Identify clusters in mixture of FACS-purified PBMC data using topic model

Last updated: 2020-11-26

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Here we perform PCA on the topic proportions to identify clusters in the mixture of FACS-purified PBMC data sets.

Load the packages used in the analysis below, as well as additional functions that we will use to generate some of the plots.

library(Matrix)
library(dplyr)
library(fastTopics)
library(Rtsne)
library(uwot)
library(ggplot2)
library(cowplot)
source("../code/plots.R")

Load the count data.

load("../data/pbmc_purified.RData")

Load the \(K = 6\) Poisson NMF model fit.

fit <- readRDS(file.path("../output/pbmc-purified/rds",
                         "fit-pbmc-purified-scd-ex-k=6.rds"))$fit

Identify clusters from principal components

From the PCs of the topic proportions, we define clusters for B-cells, CD14+ cells and CD34+ cells. The remaining cells are assigned to the U cluster (“U” for “unknown”).

pca <- prcomp(poisson2multinom(fit)$L)$x
n   <- nrow(pca)
x   <- rep("U",n)
pc1 <- pca[,1]
pc2 <- pca[,2]
pc3 <- pca[,3]
pc4 <- pca[,4]
pc5 <- pca[,5]
x[pc2 > 0.25] <- "B"
x[pc3 < -0.2 & pc4 < 0.2] <- "CD34+"
x[(pc4 + 0.1)^2 + (pc5 - 0.8)^2 < 0.07] <- "CD14+"

Next, we define an NK cells cluster from the top 2 PCs of the topic proportions in the U cluster.

rows <- which(x == "U")
n    <- length(rows)
fit2 <- select(poisson2multinom(fit),loadings = rows)
pca  <- prcomp(fit2$L)$x
y    <- rep("U",n)
pc1  <- pca[,1]
pc2  <- pca[,2]
pc3  <- pca[,3]
pc4  <- pca[,4]
y[pc1 < -0.3 & 1.1*pc1 < -pc2 - 0.57] <- "NK"
y[pc3 > 0.4 & pc4 < 0.2] <- "A"
x[rows] <- y

Among the remaining cells, we define a much less distinct cluster of CD8+ cells. The rest are labeled as T-cells.

rows <- which(x == "U")
n    <- length(rows)
fit2 <- select(poisson2multinom(fit),loadings = rows)
pca  <- prcomp(fit2$L)$x
y    <- rep("T",n)
pc1  <- pca[,1]
pc2  <- pca[,2]
y[pc1 < 0.25 & pc2 < -0.15] <- "CD8+"
x[rows] <- y

In summary, we have subdivided the cells into 7 subsets. The substructure becomes more clear when we plot T cells separately from the other cells.

cluster_colors <- c("skyblue",     # A
                    "dodgerblue",  # B-cells
                    "forestgreen", # CD14+
                    "darkmagenta", # CD34+ 
                    "red",         # CD8+
                    "gray",        # NK
                    "darkorange")  # T-cells
samples$cluster <- factor(x)
p1 <- pca_plot(poisson2multinom(fit),fill = samples$cluster) +
  scale_fill_manual(values = cluster_colors) +
  labs(fill = "cluster")
p2 <- pca_hexbin_plot(poisson2multinom(fit))
plot_grid(p1,p2,rel_widths = c(10,11))

Version	Author	Date
e7411a0	Peter Carbonetto	2020-11-23

This clustering corresponds closely to the Zheng et al (2017) FACS cell populations, although there are some differences—for example, the CD14+ cluster contains a large number of cells identified as CD34+ by FACS.

with(samples,table(celltype,cluster))
#                               cluster
# celltype                           A     B CD14+ CD34+  CD8+    NK     T
#   CD19+ B                          7 10073     0     0     3     0     2
#   CD14+ Monocyte                 156     8  2420     0     3     0    25
#   CD34+                          121   352   536  8182    20     4    17
#   CD4+ T Helper2                   9     0     0     8    45     1 11150
#   CD56+ NK                         4     0     0    17    82  8279     3
#   CD8+ Cytotoxic T                 0     0     0     0  3146    93  6970
#   CD4+/CD45RO+ Memory              1     0     0    20   355     0  9848
#   CD8+/CD45RA+ Naive Cytotoxic     2     3     0     0    52     2 11894
#   CD4+/CD45RA+/CD25- Naive T       5     1     0     8    27     1 10437
#   CD4+/CD25 T Reg                  3     2     0     2    24     0 10232

This close correspondence is also apparent when we layer the FACS cell population labels on the PCA plots:

facs_colors <- c("dodgerblue",  # B-cells
                 "forestgreen", # CD14+
                 "darkmagenta", # CD34+
                 "firebrick",   # T helper cells
                 "gray",        # NK cells
                 "tomato",      # cytotoxic T-cells
                 "yellow",      # memory T-cells
                 "magenta",     # naive cytotoxic 
                 "darkorange",  # naive T-cells
                 "gold")        # regulatory T-cells
p3 <- pca_plot(poisson2multinom(fit),fill = samples$celltype) +
  scale_fill_manual(values = facs_colors) +
  labs(fill = "FACS subtype")
print(p3)

Version	Author	Date
e7411a0	Peter Carbonetto	2020-11-23

By computing inter-cluster and inter-topic total variation distances in relative expression levels, we see that the clusters identified above show greater differentiation in gene expression, and the topics show more differentiation than the clusters.

