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Here we perform PCA on the topic proportions to identify clusters in the pulse-seq data.

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(ggplot2)
library(cowplot)

Load data and results

Load the pulse-seq data.

load("../data/pulseseq.RData")
x <- as.character(samples$tissue)
x[x == "club (hillock-associated)"] <- "club"
x[x == "goblet.1" | x == "goblet.2" | x == "goblet.progenitor"] <- "goblet"
x[x == "tuft.1" | x == "tuft.2" | x == "tuft.progenitor"] <- "tuft"
samples$tissue <- factor(x)

Load the \(k = 11\) Poisson NMF model fit.

fit <- readRDS("../output/pulseseq/rds/fit-pulseseq-scd-ex-k=11.rds")$fit

Identify clusters from principal components

To identify clusters, we begin by plotting PCs computed from the topic proportions. (Note that only 10 PCs are needed for 11 topics.)

p1 <- pca_plot(poisson2multinom(fit),pcs = 1:2,fill = "none")
p2 <- pca_plot(poisson2multinom(fit),pcs = 3:4,fill = "none")
p3 <- pca_plot(poisson2multinom(fit),pcs = 5:6,fill = "none")
p4 <- pca_plot(poisson2multinom(fit),pcs = 7:8,fill = "none")
p5 <- pca_plot(poisson2multinom(fit),pcs = 9:10,fill = "none")
plot_grid(p1,p2,p3,p4,p5,nrow = 2,ncol = 3)

Version Author Date
072ef40 Peter Carbonetto 2020-10-06
e7383b2 Peter Carbonetto 2020-09-16

Some of the structure is more evident from “hexbin” plots showing the density of the points. For example, clear clusters emerge in the hexbin plots for PCs 3 and 4, and for PCs 5 and 6:

p6  <- pca_hexbin_plot(poisson2multinom(fit),pcs = 1:2) + guides(fill = "none")
p7  <- pca_hexbin_plot(poisson2multinom(fit),pcs = 3:4) + guides(fill = "none")
p8  <- pca_hexbin_plot(poisson2multinom(fit),pcs = 5:6) + guides(fill = "none")
p9  <- pca_hexbin_plot(poisson2multinom(fit),pcs = 7:8) + guides(fill = "none")
p10 <- pca_hexbin_plot(poisson2multinom(fit),pcs = 9:10)+ guides(fill = "none")
plot_grid(p6,p7,p8,p9,p10,nrow = 2,ncol = 3)

Version Author Date
072ef40 Peter Carbonetto 2020-10-06
e7383b2 Peter Carbonetto 2020-09-16

From these PCA plots, we define 4 clusters, labeled A, D, Cil and T+N. (The reasoning behind these cluster labels will become clear later.) Points that do not fit in any of these clusters are assigned to a “background cluster”, labeled U for “unknown”.

pca <- prcomp(poisson2multinom(fit)$L)$x
x   <- rep("U",nrow(pca))
pc3 <- pca[,3]
pc4 <- pca[,4]
pc5 <- pca[,5]
pc6 <- pca[,6]
x[pc4 < 5.5*pc3 + 0.5] <- "A"
x[(pc3 + 0.7)^2 + (pc4 - 0.1)^2 < 0.18^2] <- "Cil"
x[x == "A" & pc6 > 1.3*pc5 + 0.87] <- "T+N"
x[x == "A" & pc5 > -0.4 & pc6 < 1.3*pc5 + 0.49] <- "D"

We can refine the small cluster A somewhat by plotting PCs computed from cluster A only:

rows <- which(x == "A")
fit2 <- select(poisson2multinom(fit),loadings = rows)
p11  <- pca_plot(fit2,fill = "none")
print(p11)

Version Author Date
072ef40 Peter Carbonetto 2020-10-06
65f104e Peter Carbonetto 2020-09-18
775fb91 Peter Carbonetto 2020-09-18
13a5956 Peter Carbonetto 2020-09-16

We label this refined cluster as “I”, and the rest are added back to the background cluster (U).

pca  <- prcomp(fit2$L)$x
y    <- rep("U",nrow(pca))
pc1  <- pca[,1]
y[pc1 > -0.1] <- "I"
x[rows] <- y

Similarly, we mine the much larger cluster D for substructure:

rows <- which(x == "D")
fit2 <- select(poisson2multinom(fit),loadings = rows)
p12  <- pca_plot(fit2,fill = "none")
p13  <- pca_hexbin_plot(fit2) + guides(fill = "none")
plot_grid(p12,p13)

