in a SingleCellExperiment
object (Lun and Risso 2017) and will be used to demonstrate a full
“start-to-finish” workflow.
# generate synthetic count data representing a single lineage
means <- rbind(
# non-DE genes
matrix(rep(rep(c(0.1,0.5,1,2,3), each = 300),100),
ncol = 300, byrow = TRUE),
# early deactivation
matrix(rep(exp(atan( ((300:1)-200)/50 )),50), ncol = 300, byrow = TRUE),
# late deactivation
matrix(rep(exp(atan( ((300:1)-100)/50 )),50), ncol = 300, byrow = TRUE),
# early activation
matrix(rep(exp(atan( ((1:300)-100)/50 )),50), ncol = 300, byrow = TRUE),
# late activation
matrix(rep(exp(atan( ((1:300)-200)/50 )),50), ncol = 300, byrow = TRUE),
# transient
matrix(rep(exp(atan( c((1:100)/33, rep(3,100), (100:1)/33) )),50),
ncol = 300, byrow = TRUE)
)
counts <- apply(means,2,function(cell_means){
total <- rnbinom(1, mu = 7500, size = 4)
rmultinom(1, total, cell_means)
})
rownames(counts) <- paste0('G',1:750)
colnames(counts) <- paste0('c',1:300)
sim <- SingleCellExperiment(assays = List(counts = counts))
The second dataset (the “bifurcating” dataset) consists of a matrix of
coordinates (as if obtained by PCA, ICA, diffusion maps, etc.) along with
cluster labels generated by \(k\)-means clustering. This dataset represents a
bifurcating trajectory and it will allow us to demonstrate some of the
additional functionality offered by slingshot
.
library(slingshot, quietly = FALSE)
data("slingshotExample")
rd <- slingshotExample$rd
cl <- slingshotExample$cl
dim(rd) # data representing cells in a reduced dimensional space
## [1] 140 2
length(cl) # vector of cluster labels
## [1] 140
To begin our analysis of the single lineage dataset, we need to reduce the dimensionality of our data and filtering out uninformative genes is a typical first step. This will greatly improve the speed of downstream analyses, while keeping the loss of information to a minimum.
For the gene filtering step, we retained any genes robustly expressed in at least enough cells to constitute a cluster, making them potentially interesting cell-type marker genes. We set this minimum cluster size to 10 cells and define a gene as being “robustly expressed” if it has a simulated count of at least 3 reads.
# filter genes down to potential cell-type markers
# at least M (15) reads in at least N (15) cells
geneFilter <- apply(assays(sim)$counts,1,function(x){
sum(x >= 3) >= 10
})
sim <- sim[geneFilter, ]
Another important early step in most RNA-Seq analysis pipelines is the choice of
normalization method. This allows us to remove unwanted technical or biological
artifacts from the data, such as batch, sequencing depth, cell cycle effects,
etc. In practice, it is valuable to compare a variety of normalization
techniques and compare them along different evaluation criteria, for which we
recommend the scone
package (Cole and Risso 2018). We also note that the order of these
steps may change depending on the choice of method. ZINB-WaVE (Risso et al. 2018)
performs dimensionality reduction while accounting for technical variables and
MNN (Haghverdi et al. 2018) corrects for batch effects after dimensionality reduction.
Since we are working with simulated data, we do not need to worry about batch effects or other potential confounders. Hence, we will proceed with full quantile normalization, a well-established method which forces each cell to have the same distribution of expression values.
FQnorm <- function(counts){
rk <- apply(counts,2,rank,ties.method='min')
counts.sort <- apply(counts,2,sort)
refdist <- apply(counts.sort,1,median)
norm <- apply(rk,2,function(r){ refdist[r] })
rownames(norm) <- rownames(counts)
return(norm)
}
assays(sim)$norm <- FQnorm(assays(sim)$counts)
The fundamental assumption of slingshot
is that cells which are
transcriptionally similar will be close to each other in some
reduced-dimensional space. Since we use Euclidean distances in constructing
lineages and measuring pseudotime, it is important to have a low-dimensional
representation of the data.
There are many methods available for this task and we will intentionally avoid
the issue of determining which is the “best” method, as this likely depends on
the type of data, method of collection, upstream computational choices, and many
other factors. We will demonstrate two methods of dimensionality reduction:
principal components analysis (PCA) and uniform manifold approximation and
projection (UMAP, via the uwot
package).
