- 1 Background
- 2 Data
- 3 Data processing
- 4 scBubbletree workflow
- 4.1 1. determine the clustering resolution
- 4.2 2. clustering
- 4.3 3. hierarchical grouping
- 4.4 4. visualization
- 4.5 Attaching categorical features
- 4.6 Gini impurity index
- 4.7 Attaching numeric features
- 4.8 Quality control with
*scBubbletree* - 4.9 scBubbletree can incorporate results from other clustering approaches
- 4.10 Summary
- 4.11 Session Info

Over the last decade, we have seen exponential growth of the scale of scRNA-seq datasets to millions of cells sequenced in a single study. This has enabled researchers to characterize the gene expression profiles of various cell types across tissues. The rapid growth of scRNA-seq data has also created an unique set of challenges, for instance, there is a pressing need for scalable approaches for scRNA-seq data visualization.

This vignette introduces *scBubbletree*, a transparent workflow
for quantitative exploration of single cell RNA-seq data.

In short, the algorithm of *scBubbletree* performs clustering
to identify clusters (bubbles) of transcriptionally similar cells, and then
visualizes these clusters as leafs in a hierarchical dendrogram (bubbletree)
which describes their natural relationships. The workflow comprises four
steps: 1. determining the clustering resolution, 2. clustering, 3. hierarchical
cluster grouping and 4. visualization. We explain each step in the following
using real scRNA-seq dataset of five cancer cell lines.

To run this vignette we need to load a few R-packages:

```
library(scBubbletree)
library(ggplot2)
library(ggtree)
library(patchwork)
```

Here we will analyze a scRNA-seq dataset containing a mixture of 3,918 cells from five human lung adenocarcinoma cell lines (HCC827, H1975, A549, H838 and H2228). The dataset is available here2 https://github.com/LuyiTian/sc_mixology/blob/master/data/ sincell_with_class_5cl.RData.

The library has been prepared with 10x Chromium platform and sequenced with Illumina NextSeq 500 platform. Raw data has been processed with Cellranger. The tool demuxlet has been used to predict the identity of each cell based on known genetic differences between the different cell lines.

Data processing was performed with R-package *Seurat*. Gene
expressions were normalized with the function *SCTransform*
using default parameters, and principal component analysis (PCA) was performed
with function *RunPCA* based on the 5,000 most variable genes in the dataset
identified with the function *FindVariableFeatures*.

In both datasets we saw that the first 15 principal components capture most of the variance in the data, and the proportion of variance explained by each subsequent principal component was negligible. Thus, we used the single cell projections (embeddings) in 15-dimensional feature space, \(A^{3,918\times 15}\).

```
# # This script can be used to generate data("d_ccl", package = "scBubbletree")
#
# # create directory
# dir.create(path = "case_study/")
#
# # download the data from:
# https://github.com/LuyiTian/sc_mixology/raw/master/data/
# sincell_with_class_5cl.RData
#
# # load the data
# load(file = "case_study/sincell_with_class_5cl.RData")
#
# # we are only interested in the 10x data object 'sce_sc_10x_5cl_qc'
# d <- sce_sc_10x_5cl_qc
#
# # remove the remaining objects (cleanup)
# rm(sc_Celseq2_5cl_p1, sc_Celseq2_5cl_p2, sc_Celseq2_5cl_p3, sce_sc_10x_5cl_qc)
#
# # get the meta data for each cell
# meta <- colData(d)[,c("cell_line_demuxlet","non_mt_percent","total_features")]
#
# # create Seurat object from the raw counts and append the meta data to it
# d <- Seurat::CreateSeuratObject(counts = d@assays$data$counts,
# project = '')
#
# # check if all cells are matched between d and meta
# # table(rownames(d@meta.data) == meta@rownames)
# d@meta.data <- cbind(d@meta.data, meta@listData)
#
# # cell type predictions are provided as part of the meta data
# table(d@meta.data$cell_line)
#
# # select 5,000 most variable genes
# d <- Seurat::FindVariableFeatures(object = d,
# selection.method = "vst",
# nfeatures = 5000)
#
# # Preprocessing with Seurat: SCT transformation + PCA
# d <- SCTransform(object = d,
# variable.features.n = 5000)
# d <- RunPCA(object = d,
# npcs = 50,
# features = VariableFeatures(object = d))
#
# # perform UMAP + t-SNE
# d <- RunUMAP(d, dims = 1:15)
# d <- RunTSNE(d, dims = 1:15)
#
# # save the preprocessed data
# save(d, file = "case_study/d.RData")
#
# # save the PCA matrix 'A', meta data 'm' and
# # marker genes matrix 'e'
# d <- get(load(file ="case_study/d.RData"))
# A <- d@reductions$pca@cell.embeddings[, 1:15]
# m <- d@meta.data
# e <- t(as.matrix(d@assays$SCT@data[
# rownames(d@assays$SCT@data) %in%
# c("ALDH1A1",
# "PIP4K2C",
# "SLPI",
# "CT45A2",
# "CD74"), ]))
#
# d_ccl <- list(A = A, m = m, e = e)
# save(d_ccl, file = "data/d_ccl.RData")
```