Version Author Date
072ef40 Peter Carbonetto 2020-10-06
65f104e Peter Carbonetto 2020-09-18
775fb91 Peter Carbonetto 2020-09-18
e62fb43 Peter Carbonetto 2020-09-18
13a5956 Peter Carbonetto 2020-09-16

The hexbin plot suggests two clusters. Although these clusters are not distinct, it may nonetheless be useful to subdivide these data points (somewhat arbitrarily) into two subsets, which we label as B and C.

pca  <- prcomp(fit2$L)$x
y    <- rep("C",nrow(pca))
pc1  <- pca[,1]
pc2  <- pca[,2]
y[pc2 > -pc1 - 0.15] <- "B"
x[rows] <- y

Within cluster B, there is some interesting structure along PCs 5 and 6:

rows <- which(x == "B")
fit2 <- select(poisson2multinom(fit),loadings = rows)
p14  <- pca_plot(fit2,pcs = 5:6,fill = "none")
p15  <- pca_hexbin_plot(fit2,pcs = 5:6) + guides(fill = "none")
plot_grid(p14,p15)

Version Author Date
072ef40 Peter Carbonetto 2020-10-06
65f104e Peter Carbonetto 2020-09-18
e62fb43 Peter Carbonetto 2020-09-18
13a5956 Peter Carbonetto 2020-09-16

From PCs 5 and 6, define a new cluster, “P”, recognizing that this cluster is not particularly distinct.

pca <- prcomp(fit2$L)$x
y   <- rep("B",nrow(pca))
pc5 <- pca[,5]
pc6 <- pca[,6]
y[pc5 > 0.1 & pc6 < 0] <- "P"
x[rows] <- y

Although subtle, there is variation in topic 2 and 11 within the T+N cluster that tracks closely with the tuft (here signaled by gene Gnat3) and pulmonary neuroendocrine (Chga) cell-types:

p16 <- pca_plot(poisson2multinom(fit),pcs = 5:6,k = 2)
p17 <- pca_plot(poisson2multinom(fit),pcs = 5:6,k = 11)
p18 <- pca_plot(poisson2multinom(fit),pcs = 5:6,
                fill = log10(counts[,"Chga"])) +
       labs(fill = "log10(count)",title = "Chga")
p19 <- pca_plot(poisson2multinom(fit),pcs = 5:6,
                fill = log10(counts[,"Gnat3"])) +
       labs(fill = "log10(count)",title = "Gnat3")
plot_grid(p16,p17,p18,p19)

In summary, we have subdivided the pulse-seq data into 7 subsets, which includes a background cluster (U).

samples$cluster <- factor(x,c("B","C","P","Cil","T+N","I","U"))
cluster_colors  <- c("royalblue",   # B
                     "forestgreen", # C
                     "peru",        # P
                     "firebrick",   # Cil
                     "darkorange",  # T+N
                     "darkmagenta", # I
                     "gainsboro")   # U
p20 <- pca_plot(poisson2multinom(fit),pcs = 1:2,fill = samples$cluster) +
       scale_fill_manual(values = cluster_colors) +
       labs(fill = "cluster")
p21 <- pca_plot(poisson2multinom(fit),pcs = 3:4,fill = samples$cluster) +
       scale_fill_manual(values = cluster_colors) +
       labs(fill = "cluster")
p22 <- pca_plot(poisson2multinom(fit),pcs = 5:6,fill = samples$cluster) +
       scale_fill_manual(values = cluster_colors) +
       labs(fill = "cluster")
plot_grid(p20,p21,p22,nrow = 1)

Version Author Date
072ef40 Peter Carbonetto 2020-10-06
56d99a3 Peter Carbonetto 2020-09-22
7489099 Peter Carbonetto 2020-09-18
942486b Peter Carbonetto 2020-09-18
775fb91 Peter Carbonetto 2020-09-18
e62fb43 Peter Carbonetto 2020-09-18
4b4b233 Peter Carbonetto 2020-09-18
571b311 Peter Carbonetto 2020-09-16

Comparing this to the Montoro et al (2018) clustering, we observe some close correspondence (e.g., B and “basal cells”, P and “proliferating cells”).

with(samples,table(tissue,cluster))
#                 cluster
# tissue               B     C     P   Cil   T+N     I     U
#   basal          40389  1468   199     0     0     0    37
#   ciliated           0     0     6  2896     0     0   114
#   club            1766 15870    36     0     1     6    21
#   goblet             3   396     2     0     0     0     2
#   ionocyte           0    45    15     0     8   193    15
#   neuroendocrine     0     1     0     0   619     7     3
#   proliferating     61   194   914     9     0     4   231
#   tuft               0    18     4     0   691    12     9