When performing PCA, we do not scale the genes by their variance because we do not believe that all genes are equally informative. We want to find signal in the robustly expressed, highly variable genes, not dampen this signal by forcing equal variance across genes. When plotting, we make sure to set the aspect ratio, so as not to distort the perceived distances.
pca <- prcomp(t(log1p(assays(sim)$norm)), scale. = FALSE)
rd1 <- pca$x[,1:2]
plot(rd1, col = rgb(0,0,0,.5), pch=16, asp = 1)
library(uwot)
## Loading required package: Matrix
##
## Attaching package: 'Matrix'
## The following object is masked from 'package:S4Vectors':
##
## expand
rd2 <- umap(t(log1p(assays(sim)$norm)))
colnames(rd2) <- c('UMAP1', 'UMAP2')
plot(rd2, col = rgb(0,0,0,.5), pch=16, asp = 1)
We will add both dimensionality reductions to the SingleCellExperiment
object,
but continue our analysis focusing on the PCA results.
reducedDims(sim) <- SimpleList(PCA = rd1, UMAP = rd2)
The final input to slingshot
is a vector of cluster labels for the cells. If
this is not provided, slingshot
will treat the data as a single cluster and
fit a standard principal curve. However, we recommend clustering the cells even
in datasets where only a single lineage is expected, as it allows for the
potential discovery of novel branching events.
The clusters identified in this step will be used to determine the global structure of the underlying lineages (that is, their number, when they branch off from one another, and the approximate locations of those branching events). This is different than the typical goal of clustering single-cell data, which is to identify all biologically relevant cell types present in the dataset. For example, when determining global lineage structure, there is no need to distinguish between immature and mature neurons since both cell types will, presumably, fall along the same segment of a lineage.
For our analysis, we implement two clustering methods which similarly assume
that Euclidean distance in a low-dimensional space reflect biological
differences between cells: Gaussian mixture modeling and \(k\)-means. The former
is implemented in the mclust
package (Scrucca et al. 2016) and features an automated
method for determining the number of clusters based on the Bayesian information
criterion (BIC).
library(mclust, quietly = TRUE)
## Package 'mclust' version 5.4.6
## Type 'citation("mclust")' for citing this R package in publications.
##
## Attaching package: 'mclust'
## The following object is masked from 'package:mgcv':
##
## mvn
cl1 <- Mclust(rd1)$classification
colData(sim)$GMM <- cl1
library(RColorBrewer)
plot(rd1, col = brewer.pal(9,"Set1")[cl1], pch=16, asp = 1)
While \(k\)-means does not have a similar functionality, we have shown in (Street et al. 2017) that simultaneous principal curves are quite robust to the choice of \(k\), so we select a \(k\) of 4 somewhat arbitrarily. If this is too low, we may miss a true branching event and if it is too high or there is an abundance of small clusters, we may begin to see spurious branching events.
cl2 <- kmeans(rd1, centers = 4)$cluster
colData(sim)$kmeans <- cl2
plot(rd1, col = brewer.pal(9,"Set1")[cl2], pch=16, asp = 1)
At this point, we have everything we need to run slingshot
on our simulated
dataset. This is a two-step process composed of identifying the
global lineage structure with a cluster-based minimum spanning tree (MST) and
fitting simultaneous principal curves to describe each lineage.
These two steps can be run separately with the getLineages
and getCurves
functions, or together with the wrapper function, slingshot
(recommended). We
will use the wrapper function for the analysis of the single-trajectory dataset,
but demonstrate the usage of the individual functions later, on the bifurcating
dataset.
The slingshot
wrapper function performs both steps of trajectory inference in
a single call. The necessary inputs are a reduced dimensional matrix of
coordinates and a set of cluster labels. These can be separate objects or, in
the case of the single-trajectory data, elements contained in a
SingleCellExperiment
object.
To run slingshot
with the dimensionality reduction produced by PCA and cluster
labels identified by Gaussian mixutre modeling, we would do the following:
sim <- slingshot(sim, clusterLabels = 'GMM', reducedDim = 'PCA')
## Using full covariance matrix
As noted above, if no clustering results are provided, it is assumed that all
cells are part of the same cluster and a single curve will be constructed. If no
dimensionality reduction is provided, slingshot
will use the first element of
the list returned by reducedDims
.
