Getting Started With SEraster

Introduction

SEraster is a rasterization preprocessing framework that aggregates cellular information into spatial pixels to reduce resource requirements for spatial omics data analysis.

SEraster reduces the number of spatial points in spatial omics datasets for downstream analysis through a process of rasterization where single cells’ gene expression or cell-type labels are aggregated into equally sized pixels based on a user-defined resolution. Here, we refer to a particular resolution of rasterization by the side length of the pixel such that finer resolution indicates smaller pixel size and coarser resolution indicates larger pixel size.

More details describing SEraster are available in our paper.

This tutorial walks you through the basic functionalities of SEraster and two examples of downstream analysis that can be performed with the rasterized spatial omics data. Additional vignettes are available on our documentation website.

For downstream analyses, we will be using nnSVG for spatially variable gene (SVG) analysis and CooccurrenceAffinity for cell-type co-enrichment analysis.

References for nnSVG and CooccurrenceAffinity can be found below:

Installation

To install this package using Bioconductor, start R (version “4.4.0”) and enter:

if (!require("BiocManager", quietly = TRUE))
    install.packages("BiocManager")

BiocManager::install("SEraster")

The latest development version can also be installed from GitHub using remotes:

require(remotes)
remotes::install_github('JEFworks-Lab/SEraster')

In addition, SEraster is also compatible with SeuratObject through SeuratWrappers. SeuratWrappers implementation can be installed using remotes:

require(remotes)
remotes::install_github('satijalab/seurat-wrappers@SEraster')

Documentation and tutorial for the SeuratWrappers implementation can be found in the SEraster branch of the SeuratWrappers GitHub repository.

Dataset

In the examples below, we will use the MERFISH mouse preoptic area (mPOA) dataset available in the SEraster package. The dataset is taken from Moffitt, J. et al. (2018), “Molecular, spatial, and functional single-cell profiling of the hypothalamic preoptic region”, Science and formatted as a SpatialExperiment object as shown here.

Please refer to the following documentations to see how you can format your data into a SpatialExperiment object:

Tutorial

Load libraries

library(SEraster)
library(SpatialExperiment)
library(nnSVG)
library(CooccurrenceAffinity)
library(ggplot2)

Load example dataset

data("merfish_mousePOA")

# check the dimension of the genes-by-cells matrix at single-cell resolution
dim(merfish_mousePOA)
#> [1]  155 6509

# check the number of cell-types
length(unique(colData(merfish_mousePOA)$celltype))
#> [1] 16

This MERFISH mPOA dataset contains 6,509 cells and 16 cell-types.

# plot at single-cell resolution
df <- data.frame(spatialCoords(merfish_mousePOA), celltype = colData(merfish_mousePOA)$celltype)

ggplot(df, aes(x = x, y = y, col = celltype)) +
  coord_fixed() +
  geom_point(size = 1.5, stroke = 0) +
  guides(col = guide_legend(override.aes = list(size = 3))) +
  labs(x = "x (μm)",
       y = "y (μm)",
       col = "Cell-types") +
  theme_bw() +
  theme(panel.grid = element_blank())

SEraster basic functionalities

SEraster reduces the number of spatial points in spatial omics datasets for downstream analysis through a process of rasterization where single cells’ gene expression or cell-type labels are aggregated into equally sized square or hexagonal pixels (can be changed using the square argument) based on a user-defined resolution.

Here, we demonstrate the basic functionalities of SEraster.

Rasterize gene expression

For continuous variables such as gene expression or other molecular information (e.g. protein expression if you are using spatial proteomics datasets), SEraster aggregates the observed raw counts or normalized expression values for each molecule within each pixel using means by default (can be changed using the fun argument).

Let’s try rasterizing the gene expression of the MERFISH mouse POA dataset we loaded.

rastGexp <- SEraster::rasterizeGeneExpression(merfish_mousePOA, assay_name="volnorm", resolution = 50)

# check the dimension of the genes-by-cells matrix after rasterizing gene expression
dim(rastGexp)
#> [1]  155 1301

As you can see, SEraster aggregated 6,509 single cells into 1,301 pixels.

# plot total rasterized gene expression
SEraster::plotRaster(rastGexp, name = "Total rasterized gene expression")

# plot a specific gene
SEraster::plotRaster(rastGexp, feature_name = "Esr1", name = "Esr1")

Rasterize gene expression within cell-type

Such rasterization can also be performed in a cell-type-specific manner by restricting to cells of a particular cell-type prior to rasterization. Here, we subset the dataset to Inhibitory cell-type and run SEraster on the subsetted dataset.

