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

Last updated: 2020-11-28

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File	Version	Author	Date	Message
Rmd	31103b8	Peter Carbonetto	2020-11-28	workflowr::wflow_publish(“clusters_purified_pbmc.Rmd”)
html	4781407	Peter Carbonetto	2020-11-28	Made some improvements to the PCA plots in clusters_purified_pbmc.
Rmd	80787eb	Peter Carbonetto	2020-11-28	workflowr::wflow_publish(“clusters_purified_pbmc.Rmd”)
Rmd	605ee92	Peter Carbonetto	2020-11-28	Added steps to create PCA plots for paper in clusters_pbmc_purified analysis.
Rmd	39015bd	Peter Carbonetto	2020-11-28	Cluster A in PBMC data = dendritic cells.
html	48438b3	Peter Carbonetto	2020-11-26	Added a cluster to the purified PBMC clustering.
Rmd	989e7ac	Peter Carbonetto	2020-11-26	workflowr::wflow_publish(“clusters_purified_pbmc.Rmd”)
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Rmd	9167310	Peter Carbonetto	2020-11-23	workflowr::wflow_publish(“clusters_purified_pbmc.Rmd”)
html	8abec44	Peter Carbonetto	2020-11-23	Added PCA plots to clusters_purified_pbmc analysis.
Rmd	a7e6fbc	Peter Carbonetto	2020-11-23	Various improvements to the analysis of the PBMC data sets.
Rmd	884b869	Peter Carbonetto	2020-11-23	Working on new plots for clusters_purified_pbmc analysis.
Rmd	4a8b2bd	Peter Carbonetto	2020-11-23	A couple additions to clusters_purified_pbmc.Rmd.
html	1845721	Peter Carbonetto	2020-11-22	Added Structure plot to clusters_purified_pbmc.
Rmd	90d201b	Peter Carbonetto	2020-11-22	workflowr::wflow_publish(“clusters_purified_pbmc.Rmd”)
html	015e254	Peter Carbonetto	2020-11-22	Fixed up some of the text and plots in clusters_purified_pbmc analysis.
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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 clusters for NK cells and dendritic cells 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] <- "dendritic"
x[rows] <- y

Among the remaining cells, we define a cluster for CD8+ cells, noting that this is much less distinct than the other 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. This plot shows the clustering of the cells projected onto the top two PCs:

cluster_colors <- c("dodgerblue",  # B-cells
                    "forestgreen", # CD14+
                    "darkmagenta", # CD34+ 
                    "red",         # CD8+
                    "skyblue",     # dendritic
                    "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
4781407	Peter Carbonetto	2020-11-28
48438b3	Peter Carbonetto	2020-11-26
e7411a0	Peter Carbonetto	2020-11-23

This clustering corresponds well to the Zheng et al (2017) FACS cell populations, although there are some differences.

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

This good 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+
                 "gray",        # NK cells
                 "tomato",      # cytotoxic T-cells
                 "gold")        # T-cells
x <- as.character(samples$celltype)
x[x == "CD4+ T Helper2" | x == "CD4+/CD45RO+ Memory" |
  x == "CD8+/CD45RA+ Naive Cytotoxic" | x == "CD4+/CD45RA+/CD25- Naive T" | 
  x == "CD4+/CD45RA+/CD25- Naive T" | x == "CD4+/CD25 T Reg"] <- "T cell"
x <- factor(x)
p3 <- pca_plot(poisson2multinom(fit),fill = x) +
  scale_fill_manual(values = facs_colors) +
  labs(fill = "FACS subpopulation")
print(p3)

Version	Author	Date
4781407	Peter Carbonetto	2020-11-28
48438b3	Peter Carbonetto	2020-11-26
e7411a0	Peter Carbonetto	2020-11-23

This PCA plot highlights the FACS mis-labeling of the CD34+ cells:

rows <- which(with(samples,
                   cluster == "B" |
                   cluster == "CD14+" |
                   cluster == "CD34+" |
                   cluster == "dendritic"))
p4 <- pca_plot(select(poisson2multinom(fit),loadings = rows),
               fill = x[rows,drop = FALSE]) +
  scale_fill_manual(values = facs_colors,drop = FALSE) +
  labs(fill = "FACS subpopulation")
print(p4)

Version	Author	Date
e7411a0	Peter Carbonetto	2020-11-23
8abec44	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 == "dendritic"),
               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
4781407	Peter Carbonetto	2020-11-28
48438b3	Peter Carbonetto	2020-11-26
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")