Structure plot

The structure plot summarizes the topic proportions in each of the 7 subsets:

set.seed(1)
topic_colors <- c("turquoise","darkorange","dodgerblue","gold","peru",
                  "greenyellow","firebrick","olivedrab","royalblue",
                  "forestgreen","gray")
topics <- c(11,1,3,4,5,6,8,10,9,2,7)
rows <- sort(c(sample(which(samples$cluster == "B"),1000),
               sample(which(samples$cluster == "C"),1000),
               sample(which(samples$cluster == "P"),500),
               sample(which(samples$cluster == "Cil"),500),
               sample(which(samples$cluster == "T+N"),500),
               which(samples$cluster == "I"),
               which(samples$cluster == "U")))
p23 <- structure_plot(select(poisson2multinom(fit),loadings = rows),
                      grouping = samples[rows,"cluster"],
                      topics = topics,
                      colors = topic_colors[topics],
                      perplexity = c(70,70,30,50,50,30,70),
                      n = Inf,gap = 30,num_threads = 4,verbose = FALSE)
print(p23)

Version Author Date
56d99a3 Peter Carbonetto 2020-09-22

Based on this structure plot, and from the other results above, we roughly subdivide the pulse-seq data into two subsets: (1) the Cil, T+N and I clusters that give rise to fairly well-separated clusters, and (2) the B, C and P subsets that contain interesting substructure but much less distinct clusters. Therefore, the cluster labels B, C and P are useful as a guide but should be taken with a grain of salt as the boundaries between these clusters are somewhat arbitrary.

The structure plot suggests that there is substantial heterogeneity in the C cluster beyond what can be captured by “hard” clusters. In particular, three topics (\(k = 5, 6, 10\)) are largely unique to the cells in this cluster, and two other topics (\(k = 4, 8\)) primarily contribute to the cells in this cluster, although can be found in small proportions elsewhere.

These topics indeed pick up continuous variation in gene expression among the cells in this cluster:

rows <- which(x == "C")
fit2 <- select(poisson2multinom(fit),loadings = rows)
p24  <- pca_plot(fit2,k = c(5,8,10))
print(p24)

Version Author Date
072ef40 Peter Carbonetto 2020-10-06
310ef96 Peter Carbonetto 2020-09-22
56d99a3 Peter Carbonetto 2020-09-22

And in PCs 3 and 4:

p25 <- pca_plot(fit2,pcs = 3:4,k = c(4,5,6))
print(p25)

Version Author Date
072ef40 Peter Carbonetto 2020-10-06
310ef96 Peter Carbonetto 2020-09-22
56d99a3 Peter Carbonetto 2020-09-22

The B cell also shows a lot of heterogeneity. Topic 1 is of particular interest because of its close connection to expression of the “hillock” gene Krt13:

rows <- which(x == "B")
fit2 <- select(poisson2multinom(fit),loadings = rows)
p26  <- pca_plot(fit2,pcs = 2:3,k = 1) + guides(fill = "none")
p27  <- pca_plot(fit2,pcs = 2:3,fill = log10(counts[rows,"Krt13"])) +
        labs(fill = "log10(count)")
plot_grid(p26,p27,rel_widths = c(4,5))

Version Author Date
072ef40 Peter Carbonetto 2020-10-06
aed0276 Peter Carbonetto 2020-09-27
7d78e71 Peter Carbonetto 2020-09-27
a67196a Peter Carbonetto 2020-09-27
310ef96 Peter Carbonetto 2020-09-22
56d99a3 Peter Carbonetto 2020-09-22

Save results

Save the clustering of the pulse-seq data to an RDS file.

saveRDS(samples,"clustering-pulseseq.rds")

sessionInfo()
# R version 3.6.2 (2019-12-12)
# Platform: x86_64-apple-darwin15.6.0 (64-bit)
# Running under: macOS Catalina 10.15.6
# 
# 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] cowplot_1.0.0      ggplot2_3.3.0      fastTopics_0.3-179 dplyr_0.8.3       
# [5] Matrix_1.2-18     
# 
# loaded via a namespace (and not attached):
#  [1] ggrepel_0.9.0        Rcpp_1.0.5           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_1.4.2          
# [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         hexbin_1.28.0        whisker_0.4         
# [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_4.4.2   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