# rasterize cell-type specific gene expression by subsetting to cell-type of interest
ct_interest <- "Inhibitory"
spe_subset <- merfish_mousePOA[,merfish_mousePOA$celltype == ct_interest]

# rasterize gene expression
rastGexpSubset <- SEraster::rasterizeGeneExpression(spe_subset, assay_name="volnorm", resolution = 50)
# plot
SEraster::plotRaster(rastGexpSubset, name = paste0("Total rast gexp in ", ct_interest))

SEraster::plotRaster(rastGexpSubset, feature_name = "Esr1", name = paste0("Esr1 in ", ct_interest))

Rasterize cell-type

For categorical variables such as cell-type or cluster labels, SEraster aggregates the number of cells for each label within each pixel using sums by default (can be changed using the fun argument).

Let’s try rasterizing the cell-type labels of the MERFISH mouse POA dataset.

rastCt <- SEraster::rasterizeCellType(merfish_mousePOA, col_name = "celltype", resolution = 50)

# check the dimension of the cell-types-by-cells matrix after rasterizing cell-type labels
dim(rastGexp)
#> [1]  155 1301
# plot total cell counts
SEraster::plotRaster(rastCt, name = "cell counts", option = "inferno")

# plot specific cell-type
SEraster::plotRaster(rastCt, feature_name = "Inhibitory", name = "Inhibitory neuron counts", option = "inferno")

Setting rasterization resolution

Rasterization resolution can be controlled by the resolution argument of the rasterizeGeneExpression and rasterizeCellType functions. Here, we refer to a particular resolution of rasterization by the side length for square pixels and the distance between opposite edges for hexagonal pixels such that finer resolution indicates smaller pixel size and vice versa.

Let’s see how the rasterized MERFISH mouse POA dataset look with various resolutions using square pixels.

resolutions <- c(50, 100, 200)
for (resolution in resolutions) {
  # rasterize at defined resolution
  temp <- SEraster::rasterizeGeneExpression(merfish_mousePOA, assay_name="volnorm", resolution = resolution)
  # plot a specific gene
  plt <- SEraster::plotRaster(temp, feature_name = "Esr1", name = "Esr1", plotTitle = paste0("resolution: ", resolution))
  show(plt)
}

Now, let’s see the same resolutions using hexagonal pixels.

for (resolution in resolutions) {
  # rasterize at defined resolution
  temp <- SEraster::rasterizeGeneExpression(merfish_mousePOA, assay_name="volnorm", resolution = resolution, square = FALSE)
  # plot a specific gene
  plt <- SEraster::plotRaster(temp, feature_name = "Esr1", name = "Esr1", plotTitle = paste0("resolution: ", resolution))
  show(plt)
}

Creating and rasterizing permutations

Since rasterized values may be sensitive to edge effects such as the specific boundaries of grids upon rasterization, SEraster enables permutation by rotating the dataset at various angles before rasterization.

For example, let’s create 3 permutations of the MERFISH mouse POA dataset, which would output a list of 3 SpatialExperiment objects with x,y coordinates rotated at 0, 120, and 240 degrees around the midrange point.

In addition to a single SpatialExperiment object, rasterizeGeneExpression and rasterizeCellType functions can both take a list of SpatialExperiment objects. This essentially allows users to streamline the preprocessing of permutations with SEraster; followed by a downstream analysis of choice. For instance, in our manuscript, we have shown that permutations can be used to improve the performance of SVG analysis.

# permutate
spe_list <- permutateByRotation(merfish_mousePOA, n_perm = 3)

# rasterize permutated datasets at once
out_list <- rasterizeGeneExpression(spe_list, assay_name = "volnorm", resolution = 50)

for (i in seq_along(out_list)) {
  # extract rotated angle
  angle <- gsub("rotated_", "", paste0("rotated ", names(out_list)[[i]], " degrees"))
  # plot a specific gene
  plt <- SEraster::plotRaster(out_list[[i]], feature_name = "Esr1", name = "Esr1", plotTitle = angle)
  show(plt)
}

As you can see from the plots above, when SEraster rasterizes a list of SpatialExperiment objects, all SpatialExperiment objects in the inputted list are rasterized with the same pixel coordinate framework (same bounding box, resolution, centroid coordinates). This feature may not be particularly useful for permutations; however, it can potentially be applied to compare two or more datasets, such as structurally aligned tissues as well as healthy vs. disease tissues.

Examples of downstream analyses after SEraster preprocessing

Spatial variable gene (SVG) analysis

Here, we use a previously developed tool called nnSVG. Please refer to nnSVG for more details about the package. We can directly input rasterized gene expression SpatialExperiment object from SEraster into nnSVG.

# run nnSVG
set.seed(0)
rastGexp <- nnSVG(rastGexp, assay_name = "pixelval")
# number of significant SVGs based on the selected adjusted p-value threshold
table(rowData(rastGexp)$padj <= 0.05)
#> 
#> FALSE  TRUE 
#>    17   138
# plot rasterized gene expression of top-ranked SVG
top_svg <- which(rowData(rastGexp)$rank == 1)
top_svg_name <- rownames(rowData(rastGexp))[top_svg]
SEraster::plotRaster(rastGexp, feature_name = top_svg_name, name = top_svg_name)

We can also perform cell-type specific SVG analysis by subsetting the dataset prior to applying SEraster.