The output is a SingleCellExperiment
object with slingshot
results
incorporated. Most of the output is added to the metadata in the form of a list
and is accessible via metadata(sce)$slingshot
. Additionally, all inferred
pseudotime variables (one per lineage) are added to the colData
. To extract
all slingshot
results in a single object, we can use the SlingshotDataSet
function. This can be useful for visualization, as several plotting methods for
SlingshotDataSet
objects are included with the package. Below, we visuzalize
the inferred lineage for the single-trajectory data with points colored by
pseudotime.
summary(sim$slingPseudotime_1)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.000 8.633 21.118 21.415 34.367 43.186
colors <- colorRampPalette(brewer.pal(11,'Spectral')[-6])(100)
plotcol <- colors[cut(sim$slingPseudotime_1, breaks=100)]
plot(reducedDims(sim)$PCA, col = plotcol, pch=16, asp = 1)
lines(SlingshotDataSet(sim), lwd=2, col='black')
We can also see how the lineage structure was intially estimated by the
cluster-based minimum spanning tree by using the type
argument.
plot(reducedDims(sim)$PCA, col = brewer.pal(9,'Set1')[sim$GMM], pch=16, asp = 1)
lines(SlingshotDataSet(sim), lwd=2, type = 'lineages', col = 'black')
After running slingshot
, an interesting next step may be to find genes that
change their expression over the course of development. We will demonstrate this
type of analysis using the tradeSeq
package (Van den Berge et al. 2020).
For each gene, we will fit a general additive model (GAM) using a negative
binomial noise distribution to model the (potentially nonlinear)
relationshipships between gene expression and pseudotime. We will then test for
significant associations between expression and pseudotime using the
associationTest
.
library(tradeSeq)
# fit negative binomial GAM
sim <- fitGAM(sim)
# test for dynamic expression
ATres <- associationTest(sim)
We can then pick out the top genes based on p-values and visualize their expression over developmental time with a heatmap. Here we use the top 250 most dynamically expressed genes.
topgenes <- rownames(ATres[order(ATres$pvalue), ])[1:250]
pst.ord <- order(sim$slingPseudotime_1, na.last = NA)
heatdata <- assays(sim)$counts[topgenes, pst.ord]
heatclus <- sim$GMM[pst.ord]
heatmap(log1p(heatdata), Colv = NA,
ColSideColors = brewer.pal(9,"Set1")[heatclus])
Here, we provide further details and highlight some additional functionality of
the slingshot
package. We will use the included slingshotExample
dataset for
illustrative purposes. This dataset was designed to represent cells in a low
dimensional space and comes with a set of cluster labels generated by \(k\)-means
clustering. Rather than constructing a full SingleCellExperiment
object, which
requires gene-level data, we will use the low-dimensional matrix of coordinates
directly and provide the cluster labels as an additional argument.
The getLineages
function takes as input an n
\(\times\) p
matrix and a vector of
clustering results of length n
. It maps connections between adjacent clusters
using a minimum spanning tree (MST) and identifies paths through these
connections that represent lineages. The output of this function is a
SlingshotDataSet
containing the inputs as well as the inferred MST
(represented by an adjacency matrix) and lineages (ordered vectors of cluster
names).
This analysis can be performed in an entirely unsupervised manner or in a
semi-supervised manner by specifying known initial and terminal point clusters.
If we do not specify a starting point, slingshot
selects one based on
parsimony, maximizing the number of clusters shared between lineages before a
split. If there are no splits or multiple clusters produce the same parsimony
score, the starting cluster is chosen arbitrarily.
In the case of our simulated data, slingshot
selects Cluster 1 as the starting
cluster. However, we generally recommend the specification of an initial cluster
based on prior knowledge (either time of sample collection or established gene
markers). This specification will have no effect on how the MST is constructed,
but it will impact how branching curves are constructed.
lin1 <- getLineages(rd, cl, start.clus = '1')
## Using full covariance matrix
lin1
## class: SlingshotDataSet
##
## Samples Dimensions
## 140 2
##
## lineages: 2
## Lineage1: 1 2 3 5
## Lineage2: 1 2 3 4
##
## curves: 0
plot(rd, col = brewer.pal(9,"Set1")[cl], asp = 1, pch = 16)
lines(lin1, lwd = 3, col = 'black')