Load the processed PCA matrix and the meta data

```
data("d_ccl", package = "scBubbletree")
A <- d_ccl$A
m <- d_ccl$m
e <- d_ccl$e
```

We will analyze this data with *scBubbletree*.

As first input *scBubbletree* uses matrix \(A^{n\times f}\) which
represents a low-dimensional projection of the original scRNA-seq data, with
\(n\) rows as cells and \(f\) columns as low-dimension features.

We will use the PCA data generated by *Seurat* as \(A\). In
particular, we will use the first 15 principal components (PCs) as every
additional PC explains negligible amount of variance in the data.

**Important remark about \(A\)**: the *scBubbletree* workflow
works directly with the numeric matrix \(A^{n\times f}\) and is agnostic to
the initial data processing protocol. This enables seamless integration
of *scBubbletree* with computational pipelines using objects
generated by the R-packages *Seurat* and
*SingleCellExperiment*. The users simply have to extract \(A\)
from the corresponding *Seurat* or
*SingleCellExperiment* objects.

```
# A has n=cells as rows, f=features as columns (e.g. from PCA)
dim(A)
```

`FALSE [1] 3918 15`

The *scBubbletree* workflow performs the following steps:

- determine the clustering resolution (clusters \(k\) or resolution \(r\))
- graph-based community detection (e.g. with Louvain) or k-means clustering
- hierarchical organization of clusters (bubbles)
- visualization

If we use graph-based community detection (**recommended for scRNA-seq**) with
e.g. the Louvain or Leiden method, then we need to find appropriate value for
the resolution parameter \(r\). Otherwise, we can use the simpler k-means
clustering algorithm in which case we need to find an appropriate value of the
number of clusters \(k\).

How many clusters (cell types) are there are in the data? Can we guess a reasonable value of \(k\)?

To find a reasonable value of \(k\) we can study the literature or databases such
as the human protein atlas database (HPA). We can also use the function `get_k`

for data-driven inference of \(k\) based on the Gap statistic and the within-
cluster sum of squares (WCSS).

As this is a toy dataset, we will skip the first approach and perform a
data-driven search for \(k\) using `get_k`

. As input we need to provide the
matrix \(A\) as input and a vector of \(k\)s. The output will be the Gap
statistic and WCSS estimates for each \(k\).

Lets run `get_k`

now:

```
b_k <- get_k(B_gap = 5,
ks = 1:10,
x = A,
n_start = 50,
iter_max = 200,
kmeans_algorithm = "MacQueen",
cores = 1)
```

The Gap statistic and WCSS curves have a noticeable knee (elbow) at \(k=5\).
Hence, \(k\)=5 appears to be reasonable first choice of \(k\). Means (points) and
95% confidence intervals are shown for the Gap statistic at each \(k\) computed
using `B_gap`