# subset data
ct_interest <- "Excitatory"
spe_sub <- merfish_mousePOA[,merfish_mousePOA$celltype == ct_interest]

# run SEraster
rastGexp_sub <- SEraster::rasterizeGeneExpression(spe_sub, assay_name="volnorm", resolution = 50)

# run nnSVG
set.seed(0)
rastGexp_sub <- nnSVG(rastGexp_sub, assay_name = "pixelval")
# number of significant SVGs
table(rowData(rastGexp_sub)$padj <= 0.05)
#> 
#> FALSE  TRUE 
#>    45   110
# plot rasterized gene expression of top-ranked SVG
top_svg <- which(rowData(rastGexp_sub)$rank == 1)
top_svg_name <- rownames(rowData(rastGexp_sub))[top_svg]
SEraster::plotRaster(rastGexp_sub, feature_name = top_svg_name, name = top_svg_name)

Cell-type co-enrichment analysis

Rasterized cell-type labels can be used to analyze pair-wise cell-type co-enrichment To do so, we binarize the rasterized cell-type labels using a relative enrichment metric and a previously developed tool called CooccurrenceAffinity. Please refer to our paper for more details about the methodology and CooccurrenceAffinity for more details about the package.

# extract cell-type labels
ct_labels <- as.factor(colData(merfish_mousePOA)$celltype)

# compute relative enrichment (RE) metric
mat <- assay(rastCt, "pixelval")
mat_re <- do.call(rbind, lapply(rownames(rastCt), function(ct_label) {
    mat[ct_label,] / (sum(mat[ct_label,]) / sum(mat) * colSums(mat))
}))
rownames(mat_re) <- rownames(mat)

# binarize
mat_bin <- ifelse(mat_re >= 1, 1, 0)

# add RE and binarized layers to SpatialExperiment object
assays(rastCt) <- list(pixelval = assay(rastCt, "pixelval"), re = mat_re, bin = mat_bin)
ct_interest <- "Ependymal"

# plot pixel value for a cell-type of interest
plotRaster(rastCt, assay_name = "pixelval", feature_name = ct_interest, name = "cell-type counts", option = "inferno")

# plot RE value for a cell-type of interest
plotRaster(rastCt, assay_name = "re", feature_name = ct_interest, name = "RE", option = "inferno")

# plot binarized value for a cell-type of interest
plotRaster(rastCt, assay_name = "bin", feature_name = ct_interest, factor_levels = c(0,1), name = "binarized", option = "inferno")

