Last updated: 2020-08-23

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TO DO: Add introductory text here.

Load the packages used in the analysis below.

library(dplyr)
library(fastTopics)
library(ggplot2)
library(cowplot)
library(Ternary)
source("../code/plots.R")

Load the sample annotations. (The count data are no longer needed at this stage of the analysis, so I have removed them.)

load("../data/pbmc_purified.RData")
samples_purified <- samples
load("../data/pbmc_68k.RData")
samples_68k <- samples
rm(genes,counts)

Load the \(k = 6\) Poisson NMF model fits for both PBMC data sets. In the descriptions below, I refer to these Poisson NMF model fits as the “purified” and “68k” fits.

To aid presentation of the results, topics in the 68k fit are reordered to better align with the topics in purified Poisson NMF fit.

fit_purified <-
  readRDS("../output/pbmc-purified/rds/fit-pbmc-purified-scd-ex-k=6.rds")$fit
fit_68k <- readRDS("../output/pbmc-68k/rds/fit-pbmc-68k-scd-ex-k=6.rds")$fit
cols      <- c(4,1,5,3,6,2)
fit_68k$F <- fit_68k$F[,cols]
fit_68k$L <- fit_68k$L[,cols]
colnames(fit_68k$F) <- paste0("k",1:6)
colnames(fit_68k$L) <- paste0("k",1:6)

We begin by exploring structure in the data as inferred by the topic model. We will visualize this structure by plotting principal components (PCs) of the topic proportions. Although PCA is simple, we will see that it quite effective, and avoids the complications of the popular t-SNE and UMAP nonlinear dimensionality reduction methods.

We begin with the mixture of FACS-purified PBMC data.

fit <- poisson2multinom(fit_purified)
pca <- prcomp(fit$L)$x

Three large clusters are clearly evident from first two PCs (there is also finer-scale structure which we will examine below). We label these clusters simply as “A”, “B” and “C”.

n   <- nrow(pca)
x   <- rep("C",n)
pc1 <- pca[,"PC1"]
pc2 <- pca[,"PC2"]
x[pc1 + 0.2 > pc2] <- "A"
x[pc2 > 0.25] <- "B"
x[(pc1 + 0.4)^2 + (pc2 + 0.1)^2 < 0.07] <- "C"
samples_purified$cluster <- x
p1 <- pca_plot_with_labels(fit_purified,c("PC1","PC2"),
                           samples_purified$cluster) +
      labs(fill = "cluster")
print(p1)

Version Author Date
7900d17 Peter Carbonetto 2020-08-22
38f07a2 Peter Carbonetto 2020-08-20

Most of the samples are in cluster A:

table(x)
# x
#     A     B     C 
# 72614 10439 11602

In cluster C, there are two well-defined subclusters, which we label “C1” and “C2”. There are perhaps other subclusters that are less defined, but we here we ignore this more subtle structure, and focus on the most obvious clusters:

rows <- which(samples_purified$cluster == "C")
fit  <- select(poisson2multinom(fit_purified),loadings = rows)
pca  <- prcomp(fit$L)$x
n    <- nrow(pca)
x    <- rep("C3",n)
pc1  <- pca[,1]
pc2  <- pca[,2]
x[pc1 < 0 & pc2 < 0.4] <- "C1"
x[pc1 > 0.5 & pc2 < 0.3] <- "C2"
samples_purified[rows,"cluster"] <- x
p5 <- pca_plot_with_labels(fit,c("PC1","PC2"),x) +
      labs(fill = "cluster")
print(p5)

Version Author Date
7900d17 Peter Carbonetto 2020-08-22

The two subclusters, C1 and C2, account for most of the samples in cluster C:

table(x)
# x
#   C1   C2   C3 
# 7822 2990  790

Let’s now look more closely at cluster A. There is a large, much less distinct subcluster, which we label as “A1”. Otherwise, there are no other clearly distinct clusters.

rows <- which(samples_purified$cluster == "A")
fit  <- select(poisson2multinom(fit_purified),loadings = rows)
pca  <- prcomp(fit$L)$x
n    <- nrow(fit$L)
x    <- rep("A2",n)
pc1  <- pca[,1]
pc2  <- pca[,2]
x[pc1 > 0.58 - pc2 | pc1 > 0.7] <- "A1"
samples_purified[rows,"cluster"] <- x
p6 <- pca_plot_with_labels(fit,c("PC1","PC2"),x) +
      labs(fill = "cluster")
print(p6)