=5 MCMC simulations.

```
g0 <- ggplot(data = b_k$gap_stats_summary)+
geom_line(aes(x = k, y = gap_mean))+
geom_point(aes(x = k, y = gap_mean), size = 1)+
geom_errorbar(aes(x = k, y = gap_mean, ymin = L95, ymax = H95), width = 0.1)+
ylab(label = "Gap")|
ggplot(data = b_k$wcss_stats_summary)+
geom_line(aes(x = k, y = wcss_mean))+
geom_point(aes(x = k, y = wcss_mean), size = 1)+
ylab(label = "WCSS")+
scale_y_log10()+
annotation_logticks(base = 10, sides = "l")
```

`g0`

For Louvain clustering we need to select a clustering resolution \(r\). Higher resolutions lead to more communities and lower resolutions lead to fewer communities. We can use the same strategy as before to find a reasonable reasonable value of \(r\).

Lets use the function `get_r`

for data-driven estimation of \(r\) based on
the Gap statistic and WCSS. As input we need to provide the matrix \(A\) and
a vector of \(r\)s. The output will be the Gap statistic and WCSS estimate
for each \(r\) (or the number of communities \(k'\) detected at resolution \(r\)).

```
b_r <- get_r(B_gap = 5,
rs = 10^seq(from = -4, to = 0, by = 0.35),
x = A,
n_start = 10,
iter_max = 50,
algorithm = "original",
knn_k = 50,
cores = 1)
```

The Gap statistic and WCSS curves have noticeable knees (elbows) at \(k'=5\)
(\(r=0.0025\)). Means (points) and 95% confidence intervals are shown for the
Gap statistic at each \(k\) computed using `B_gap`

=5 MCMC simulations.

```
g0_r <- (ggplot(data = b_r$gap_stats_summary)+
geom_line(aes(x = k, y = gap_mean))+
geom_point(aes(x = k, y = gap_mean), size = 1)+
geom_errorbar(aes(x = k, y = gap_mean, ymin = L95, ymax = H95), width = 0.1)+
ylab(label = "Gap")+
xlab(label = "k'")|
ggplot(data = b_r$gap_stats_summary)+
geom_line(aes(x = r, y = gap_mean))+
geom_point(aes(x = r, y = gap_mean), size = 1)+
geom_errorbar(aes(x = r, y = gap_mean, ymin = L95, ymax = H95), width = 0.1)+
ylab(label = "Gap")+
xlab(label = "r")+
scale_x_log10()+
annotation_logticks(base = 10, sides = "b"))/
(ggplot(data = b_r$wcss_stats_summary)+
geom_line(aes(x = k, y = wcss_mean))+
geom_point(aes(x = k, y = wcss_mean), size = 1)+
ylab(label = "WCSS")+
xlab(label = "k'")|
ggplot(data = b_r$wcss_stats_summary)+
geom_line(aes(x = r, y = wcss_mean))+
geom_point(aes(x = r, y = wcss_mean), size = 1)+
ylab(label = "WCSS")+
xlab(label = "r")+
scale_x_log10()+
annotation_logticks(base = 10, sides = "b"))
```

`g0_r`

A range of resolutions yields \(k=5\) number of communities, i.e. \(r = 0.0025\) and \(r = 0.125\) result in \(k=5\). Lets use \(r=0.1\) for clustering

```
ggplot(data = b_r$gap_stats_summary)+
geom_point(aes(x = r, y = k), size = 1)+
xlab(label = "r")+
ylab(label = "k'")+
scale_x_log10()+
annotation_logticks(base = 10, sides = "b")
```

```
knitr::kable(x = b_r$gap_stats_summary[b_r$gap_stats_summary$k == 5, ],
digits = 4, row.names = FALSE)
```

gap_mean | r | k | gap_SE | L95 | H95 |
---|---|---|---|---|---|

2.1634 | 0.0025 | 5 | 0.0060 | 2.1517 | 2.1751 |

2.1660 | 0.0056 | 5 | 0.0036 | 2.1590 | 2.1730 |

2.1640 | 0.0126 | 5 | 0.0041 | 2.1560 | 2.1720 |

2.1674 | 0.0282 | 5 | 0.0059 | 2.1559 | 2.1789 |

2.1603 | 0.0631 | 5 | 0.0063 | 2.1479 | 2.1726 |

Now that we found out that \(k=5\) is a reasonable choice based on the data,
we will perform k-means clustering with \(k=5\) and \(A\) as inputs. For this
we will use the function kmeans (R-package stats) which offers various
variants of k-means. Here we will use MacQueen’s k-means variant and
perform \(n_\textit{start} = 1000\) (default in *scBubbletree*)
random starts and a maximum number of iterations \(iter_\textit{max}=300\).