# run CooccurrenceAffinity
ct_coocc <- CooccurrenceAffinity::affinity(data = mat_bin, row.or.col = "row", squarematrix = c("all"))
#> 
#> ------ as expected, the data ready for analysis has only 1 and 0... 1 = present, 0 = absent used for the interpretation ------
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AcceptAffCI(x, marg, lev, Int2): NAs introduced by coercion
#> Warning in AcceptAffCI(x, marg, lev, Int2): NAs introduced by coercion
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = Infty is capped, along with upper confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = Infty is capped, along with upper confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> Warning in AlphInts(x, marg, lev = lev, scal = scal, pvalType = pvalType): MLE = -Infty is capped, along with lower confidence limits
#> ~~~~~~~~~~ printing head of all elements of the output list ~~~~~~~~~~
#> $all
#>    entity_1      entity_2 entity_1_count_mA entity_2_count_mB obs_cooccur_X
#> 1 Ambiguous     Astrocyte               561               557           232
#> 2 Ambiguous Endothelial 1               561               308           136
#> 3 Ambiguous Endothelial 2               561                20             9
#> 4 Ambiguous Endothelial 3               561               102            49
#> 5 Ambiguous     Ependymal               561                47             4
#> 6 Ambiguous    Excitatory               561               504           192
#>   total_N    p_value exp_cooccur alpha_mle  alpha_medianInt conf_level
#> 1    1301     0.3657     240.182    -0.105 [-0.111, -0.098]       0.95
#> 2    1301      0.693     132.812     0.055   [0.047, 0.064]       0.95
#> 3    1301          1       8.624     0.077  [-0.021, 0.181]       0.95
#> 4    1301     0.2998      43.983     0.215   [0.194, 0.237]       0.95
#> 5    1301 2.1435e-07      20.267    -2.150 [-2.252, -1.986]       0.95
#> 6    1301     0.0041     217.328    -0.337  [-0.343, -0.33]       0.95
#>          ci_blaker            ci_cp          ci_midQ         ci_midP jaccard
#> 1  [-0.331, 0.119]  [-0.333, 0.123]  [-0.327, 0.117] [-0.327, 0.117]   0.262
#> 2  [-0.208, 0.313]  [-0.212, 0.321]  [-0.203, 0.312] [-0.203, 0.313]   0.186
#> 3   [-0.894, 1.04]  [-0.934, 1.061]  [-0.823, 0.959]  [-0.846, 0.98]   0.016
#> 4  [-0.201, 0.625]  [-0.212, 0.641]    [-0.19, 0.62] [-0.192, 0.622]   0.080
#> 5  [-3.27, -1.164]   [-3.5, -1.128] [-3.291, -1.223]  [-3.341, -1.2]   0.007
#> 6 [-0.569, -0.104] [-0.571, -0.104]  [-0.565, -0.11] [-0.565, -0.11]   0.220
#>   sorensen simpson errornote
#> 1    0.415   0.417        NA
#> 2    0.313   0.442        NA
#> 3    0.031   0.450        NA
#> 4    0.148   0.480        NA
#> 5    0.013   0.085        NA
#> 6    0.361   0.381        NA
#> 
#> $occur_mat
#>         Ambiguous Astrocyte Endothelial 1 Endothelial 2 Endothelial 3 Ependymal
#> pixel23         1         0             0             0             0         0
#> pixel24         0         0             1             0             0         0
#> pixel25         0         1             0             0             0         0
#> pixel26         0         0             0             0             0         0
#> pixel27         1         0             1             0             0         0
#> pixel28         0         1             0             0             0         0
#>         Excitatory Inhibitory Microglia OD Immature 1 OD Immature 2 OD Mature 1
#> pixel23          0          1         0             0             0           0
#> pixel24          0          1         0             0             0           0
#> pixel25          0          0         0             1             0           0
#> pixel26          1          0         0             0             0           0
#> pixel27          0          0         0             0             0           0
#> pixel28          1          0         0             0             0           0
#>         OD Mature 2 OD Mature 3 OD Mature 4 Pericytes
#> pixel23           0           0           0         0
#> pixel24           0           0           0         0
#> pixel25           0           0           0         0
#> pixel26           0           0           0         0
#> pixel27           0           0           0         0
#> pixel28           0           0           0         0
#> 
#> $alpha_mle
#>               Ambiguous Astrocyte Endothelial 1 Endothelial 2 Endothelial 3
#> Ambiguous            NA        NA            NA            NA            NA
#> Astrocyte        -0.105        NA            NA            NA            NA
#> Endothelial 1     0.055    -0.015            NA            NA            NA
#> Endothelial 2     0.077    -0.118         0.779            NA            NA
#> Endothelial 3     0.215    -0.029         0.322         1.902            NA
#> Ependymal        -2.150    -0.807        -0.143         0.345        -0.667
#>               Ependymal Excitatory Inhibitory Microglia OD Immature 1
#> Ambiguous            NA         NA         NA        NA            NA
#> Astrocyte            NA         NA         NA        NA            NA
#> Endothelial 1        NA         NA         NA        NA            NA
#> Endothelial 2        NA         NA         NA        NA            NA
#> Endothelial 3        NA         NA         NA        NA            NA
#> Ependymal            NA         NA         NA        NA            NA
#>               OD Immature 2 OD Mature 1 OD Mature 2 OD Mature 3 OD Mature 4
#> Ambiguous                NA          NA          NA          NA          NA
#> Astrocyte                NA          NA          NA          NA          NA
#> Endothelial 1            NA          NA          NA          NA          NA
#> Endothelial 2            NA          NA          NA          NA          NA
#> Endothelial 3            NA          NA          NA          NA          NA
#> Ependymal                NA          NA          NA          NA          NA
#>               Pericytes
#> Ambiguous            NA
#> Astrocyte            NA
#> Endothelial 1        NA
#> Endothelial 2        NA
#> Endothelial 3        NA