fit_zheng <- init_poisson_nmf_from_clustering(counts,samples$celltype)
d_zheng   <- totalvardist(poisson2multinom(fit_zheng)$F)
d_topics  <- totalvardist(poisson2multinom(fit)$F)

Here is a plot summarizing these differences:

pdat <-
  rbind(data.frame(method = "zheng.et.al",d = d_zheng[upper.tri(d_zheng)]),
        data.frame(method = "topics",     d = d_topics[upper.tri(d_topics)]))
p4 <- ggplot(pdat,aes(x = method,y = d)) +
  geom_boxplot(width = 0.25) +
  labs(x = "",y = "total variation dist") +
  theme_cowplot(font_size = 9)
print(p4)

Version	Author	Date
e7411a0	Peter Carbonetto	2020-11-23

Structure plot

The structure plot summarizes the topic proportions in each of these 6 subsets:

set.seed(1)
topic_colors <- c("gold","forestgreen","dodgerblue","gray",
                  "darkmagenta","violet")
topics <- c(5,3,2,4,1,6)
rows <- sort(c(sample(which(samples$cluster == "B"),1000),
               sample(which(samples$cluster == "CD14+"),300),
               sample(which(samples$cluster == "CD34+"),500),
               which(samples$cluster == "A"),
               sample(which(samples$cluster == "CD8+"),400),
               sample(which(samples$cluster == "NK"),500),
               sample(which(samples$cluster == "T"),1000)))
p5 <- structure_plot(select(poisson2multinom(fit),loadings = rows),
                     grouping = samples[rows,"cluster"],
                     topics = topics,colors = topic_colors[topics],
                     perplexity = c(70,30,30,30,30,30,70),
                     n = Inf,gap = 50,num_threads = 4,verbose = FALSE)
print(p5)

Version	Author	Date
1845721	Peter Carbonetto	2020-11-22

Note that CD8+ cells are identified as a distinctive mixture of topics capturing NK cells and T-cells.

Analysis of single-cell likelihoods

Create scatterplots comparing single-cell likelihoods using a “hard” clustering (based on the FACS subpopulations).

PCA vs. t-SNE and UMAP: an illustration

Here we illustrate one of the benefits of using a simple linear dimensionality reduction technique, PCA, over more widely used nonlinear dimensionality reduction methods t-SNE and UMAP. In particular, we compare a 2-d linear embedding produced by PCA against nonlinear embeddings generated by t-SNE and UMAP.

To begin, draw a random subset of 2,000 cells from the B, CD14+ and CD34+ clusters identified above. (The main reason for taking a random subset is that we don’t want to wait a long time for t-SNE and UMAP to complete.) Then run PCA on the topic proportions for this random subset of 2,000 samples.

set.seed(5)
rows <- which(with(samples,
                   cluster == "B" | cluster == "CD14+" | cluster == "CD34+"))
rows <- sort(sample(rows,2000))
fit2 <- select(poisson2multinom(fit),loadings = rows)
x    <- samples$cluster[rows,drop = TRUE]
p6   <- pca_plot(fit2,fill = x) + labs(fill = "cluster")

Next, run t-SNE on the topic proportions.

tsne <- Rtsne(fit2$L,dims = 2,pca = FALSE,normalize = FALSE,perplexity = 100,
              theta = 0.1,max_iter = 1000,eta = 200,verbose = FALSE)
tsne$x <- tsne$Y
colnames(tsne$x) <- c("tsne1","tsne2")
p7 <- pca_plot(fit2,out.pca = tsne,fill = x) + labs(fill = "cluster")

Then run UMAP on the topic proportions.

out.umap <- umap(fit2$L,n_neighbors = 30,metric = "euclidean",n_epochs = 1000,
                 min_dist = 0.1,scale = "none",learning_rate = 1,
                 verbose = FALSE)
out.umap <- list(x = out.umap)
colnames(out.umap$x) <- c("umap1","umap2")
p8 <- pca_plot(fit2,out.pca = out.umap,fill = x) + labs(fill = "cluster")

plot_grid(p6,p7,p8,nrow = 1)

Version	Author	Date
e7411a0	Peter Carbonetto	2020-11-23

By the projection of the samples onto the first two PCs, we see that the B-cells cluster is distinct from the others, whereas the CD14+ and CD34+ cells do not separate quite so neatly.

However, this this finer scale detail is not captured in the t-SNE and UMAP embeddings; this illustrates the tendency of t-SNE and UMAP to accentuate clusters in the data at the risk of distorting or obscure finer scale substructure.

Note that the first 2 PCs should be sufficient for capturing the full structure in the topic proportions as they explain >96% of the variance:

summary(prcomp(fit2$L))
# Importance of components:
#                           PC1    PC2     PC3     PC4     PC5      PC6
# Standard deviation     0.4831 0.3269 0.10351 0.03397 0.02396 3.49e-16
# Proportion of Variance 0.6618 0.3030 0.03038 0.00327 0.00163 0.00e+00
# Cumulative Proportion  0.6618 0.9647 0.99510 0.99837 1.00000 1.00e+00

Save results

Save the clustering of the PBMC data to an RDS file.

saveRDS(samples,"clustering-pbmc-purified.rds")