Version Author Date
97d7e86 Peter Carbonetto 2020-08-23
7900d17 Peter Carbonetto 2020-08-22

In summary, we have subdivided these data into 6 clusters:

samples_purified$cluster <- factor(samples_purified$cluster)
table(samples_purified$cluster)
# 
#    A1    A2     B    C1    C2    C3 
#  8271 64343 10439  7822  2990   790

The Structure plot provides a visual summary of topic proportions in each of these six clusters:

set.seed(1)
pbmc_purified_topics       <- c(2,5,1,3,4,6)
pbmc_purified_topic_colors <- c("gold","forestgreen","dodgerblue",
                                "gray","greenyellow","magenta")
rows <- sort(c(sample(which(samples_purified$cluster == "A1"),250),
               sample(which(samples_purified$cluster == "A2"),1200),
               sample(which(samples_purified$cluster == "B"),250),
               sample(which(samples_purified$cluster == "C1"),250),
               sample(which(samples_purified$cluster == "C2"),250),
               sample(which(samples_purified$cluster == "C3"),200)))
p7 <- structure_plot(select(poisson2multinom(fit_purified),loadings = rows),
                     grouping = samples_purified[rows,"cluster"],
                     topics = pbmc_purified_topics,
                     colors = pbmc_purified_topic_colors[pbmc_purified_topics],
                     gap = 40,num_threads = 4,verbose = FALSE)
print(p7)

Version Author Date
13ee038 Peter Carbonetto 2020-08-23
97d7e86 Peter Carbonetto 2020-08-23
59777e7 Peter Carbonetto 2020-08-22
c87ddf8 Peter Carbonetto 2020-08-22
7900d17 Peter Carbonetto 2020-08-22
fbb0697 Peter Carbonetto 2020-08-21
216027a Peter Carbonetto 2020-08-21

Out of the 6 topics, 4 of them (\(k = 2, 3, 4, 5\)) align closely with the clusters (labeled A1, B, C1, C2). Indeed, they also align closely with the FACS-purified data sets:

with(samples_purified,table(celltype,cluster))
#                               cluster
# celltype                          A1    A2     B    C1    C2    C3
#   CD19+ B                          0     3 10073     0     1     8
#   CD14+ Monocyte                   0    30     8     1  2443   130
#   CD34+                            4    43   352  7740   545   548
#   CD4+ T Helper2                   1 11183     0    16     0    13
#   CD56+ NK                      8243   120     0    17     1     4
#   CD8+ Cytotoxic T                21 10135     0     0     0    53
#   CD4+/CD45RO+ Memory              0 10201     0    19     0     4
#   CD8+/CD45RA+ Naive Cytotoxic     1 11945     3     0     0     4
#   CD4+/CD45RA+/CD25- Naive T       1 10440     1    25     0    12
#   CD4+/CD25 T Reg                  0 10243     2     4     0    14

For example, cluster B corresponds almost perfectly to the B-cell data set, and the largest cluster—cluster A2—is comprised of the T-cell data sets. It is also interesting that many of the samples labeled as “CD34+” are not assigned to the CD34+ cluster (C1), which probably reflects the fact that the this population was much less pure (45%) than the others, and so probably contained other cell types.

Cluster C3 is a heterogeneous cluster that we do not investigate further. Cluster A2—see also the PCA plot above—is a clear example where topic modeling is more appropriate than clustering because any additional clustering of the data will be arbitrary.