#> Ependymal            NA
#> 
#> $alpha_mle_sig
#>               Ambiguous Astrocyte Endothelial 1 Endothelial 2 Endothelial 3
#> Ambiguous            NA        NA            NA            NA            NA
#> Astrocyte            NA        NA            NA            NA            NA
#> Endothelial 1        NA        NA            NA            NA            NA
#> Endothelial 2        NA        NA            NA            NA            NA
#> Endothelial 3        NA        NA            NA         1.902            NA
#> Ependymal         -2.15    -0.807            NA            NA            NA
#>               Ependymal Excitatory Inhibitory Microglia OD Immature 1
#> Ambiguous            NA         NA         NA        NA            NA
#> Astrocyte            NA         NA         NA        NA            NA
#> Endothelial 1        NA         NA         NA        NA            NA
#> Endothelial 2        NA         NA         NA        NA            NA
#> Endothelial 3        NA         NA         NA        NA            NA
#> Ependymal            NA         NA         NA        NA            NA
#>               OD Immature 2 OD Mature 1 OD Mature 2 OD Mature 3 OD Mature 4
#> Ambiguous                NA          NA          NA          NA          NA
#> Astrocyte                NA          NA          NA          NA          NA
#> Endothelial 1            NA          NA          NA          NA          NA
#> Endothelial 2            NA          NA          NA          NA          NA
#> Endothelial 3            NA          NA          NA          NA          NA
#> Ependymal                NA          NA          NA          NA          NA
#>               Pericytes
#> Ambiguous            NA
#> Astrocyte            NA
#> Endothelial 1        NA
#> Endothelial 2        NA
#> Endothelial 3        NA
#> Ependymal            NA
#> 
#> $p_value
#>                Ambiguous Astrocyte Endothelial 1 Endothelial 2 Endothelial 3
#> Ambiguous           <NA>      <NA>          <NA>          <NA>            NA
#> Astrocyte         0.3657      <NA>          <NA>          <NA>            NA
#> Endothelial 1      0.693    0.9475          <NA>          <NA>            NA
#> Endothelial 2          1     0.825        0.1079          <NA>            NA
#> Endothelial 3     0.2998    0.9173        0.1813         5e-04            NA
#> Ependymal     2.1435e-07    0.0159        0.7323             1        0.4274
#>               Ependymal Excitatory Inhibitory Microglia OD Immature 1
#> Ambiguous          <NA>       <NA>       <NA>        NA            NA
#> Astrocyte          <NA>       <NA>       <NA>        NA            NA
#> Endothelial 1      <NA>       <NA>       <NA>        NA            NA
#> Endothelial 2      <NA>       <NA>       <NA>        NA            NA
#> Endothelial 3      <NA>       <NA>       <NA>        NA            NA
#> Ependymal          <NA>       <NA>       <NA>        NA            NA
#>               OD Immature 2 OD Mature 1 OD Mature 2 OD Mature 3 OD Mature 4
#> Ambiguous                NA          NA          NA          NA          NA
#> Astrocyte                NA          NA          NA          NA          NA
#> Endothelial 1            NA          NA          NA          NA          NA
#> Endothelial 2            NA          NA          NA          NA          NA
#> Endothelial 3            NA          NA          NA          NA          NA
#> Ependymal                NA          NA          NA          NA          NA
#>               Pericytes
#> Ambiguous            NA
#> Astrocyte            NA
#> Endothelial 1        NA
#> Endothelial 2        NA
#> Endothelial 3        NA
#> Ependymal            NA
#> 
#> $cooccur.null
#>               Ambiguous Astrocyte Endothelial 1 Endothelial 2 Endothelial 3
#> Ambiguous            NA        NA            NA            NA            NA
#> Astrocyte       240.182        NA            NA            NA            NA
#> Endothelial 1   132.812   131.865            NA            NA            NA
#> Endothelial 2     8.624     8.563         4.735            NA            NA
#> Endothelial 3    43.983    43.669        24.148         1.568            NA
#> Ependymal        20.267    20.122        11.127         0.723         3.685
#>               Ependymal Excitatory Inhibitory Microglia OD Immature 1
#> Ambiguous            NA         NA         NA        NA            NA
#> Astrocyte            NA         NA         NA        NA            NA
#> Endothelial 1        NA         NA         NA        NA            NA
#> Endothelial 2        NA         NA         NA        NA            NA
#> Endothelial 3        NA         NA         NA        NA            NA
#> Ependymal            NA         NA         NA        NA            NA
#>               OD Immature 2 OD Mature 1 OD Mature 2 OD Mature 3 OD Mature 4
#> Ambiguous                NA          NA          NA          NA          NA
#> Astrocyte                NA          NA          NA          NA          NA
#> Endothelial 1            NA          NA          NA          NA          NA
#> Endothelial 2            NA          NA          NA          NA          NA
#> Endothelial 3            NA          NA          NA          NA          NA
#> Ependymal                NA          NA          NA          NA          NA
#>               Pericytes
#> Ambiguous            NA
#> Astrocyte            NA
#> Endothelial 1        NA
#> Endothelial 2        NA
#> Endothelial 3        NA
#> Ependymal            NA
#> 
#> $cooccur.obs
#>               Ambiguous Astrocyte Endothelial 1 Endothelial 2 Endothelial 3
#> Ambiguous            NA        NA            NA            NA            NA
#> Astrocyte           232        NA            NA            NA            NA
#> Endothelial 1       136       131            NA            NA            NA
#> Endothelial 2         9         8             8            NA            NA
#> Endothelial 3        49        43            30             7            NA
#> Ependymal             4        12            10             1             2