**Important remark**: for smaller datasets (e.g. \(n<50,000\)) \(n_{start}=1000\)
and \(n_{iter} = 300\) are unnecessarily high, however for larger datasets this
is necessary to make sure that k-means converges.

After the clustering is complete we will organize the bubbles in a natural hierarchy. For this we perform \(B\) bootstrap iterations (default \(B=200\)). In iteration \(b\) the algorithm draws a random subset of \(N_\textit{eff}\) (default \(N_\textit{eff}=200\)) cells with replacement from each cluster and computes the average inter-cluster Euclidean distances. This data is used to populate the distance matrix (\(D^{k\times k}_b\)), which is provided as input for hierarchical clustering with average linkage to generate a hierarchical clustering dendrogram \(H_b\).

The collection of distance matrices that are computed during \(B\) iterations are used to compute a consensus (average) distance matrix (\(\hat{D}^{k\times k}\)) and from this a corresponding consensus hierarchical dendrogram (bubbletree; \(\hat{H}\)) is constructed. The collection of dendrograms are used to quantify the robustness of the bubbletree topology, i.e. to count the number of times each branch in the bubbletree is found among the topologies of the bootstrap dendrograms. Branches can have has variable degrees of support ranging between 0 (no support) and \(B\) (complete support). Distances between bubbles (inter- bubble relationships) are described quantitatively in the bubbletree as sums of branch lengths.

Steps 2.1 and 3. are performed next

```
k5_kmeans <- get_bubbletree_kmeans(
x = A,
k = 5,
cores = 1,
B = 200,
N_eff = 200,
round_digits = 1,
show_simple_count = FALSE,
kmeans_algorithm = "MacQueen")
```

… and plot the bubbletree

`k5_kmeans$tree`

Lets describe the bubbletree:

**bubbles**: The bubbletree has `k=5`

bubbles (clusters) shown as leaves. The
absolute and relative cell frequencies in each bubble and the bubble IDs are
shown as labels. Bubble radii scale linearly with absolute cell count in each
bubble, i.e. large bubbles have many cells and small bubbles contain few cells.

Bubble 1 is the largest one in the dendrogram and contains 1,253 cells (\(\approx\) 32% of all cells in the dataset). Bubble 4 is the smallest one and contains only 436 cells (\(\approx\) 11% of all cells in the dataset).

We can access the bubble data shown in the bubbletree

```
knitr::kable(k5_kmeans$tree_meta,
digits = 2, row.names = FALSE)
```

label | Cells | n | p | pct | lab_short | lab_long | tree_order |
---|---|---|---|---|---|---|---|

4 | 436 | 3918 | 0.11 | 11.1 | 4 (0.4K, 11.1%) | 4 (436, 11.1%) | 5 |

1 | 593 | 3918 | 0.15 | 15.1 | 1 (0.6K, 15.1%) | 1 (593, 15.1%) | 4 |

3 | 1253 | 3918 | 0.32 | 32.0 | 3 (1.3K, 32%) | 3 (1253, 32%) | 3 |

2 | 760 | 3918 | 0.19 | 19.4 | 2 (0.8K, 19.4%) | 2 (760, 19.4%) | 2 |

5 | 876 | 3918 | 0.22 | 22.4 | 5 (0.9K, 22.4%) | 5 (876, 22.4%) | 1 |

**topology**: inter-bubble distances are represented by sums of branch
lengths in the dendrogram. Branches of the bubbletree are annotated with
their bootstrap support values (red branch labels). The branch support
value tells us how manytimes a given branch from the bubbletree was found
among the \(B\) bootstrap dendrograms. We ran `get_bubbletree_kmeans`

with
\(B=200\). All but one branch have complete (200 out of 200) support, and
one branch has lower support of 179 (85%). This tells us that the branch
between bubbles (3, 4) and 1 is not as robust.

