Introduction
To group tracks with similar properties, one can in principle perform
any clustering method of interest on a feature matrix of
quantification metrics for each track in the dataset. The package comes
with three convenience functions –
getFeatureMatrix(),trackFeatureMap(), and
clusterTracks() – to easily compute several metrics on all
tracks at once, visualize them in 2 dimensions, and to cluster tracks
accordingly. This tutorial shows how to use these functions to explore
heterogeneity in a track dataset.
Datasets
First load the package:
The package contains a dataset of B and T cells in a mouse cervical
lymph node, and neutrophils responding to an S. aureus
infection in a mouse ear; all are imaged using two-photon microscopy.
While the original data contained 3D coordinates, we’ll use the 2D
projection on the XY plane (see the vignettes on quality control methods and preprocessing of the package datasets for
details).
The T-cell dataset consists of 199 tracks of individual cells in a
tracks object:
str( TCells, list.len = 2 )
#> List of 199
#> $ 1 : num [1:39, 1:3] 48 72 96 120 144 168 192 216 240 264 ...
#> ..- attr(*, "dimnames")=List of 2
#> .. ..$ : NULL
#> .. ..$ : chr [1:3] "t" "x" "y"
#> $ 3 : num [1:19, 1:3] 24 48 72 96 120 144 168 192 216 240 ...
#> ..- attr(*, "dimnames")=List of 2
#> .. ..$ : NULL
#> .. ..$ : chr [1:3] "t" "x" "y"
#> [list output truncated]
#> - attr(*, "class")= chr "tracks"
Each element in this list is a track from a single cell, consisting
of a matrix with \((x,y)\) coordinates
and the corresponding measurement timepoints:
head( TCells[[1]] )
#> t x y
#> [1,] 48 90.8534 65.3943
#> [2,] 72 89.5923 64.9042
#> [3,] 96 88.6958 67.1125
#> [4,] 120 87.3437 68.2392
#> [5,] 144 86.2740 67.9236
#> [6,] 168 84.0549 68.2502
Similarly, we will also use the BCells and
Neutrophils data:
str( BCells, list.len = 2 )
#> List of 74
#> $ 130 : num [1:24, 1:3] 48 72 96 120 144 168 192 216 240 264 ...
#> ..- attr(*, "dimnames")=List of 2
#> .. ..$ : NULL
#> .. ..$ : chr [1:3] "t" "x" "y"
#> $ 210 : num [1:39, 1:3] 48 72 96 120 144 168 192 216 240 264 ...
#> ..- attr(*, "dimnames")=List of 2
#> .. ..$ : NULL
#> .. ..$ : chr [1:3] "t" "x" "y"
#> [list output truncated]
#> - attr(*, "class")= chr "tracks"
str( Neutrophils, list.len = 2 )
#> List of 411
#> $ 21 : num [1:7, 1:3] 48 72 96 120 144 ...
#> ..- attr(*, "dimnames")=List of 2
#> .. ..$ : NULL
#> .. ..$ : chr [1:3] "t" "x" "y"
#> $ 22 : num [1:8, 1:3] 48 72 96 120 144 ...
#> ..- attr(*, "dimnames")=List of 2
#> .. ..$ : NULL
#> .. ..$ : chr [1:3] "t" "x" "y"
#> [list output truncated]
#> - attr(*, "class")= chr "tracks"
Since there are quite many cells, we’ll sample just some of the
tracks for the legibility of the plots in this tutorial – but everything
we will do could also be done on the complete datasets.
# Take a sample
set.seed(1234)
TCells <- TCells[ sample( names(TCells), 30 ) ]
BCells <- BCells[ sample( names(BCells), 30 ) ]
Neutrophils <- Neutrophils[ sample( names(Neutrophils), 30 ) ]
Combine them in a single dataset, where labels also indicate
celltype:
T2 <- TCells
names(T2) <- paste0( "T", names(T2) )
tlab <- rep( "T", length(T2) )
B2 <- BCells
names(B2) <- paste0( "B", names(B2) )
blab <- rep( "B", length(B2) )
N2 <- Neutrophils
names(N2) <- paste0( "N", names(Neutrophils) )
nlab <- rep( "N", length( N2) )
all.tracks <- c( T2, B2, N2 )
real.celltype <- c( tlab, blab, nlab )
2 Dimensionality reduction methods: PCA, MDS, and UMAP
When using more than two metrics at once to quantify track
properties, it becomes hard to visualize which tracks are similar to
each other. Like with single-cell data, dimensionality reduction methods
can help visualize high-dimensional track feature datasets. The function
trackFeatureMap() is a wrapper method that helps to quickly
visualize data using three popular methods: principal component analysis
(PCA), multidimensional scaling (MDS), and uniform manifold approximate
and projection (UMAP). The function trackFeatureMap() can
be used for a quick visualization of data, or return the coordinates in
the new axis system if the argument
return.mapping=TRUE.