#>               Ependymal Excitatory Inhibitory Microglia OD Immature 1
#> Ambiguous            NA         NA         NA        NA            NA
#> Astrocyte            NA         NA         NA        NA            NA
#> Endothelial 1        NA         NA         NA        NA            NA
#> Endothelial 2        NA         NA         NA        NA            NA
#> Endothelial 3        NA         NA         NA        NA            NA
#> Ependymal            NA         NA         NA        NA            NA
#>               OD Immature 2 OD Mature 1 OD Mature 2 OD Mature 3 OD Mature 4
#> Ambiguous                NA          NA          NA          NA          NA
#> Astrocyte                NA          NA          NA          NA          NA
#> Endothelial 1            NA          NA          NA          NA          NA
#> Endothelial 2            NA          NA          NA          NA          NA
#> Endothelial 3            NA          NA          NA          NA          NA
#> Ependymal                NA          NA          NA          NA          NA
#>               Pericytes
#> Ambiguous            NA
#> Astrocyte            NA
#> Endothelial 1        NA
#> Endothelial 2        NA
#> Endothelial 3        NA
#> Ependymal            NA
#> 
#> $jaccard
#>               Ambiguous Astrocyte Endothelial 1 Endothelial 2 Endothelial 3
#> Ambiguous            NA        NA            NA            NA            NA
#> Astrocyte         0.262        NA            NA            NA            NA
#> Endothelial 1     0.186     0.178            NA            NA            NA
#> Endothelial 2     0.016     0.014         0.025            NA            NA
#> Endothelial 3     0.080     0.070         0.079         0.061            NA
#> Ependymal         0.007     0.020         0.029         0.015         0.014
#>               Ependymal Excitatory Inhibitory Microglia OD Immature 1
#> Ambiguous            NA         NA         NA        NA            NA
#> Astrocyte            NA         NA         NA        NA            NA
#> Endothelial 1        NA         NA         NA        NA            NA
#> Endothelial 2        NA         NA         NA        NA            NA
#> Endothelial 3        NA         NA         NA        NA            NA
#> Ependymal            NA         NA         NA        NA            NA
#>               OD Immature 2 OD Mature 1 OD Mature 2 OD Mature 3 OD Mature 4
#> Ambiguous                NA          NA          NA          NA          NA
#> Astrocyte                NA          NA          NA          NA          NA
#> Endothelial 1            NA          NA          NA          NA          NA
#> Endothelial 2            NA          NA          NA          NA          NA
#> Endothelial 3            NA          NA          NA          NA          NA
#> Ependymal                NA          NA          NA          NA          NA
#>               Pericytes
#> Ambiguous            NA
#> Astrocyte            NA
#> Endothelial 1        NA
#> Endothelial 2        NA
#> Endothelial 3        NA
#> Ependymal            NA
#> 
#> $jaccard_sig
#>               Ambiguous Astrocyte Endothelial 1 Endothelial 2 Endothelial 3
#> Ambiguous            NA        NA            NA            NA            NA
#> Astrocyte            NA        NA            NA            NA            NA
#> Endothelial 1        NA        NA            NA            NA            NA
#> Endothelial 2        NA        NA            NA            NA            NA
#> Endothelial 3        NA        NA            NA         0.061            NA
#> Ependymal         0.007      0.02            NA            NA            NA
#>               Ependymal Excitatory Inhibitory Microglia OD Immature 1
#> Ambiguous            NA         NA         NA        NA            NA
#> Astrocyte            NA         NA         NA        NA            NA
#> Endothelial 1        NA         NA         NA        NA            NA
#> Endothelial 2        NA         NA         NA        NA            NA
#> Endothelial 3        NA         NA         NA        NA            NA
#> Ependymal            NA         NA         NA        NA            NA
#>               OD Immature 2 OD Mature 1 OD Mature 2 OD Mature 3 OD Mature 4
#> Ambiguous                NA          NA          NA          NA          NA
#> Astrocyte                NA          NA          NA          NA          NA
#> Endothelial 1            NA          NA          NA          NA          NA
#> Endothelial 2            NA          NA          NA          NA          NA
#> Endothelial 3            NA          NA          NA          NA          NA
#> Ependymal                NA          NA          NA          NA          NA
#>               Pericytes
#> Ambiguous            NA
#> Astrocyte            NA
#> Endothelial 1        NA
#> Endothelial 2        NA
#> Endothelial 3        NA
#> Ependymal            NA
#> 
#> $sorensen
#>               Ambiguous Astrocyte Endothelial 1 Endothelial 2 Endothelial 3
#> Ambiguous            NA        NA            NA            NA            NA
#> Astrocyte         0.415        NA            NA            NA            NA
#> Endothelial 1     0.313     0.303            NA            NA            NA
#> Endothelial 2     0.031     0.028         0.049            NA            NA
#> Endothelial 3     0.148     0.131         0.146         0.115            NA
#> Ependymal         0.013     0.040         0.056         0.030         0.027
#>               Ependymal Excitatory Inhibitory Microglia OD Immature 1
#> Ambiguous            NA         NA         NA        NA            NA
#> Astrocyte            NA         NA         NA        NA            NA
#> Endothelial 1        NA         NA         NA        NA            NA
#> Endothelial 2        NA         NA         NA        NA            NA
#> Endothelial 3        NA         NA         NA        NA            NA
#> Ependymal            NA         NA         NA        NA            NA
#>               OD Immature 2 OD Mature 1 OD Mature 2 OD Mature 3 OD Mature 4
#> Ambiguous                NA          NA          NA          NA          NA