Next, we turn to the 68k fit.

fit <- poisson2multinom(fit_68k)
pca <- prcomp(fit$L)$x

In this case, we find least three distinct clusters in the projection onto PCs 3 and 4. We label these clusters “A”, “B” and “C”, as above, but this labeling does not imply a connection between the two sets of clusters.

n <- nrow(pca)
x <- rep("A",n)
pc3 <- pca[,"PC3"]
pc4 <- pca[,"PC4"]
x[pc4 > 0.13 | 0.17 - pc3/1.9 < pc4] <- "B"
x[pc4 > 0.75] <- "C"
samples_68k$cluster <- x
p7 <- pca_plot_with_labels(fit_68k,c("PC3","PC4"),x) +
      labs(fill = "cluster")
print(p7)

Version Author Date
a406a2f Peter Carbonetto 2020-08-22
7900d17 Peter Carbonetto 2020-08-22
fbb0697 Peter Carbonetto 2020-08-21
216027a Peter Carbonetto 2020-08-21
6d3d7e4 Peter Carbonetto 2020-08-20

The vast majority of the cells are in cluster A:

table(samples_68k$cluster)
# 
#     A     B     C 
# 63408  5006   165

Looking more closely at cluster B:

rows <- which(samples_68k$cluster == "B")
fit  <- select(poisson2multinom(fit_68k),loadings = rows)
pca  <- prcomp(fit$L)$x
n    <- nrow(pca)
x    <- rep("B3",n)
pc1  <- pca[,"PC1"]
x[pc1 < 0.05] <- "B1"
x[pc1 > 0.3] <- "B2"
samples_68k[rows,"cluster"] <- x
p8 <- pca_plot_with_labels(fit,c("PC1","PC2"),x) +
      labs(fill = "cluster")
print(p8)

Looking more closely at cluster A:

rows <- which(samples_68k$cluster == "A")
fit  <- select(poisson2multinom(fit_68k),loadings = rows)
pca  <- prcomp(fit$L)$x
n    <- nrow(pca)
x    <- rep("A3",n)
pc2  <- pca[,"PC2"]
pc3  <- pca[,"PC3"]
x[2.5*pc3 < pc2 + 0.3] <- "A1"
x[pc3 > pc2 + 0.8] <- "A2"
samples_68k[rows,"cluster"] <- x
p9 <- pca_plot_with_labels(fit,c("PC2","PC3"),x) +
      labs(fill = "cluster")
print(p9)

Within cluster A, the vast majority of the samples are assigned to the A1 subcluster:

table(x)
# x
#    A1    A2    A3 
# 59260  3555   593

In summary, we have subdivided these data into 7 clusters:

samples_68k$cluster <- factor(samples_68k$cluster)
table(samples_68k$cluster)
# 
#    A1    A2    A3    B1    B2    B3     C 
# 59260  3555   593  3869   819   318   165

TO DO: Add text here.

set.seed(1)
pbmc_68k_topics       <- c(2,5,1,3,4,6)
pbmc_68k_topic_colors <- c("darkorange","olivedrab","dodgerblue",
                           "gray","royalblue","magenta")
rows <- sort(c(sample(which(samples_68k$cluster == "c1"),1400),
               sample(which(samples_68k$cluster == "c2"),500),
               which(samples_68k$cluster == "c3")))
p4 <- structure_plot(select(poisson2multinom(fit_68k),loadings = rows),
                     grouping = samples_68k[rows,"cluster"],
                     topics = pbmc_68k_topics,
                     colors = pbmc_68k_topic_colors[pbmc_68k_topics],
                     gap = 40,num_threads = 4,verbose = FALSE)
print(p4)

TO DO: Before comparing to Zheng et al (2017) labeling, do more manual identification of clusters from the PCA plots.

Comparison to Zheng et al (2017) cell-type labeling of the FACS-purified PBMC data. In fit_purified, cluster 2 captures B-cells; cluster 3 is almost exclusively CD34+ and CD14+ monocytes:

Now let’s look more closely at cluster 1 in fit_purified:

par(mar = c(0,0,0,0))
rows <- which(samples_purified$cluster == "c1")
TernaryPlot(alab = "k1",blab = "k4",clab = "k6",
            grid.col = "gainsboro",grid.minor.lines = 0)
TernaryPoints(pdat[rows,c(1,4,6)],pch = 21,cex = 0.65,col = "white",
              bg = as.character(pdat[rows,"celltype"]))

In fit_68k, cluster 2 mostly consists of CD14+ monocyte and dendritic cells, whereas cluster 3 is a small population of CD34+ cells.

with(samples_68k,table(celltype,cluster))