Lets also perform clustering with the Louvain algorithm (function FindClusters,
R-package *Seurat*) and resolution parameter \(r=0.1\). There are
numerous variants of the Louvain algorithm. Here we will use the original
implementation. We will do clustering with \(n_\textit{start} = 20\) random
starts and a maximum number of iterations \(iter_\textit{max} = 100\).

Steps 2.2 and 3. (hierarchical clustering) are performed next

```
k5_louvain <- get_bubbletree_graph(x = A,
r = 0.0025,
n_start = 20,
iter_max = 100,
algorithm = "original",
knn_k = 50,
cores = 1,
B = 200,
N_eff = 200,
round_digits = 1,
show_simple_count = FALSE)
```

… and plot the bubbletree. We see nearly identical dendrogram as the one generated by kmeans clustering. The bubble IDs are different but we see similar bubble sizes, topology and branch robustness values.

`k5_louvain$tree`

The two dendrograms shown side-by-side:

`k5_kmeans$tree|k5_louvain$tree`

Given the high degree of similarity between the two clustering solutions we proceed in the next with the k-means results.

To extract biologically useful information from the bubbletree (and also for
2D UMAP or t-SNE plots) we need to adorn it with biologically relevant cell
features. This includes both **numeric** and **categorical** cell features.

Numeric cell features:

- gene expression
- % of mitochondrial transcripts
- number of UMIs, genes detected
- …

Categorical cell features:

- cell type label (e.g. B-cells, T-cells, moncytes, …)
- cell cycle phase (e.g. S, M, G1, …)
- sample name (e.g. S1, S2, S3, …)
- treatment group (e.g. cancer vs. control cell)
- multiplet status (e.g. singlet, doublet or multiplet)
- …

In the next two paragraph we will explain how to ‘attach’ numeric and
categorical features to the bubbletree using *scBubbletree*.

Categorical cell features can be ‘attached’ to the bubbletree using the function
`get_cat_tiles`

. Here we will show the relative frequency of cell type labels
across the bubbles (parameter `integrate_vertical=TRUE`

).

Interpretation of the figure below:

- we see high degree of co-occurrence between cell lines and bubbles, i.e. each bubble is made up of cells from a distinct cell line
- for instance, 99.8% of cells that have feature HCC827 are found in bubble 2
- columns in the tile plot integrate to 100%

```
w1 <- get_cat_tiles(btd = k5_kmeans,
f = m$cell_line_demuxlet,
integrate_vertical = TRUE,
round_digits = 1,
x_axis_name = 'Cell line',
rotate_x_axis_labels = TRUE,
tile_text_size = 2.75)
(k5_kmeans$tree|w1$plot)+
patchwork::plot_layout(widths = c(1, 1))
```

We can also show the inter-bubble cell type composition, i.e. the relative
frequencies of different cell types in a specific bubble (with parameter
`integrate_vertical=FALSE`

).

Interpretation of the figure below:

- the bubbles appear to be “pure” \(\rightarrow\) made up of cells from distinct cell lines
- the cell line composition of bubble 2 is: 0.1% H838, 99.9% H2228, 0.1% A549, 0.1% H1975 and 0% HCC827 cells
- rows integrate to 100%

```
w2 <- get_cat_tiles(btd = k5_kmeans,
f = m$cell_line_demuxlet,
integrate_vertical = FALSE,
round_digits = 1,
x_axis_name = 'Cell line',
rotate_x_axis_labels = TRUE,
tile_text_size = 2.75)
(k5_kmeans$tree|w2$plot)+
patchwork::plot_layout(widths = c(1, 1))
```

*scBubbletree* uses R-package *ggtree* to
visualize the bubbletree, and *ggplot2* to visualize
annotations. Furthermore, R-package *patchwork* is used to
combine plots.

```
(k5_kmeans$tree|w1$plot|w2$plot)+
patchwork::plot_layout(widths = c(1, 2, 2))+
patchwork::plot_annotation(tag_levels = "A")
```