#> Astrocyte                NA          NA          NA          NA          NA
#> Endothelial 1            NA          NA          NA          NA          NA
#> Endothelial 2            NA          NA          NA          NA          NA
#> Endothelial 3            NA          NA          NA          NA          NA
#> Ependymal                NA          NA          NA          NA          NA
#>               Pericytes
#> Ambiguous            NA
#> Astrocyte            NA
#> Endothelial 1        NA
#> Endothelial 2        NA
#> Endothelial 3        NA
#> Ependymal            NA
#> 
#> $sorensen_sig
#>               Ambiguous Astrocyte Endothelial 1 Endothelial 2 Endothelial 3
#> Ambiguous            NA        NA            NA            NA            NA
#> Astrocyte            NA        NA            NA            NA            NA
#> Endothelial 1        NA        NA            NA            NA            NA
#> Endothelial 2        NA        NA            NA            NA            NA
#> Endothelial 3        NA        NA            NA         0.115            NA
#> Ependymal         0.013      0.04            NA            NA            NA
#>               Ependymal Excitatory Inhibitory Microglia OD Immature 1
#> Ambiguous            NA         NA         NA        NA            NA
#> Astrocyte            NA         NA         NA        NA            NA
#> Endothelial 1        NA         NA         NA        NA            NA
#> Endothelial 2        NA         NA         NA        NA            NA
#> Endothelial 3        NA         NA         NA        NA            NA
#> Ependymal            NA         NA         NA        NA            NA
#>               OD Immature 2 OD Mature 1 OD Mature 2 OD Mature 3 OD Mature 4
#> Ambiguous                NA          NA          NA          NA          NA
#> Astrocyte                NA          NA          NA          NA          NA
#> Endothelial 1            NA          NA          NA          NA          NA
#> Endothelial 2            NA          NA          NA          NA          NA
#> Endothelial 3            NA          NA          NA          NA          NA
#> Ependymal                NA          NA          NA          NA          NA
#>               Pericytes
#> Ambiguous            NA
#> Astrocyte            NA
#> Endothelial 1        NA
#> Endothelial 2        NA
#> Endothelial 3        NA
#> Ependymal            NA
#> 
#> $simpson
#>               Ambiguous Astrocyte Endothelial 1 Endothelial 2 Endothelial 3
#> Ambiguous            NA        NA            NA            NA            NA
#> Astrocyte         0.417        NA            NA            NA            NA
#> Endothelial 1     0.442     0.425            NA            NA            NA
#> Endothelial 2     0.450     0.400         0.400            NA            NA
#> Endothelial 3     0.480     0.422         0.294          0.35            NA
#> Ependymal         0.085     0.255         0.213          0.05         0.043
#>               Ependymal Excitatory Inhibitory Microglia OD Immature 1
#> Ambiguous            NA         NA         NA        NA            NA
#> Astrocyte            NA         NA         NA        NA            NA
#> Endothelial 1        NA         NA         NA        NA            NA
#> Endothelial 2        NA         NA         NA        NA            NA
#> Endothelial 3        NA         NA         NA        NA            NA
#> Ependymal            NA         NA         NA        NA            NA
#>               OD Immature 2 OD Mature 1 OD Mature 2 OD Mature 3 OD Mature 4
#> Ambiguous                NA          NA          NA          NA          NA
#> Astrocyte                NA          NA          NA          NA          NA
#> Endothelial 1            NA          NA          NA          NA          NA
#> Endothelial 2            NA          NA          NA          NA          NA
#> Endothelial 3            NA          NA          NA          NA          NA
#> Ependymal                NA          NA          NA          NA          NA
#>               Pericytes
#> Ambiguous            NA
#> Astrocyte            NA
#> Endothelial 1        NA
#> Endothelial 2        NA
#> Endothelial 3        NA
#> Ependymal            NA
#> 
#> $simpson_sig
#>               Ambiguous Astrocyte Endothelial 1 Endothelial 2 Endothelial 3
#> Ambiguous            NA        NA            NA            NA            NA
#> Astrocyte            NA        NA            NA            NA            NA
#> Endothelial 1        NA        NA            NA            NA            NA
#> Endothelial 2        NA        NA            NA            NA            NA
#> Endothelial 3        NA        NA            NA          0.35            NA
#> Ependymal         0.085     0.255            NA            NA            NA
#>               Ependymal Excitatory Inhibitory Microglia OD Immature 1
#> Ambiguous            NA         NA         NA        NA            NA
#> Astrocyte            NA         NA         NA        NA            NA
#> Endothelial 1        NA         NA         NA        NA            NA
#> Endothelial 2        NA         NA         NA        NA            NA
#> Endothelial 3        NA         NA         NA        NA            NA
#> Ependymal            NA         NA         NA        NA            NA
#>               OD Immature 2 OD Mature 1 OD Mature 2 OD Mature 3 OD Mature 4
#> Ambiguous                NA          NA          NA          NA          NA
#> Astrocyte                NA          NA          NA          NA          NA
#> Endothelial 1            NA          NA          NA          NA          NA
#> Endothelial 2            NA          NA          NA          NA          NA
#> Endothelial 3            NA          NA          NA          NA          NA
#> Ependymal                NA          NA          NA          NA          NA
#>               Pericytes
#> Ambiguous            NA
#> Astrocyte            NA
#> Endothelial 1        NA
#> Endothelial 2        NA
#> Endothelial 3        NA
#> Ependymal            NA
#> ~~~~~~~~~~ COMPLETED: printing head of all elements of the output list ~~~~~~~~~~