1.1 PCA
Use trackFeatureMap() to perform a principal component
analysis (PCA) based on the measures “speed”, “meanTurningAngle”,
“squareDisplacement”, “maxDisplacement”, and “outreachRatio” using the
optional labels argument to color points by their real
celltype and return.mapping=TRUE to also return the data
rather than just the plot:
pca <- trackFeatureMap( all.tracks,
c(speed,meanTurningAngle,squareDisplacement,
maxDisplacement,outreachRatio ), method = "PCA",
labels = real.celltype, return.mapping = TRUE )
Note that the B cells and Neutrophils are relatively well-separated
from each other in this plot, but the T cells are hard to distinguish
from neutrophils based on these features.
We can then inspect the data stored in pca. This
reveals, for example, that the first principal component is correlated
with speed:
pc1 <- pca[,1]
pc2 <- pca[,2]
track.speed <- sapply( all.tracks, speed )
cor.test( pc1, track.speed )
#>
#> Pearson's product-moment correlation
#>
#> data: pc1 and track.speed
#> t = 4.5449, df = 88, p-value = 1.743e-05
#> alternative hypothesis: true correlation is not equal to 0
#> 95 percent confidence interval:
#> 0.2516387 0.5898408
#> sample estimates:
#> cor
#> 0.4360085
See ?prcomp for details on how principal components are
computed, and for further arguments that can be passed on to
trackFeatureMap().
1.2 MDS
Another popular method for visualization is multidimensional scaling
(MDS), which is also supported by trackFeatureMap():
trackFeatureMap( all.tracks,
c(speed,meanTurningAngle,squareDisplacement,maxDisplacement,
outreachRatio ), method = "MDS",
labels = real.celltype )
Internally, trackFeatureMap() computes a distance matrix
using dist() and then applies MDS using
cmdscale(). See the documentation of cmdscale
for details and further arguments that can be passed on via
trackFeatureMap().
Again, we find that the B cells and Neutrophils are separated in this
plot, while T cells mix with neutrophils.
1.3 UMAP
Uniform manifold approximate and projection (UMAP) is another
powerful method to explore structure in high-dimensional datasets.
trackFeatureMap() supports visualization of tracks in a
UMAP. Note that this option requires the uwot package.
Please install this package first using
install.packages("uwot").
trackFeatureMap( all.tracks,
c(speed,meanTurningAngle,squareDisplacement,
maxDisplacement,outreachRatio ), method = "UMAP",
labels = real.celltype )
3 Clustering: hierarchical clustering and k-means
To go beyond visualizing similar and dissimilar tracks using multiple
track features, clusterTracks() supports the explicit
grouping of tracks into clusters using two common methods: hierarchical
and k-means clustering.
3.1 Hierarchical clustering
Hierarchical clustering is performed by calling hclust()
on a distance matrix computed via dist() on the feature
matrix:
clusterTracks( all.tracks,
c(speed,meanTurningAngle,squareDisplacement,maxDisplacement,
outreachRatio ), method = "hclust", labels = real.celltype )
See methods dist() and hclust() for
details.
3.2 K-means clustering
Secondly, clusterTracks() also supports k-means
clustering of tracks. Note that this requires an extra argument
centers that is passed on to the kmeans()
function and specifies the number of clusters to make. In this case,
let’s use three clusters because we have three celltypes:
clusterTracks( all.tracks,
c(speed,meanTurningAngle,squareDisplacement,maxDisplacement,
outreachRatio ), method = "kmeans",
labels = real.celltype, centers = 3 )
In these plots, we see the value of each feature in the feature
matrix plotted for the different clusters, whereas the color indicates
the “real” celltype the track came from.