Finally, let’s look more closely at cluster 1 in fit_68k:

par(mar = c(0,0,0,0))
rows <- which(samples_68k$cluster == "c1")
TernaryPlot(alab = "k2",blab = "k4",clab = "k6",
            grid.col = "gainsboro",grid.minor.lines = 0)
TernaryPoints(pdat[rows,c(2,4,6)],pch = 21,cex = 0.65,col = "white",
              bg = as.character(pdat[rows,"celltype"]))
p4 <- pca_plot_with_labels(fit_purified,c("PC1","PC2"),
                           samples_purified$celltype,
                           purified_celltype_colors) + labs(fill = "celltype")
p5 <- pca_plot_with_labels(fit_purified,c("PC4","PC5"),
                           samples_purified$celltype,
                           purified_celltype_colors) + labs(fill = "celltype")
pbmc_purified_celltype_colors <-
  c("dodgerblue",  # CD19+ B
    "forestgreen", # CD14+ Monocyte
    "palegreen",   # CD34+
    "plum",        # CD4+ T Helper2
    "gray",        # CD56+ NK
    "tomato",      # CD8+ Cytotoxic T
    "gold",        # CD4+/CD45RO+ Memory
    "magenta",     # CD8+/CD45RA+ Naive Cytotoxic
    "darkorange",  # CD4+/CD45RA+/CD25- Naive T
    "yellowgreen") # CD4+/CD25 T Reg

Loadings plot:

loadings_plot(poisson2multinom(fit_purified),samples_purified$celltype)
loadings_plot(poisson2multinom(fit_68k),samples_68k$celltype)

PCA plot:

clrs <- c("forestgreen",  # CD14+ Monocyte
          "dodgerblue",   # CD19+ B
          "darkmagenta",  # CD34+"
          "yellowgreen",  # CD4+ T Helper2
          "gold",         # CD4+/CD25 T Reg
          "limegreen",    # CD4+/CD45RA+/CD25- Naive T
          "orange",       # CD4+/CD45RO+ Memory"
          "gray",         # CD56+ NK
          "tomato",       # CD8+ Cytotoxic T
          "magenta",      # CD8+/CD45RA+ Naive Cytotoxic"
          "darkblue")     # Dendritic"
fit2 <- poisson2multinom(fit)
pca  <- prcomp(fit2$L)
pdat <- cbind(samples,pca$x)
ggplot(pdat,aes(x = PC3,y = PC4,fill = celltype)) +
  geom_point(shape = 21,color = "white",size = 1.5) +
  scale_fill_manual(values = clrs) +
  theme_cowplot(font_size = 10)

t-SNE plot:

set.seed(1)
p2 <- tsne_plot(fit,n = 8000,num_threads = 4)

Differential count analysis:

diff_count_res <- diff_count_analysis(fit,counts)

Volcano plots:

p3 <- volcano_plot(diff_count_res,labels = genes$symbol,
                   label_above_quantile = 0.995)

Structure plots:

set.seed(1)
fit2 <- select(poisson2multinom(fit),
               loadings = which(samples$celltype == "CD19+ B"))
p4   <- structure_plot(fit2,n = 2000,num_threads = 4) # B-cells.
set.seed(1)
fit2 <- select(poisson2multinom(fit),
               loadings = which(samples$celltype == "CD56+ NK"))
p5   <- structure_plot(fit2,n = 2000,num_threads = 4) # NK cells.
set.seed(1)
fit2 <- select(poisson2multinom(fit),
               loadings = which(samples$celltype == "CD34+"))
p6   <- structure_plot(fit2,num_threads = 4,perplexity = 50) # CD34+ cells
set.seed(1)
fit2 <- select(poisson2multinom(fit),
               loadings = which(samples$celltype == "CD14+ Monocyte"))
p7   <- structure_plot(fit2,num_threads = 4) # CD14+ monocytes
set.seed(1)
fit2 <- select(poisson2multinom(fit),
               loadings = which(samples$celltype == "Dendritic"))
p8   <- structure_plot(fit2,num_threads = 4) # dendritic cells
plot_grid(p7,p8,nrow = 2)
set.seed(1)
fit2 <- select(poisson2multinom(fit),
               loadings = which(samples$celltype == "CD4+ T Helper2"))
p9   <- structure_plot(fit2,num_threads = 4,perplexity = 30) +
          ggtitle("CD4+ T Helper2") +
set.seed(1)
fit2 <- select(poisson2multinom(fit),
          loadings = which(samples$celltype == "CD4+/CD45RA+/CD25- Naive T"))
p10  <- structure_plot(fit2,num_threads = 4) +
          ggtitle("CD4+/CD45RA+/CD25- Naive T")
set.seed(1)
fit2 <- select(poisson2multinom(fit),
               loadings = which(samples$celltype == "CD4+/CD45RO+ Memory"))
p11  <- structure_plot(fit2,num_threads = 4) +
          ggtitle("CD4+/CD45RO+ Memory")
set.seed(1)
fit2 <- select(poisson2multinom(fit),
               loadings = which(samples$celltype == "CD4+/CD25 T Reg"))
p12  <- structure_plot(fit2,num_threads = 4) +
          ggtitle("CD4+/CD25 T Reg")
fit2 <- select(poisson2multinom(fit),
          loadings = which(samples$celltype == "CD8+/CD45RA+ Naive Cytotoxic"))
p13  <- structure_plot(fit2,num_threads = 4) +
          ggtitle("CD8+/CD45RA+ Naive Cytotoxic")
fit2 <- select(poisson2multinom(fit),
          loadings = which(samples$celltype == "CD8+ Cytotoxic T"))
p14  <- structure_plot(fit2,num_threads = 4) +
          ggtitle("CD8+ Cytotoxic T")
plot_grid(p9,p10,p11,p12,p13,p14,nrow = 6)

Another structure plot:

p15 <- structure_plot(fit,num_threads = 4)

sessionInfo()
# R version 3.6.2 (2019-12-12)
# Platform: x86_64-apple-darwin15.6.0 (64-bit)
# Running under: macOS Catalina 10.15.5
# 
# Matrix products: default
# BLAS:   /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
# LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.dylib
# 
# locale:
# [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
# 
# attached base packages:
# [1] stats     graphics  grDevices utils     datasets  methods   base     
# 
# other attached packages:
# [1] Ternary_1.1.4      cowplot_1.0.0      ggplot2_3.3.0      fastTopics_0.3-163
# [5] dplyr_0.8.3       
# 
# loaded via a namespace (and not attached):
#  [1] ggrepel_0.9.0        Rcpp_1.0.3           lattice_0.20-38     
#  [4] tidyr_1.0.0          prettyunits_1.1.1    assertthat_0.2.1    
#  [7] zeallot_0.1.0        rprojroot_1.3-2      digest_0.6.23       
# [10] R6_2.4.1             backports_1.1.5      MatrixModels_0.4-1  
# [13] evaluate_0.14        coda_0.19-3          httr_1.4.1          
# [16] pillar_1.4.3         rlang_0.4.5          progress_1.2.2      
# [19] lazyeval_0.2.2       data.table_1.12.8    irlba_2.3.3         
# [22] SparseM_1.78         whisker_0.4          Matrix_1.2-18       
# [25] rmarkdown_2.3        labeling_0.3         Rtsne_0.15          
# [28] stringr_1.4.0        htmlwidgets_1.5.1    munsell_0.5.0       
# [31] compiler_3.6.2       httpuv_1.5.2         xfun_0.11           
# [34] pkgconfig_2.0.3      mcmc_0.9-6           htmltools_0.4.0     
# [37] tidyselect_0.2.5     tibble_2.1.3         workflowr_1.6.2.9000
# [40] quadprog_1.5-8       viridisLite_0.3.0    crayon_1.3.4        
# [43] withr_2.1.2          later_1.0.0          MASS_7.3-51.4       
# [46] grid_3.6.2           jsonlite_1.6         gtable_0.3.0        
# [49] lifecycle_0.1.0      git2r_0.26.1         magrittr_1.5        
# [52] scales_1.1.0         RcppParallel_4.4.4   stringi_1.4.3       
# [55] farver_2.0.1         fs_1.3.1             promises_1.1.0      
# [58] vctrs_0.2.1          tools_3.6.2          glue_1.3.1          
# [61] purrr_0.3.3          hms_0.5.2            yaml_2.2.0          
# [64] colorspace_1.4-1     plotly_4.9.2         knitr_1.26          
# [67] quantreg_5.54        MCMCpack_1.4-5