# plot maximum likelihood estimates of affinity metric (alpha MLE)
CooccurrenceAffinity::plotgg(data = ct_coocc, variable = "alpha_mle", legendlimit = "datarange")
#> you can hide the printed values with show.value=F
#> use the argument value.digit to change number of digits and text.size to adjust the text size

Session Information

sessionInfo()
#> R Under development (unstable) (2025-03-13 r87965)
#> Platform: x86_64-pc-linux-gnu
#> Running under: Ubuntu 24.04.2 LTS
#> 
#> Matrix products: default
#> BLAS:   /home/biocbuild/bbs-3.21-bioc/R/lib/libRblas.so 
#> LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.12.0  LAPACK version 3.12.0
#> 
#> locale:
#>  [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
#>  [3] LC_TIME=en_GB              LC_COLLATE=C              
#>  [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
#>  [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                 
#>  [9] LC_ADDRESS=C               LC_TELEPHONE=C            
#> [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       
#> 
#> time zone: America/New_York
#> tzcode source: system (glibc)
#> 
#> attached base packages:
#> [1] stats4    stats     graphics  grDevices utils     datasets  methods  
#> [8] base     
#> 
#> other attached packages:
#>  [1] ggplot2_3.5.1               CooccurrenceAffinity_1.0   
#>  [3] BiasedUrn_2.0.12            nnSVG_1.11.4               
#>  [5] SpatialExperiment_1.17.0    SingleCellExperiment_1.29.2
#>  [7] SummarizedExperiment_1.37.0 Biobase_2.67.0             
#>  [9] GenomicRanges_1.59.1        GenomeInfoDb_1.43.4        
#> [11] IRanges_2.41.3              S4Vectors_0.45.4           
#> [13] BiocGenerics_0.53.6         generics_0.1.3             
#> [15] MatrixGenerics_1.19.1       matrixStats_1.5.0          
#> [17] SEraster_0.99.5            
#> 
#> loaded via a namespace (and not attached):
#>  [1] tidyselect_1.2.1        viridisLite_0.4.2       dplyr_1.1.4            
#>  [4] farver_2.1.2            BRISC_1.0.6             fastmap_1.2.0          
#>  [7] reshape_0.8.9           RANN_2.6.2              digest_0.6.37          
#> [10] lifecycle_1.0.4         sf_1.0-20               magrittr_2.0.3         
#> [13] compiler_4.6.0          rlang_1.1.5             sass_0.4.9             
#> [16] tools_4.6.0             yaml_2.3.10             knitr_1.50             
#> [19] S4Arrays_1.7.3          labeling_0.4.3          classInt_0.4-11        
#> [22] DelayedArray_0.33.6     plyr_1.8.9              rdist_0.0.5            
#> [25] abind_1.4-8             BiocParallel_1.41.5     KernSmooth_2.23-26     
#> [28] withr_3.0.2             purrr_1.0.4             grid_4.6.0             
#> [31] e1071_1.7-16            colorspace_2.1-1        scales_1.3.0           
#> [34] cli_3.6.4               rmarkdown_2.29          crayon_1.5.3           
#> [37] httr_1.4.7              rearrr_0.3.5            rjson_0.2.23           
#> [40] DBI_1.2.3               pbapply_1.7-2           cachem_1.1.0           
#> [43] proxy_0.4-27            parallel_4.6.0          XVector_0.47.2         
#> [46] vctrs_0.6.5             Matrix_1.7-3            jsonlite_2.0.0         
#> [49] magick_2.8.6            jquerylib_0.1.4         units_0.8-7            
#> [52] glue_1.8.0              codetools_0.2-20        cowplot_1.1.3          
#> [55] gtable_0.3.6            UCSC.utils_1.3.1        munsell_0.5.1          
#> [58] tibble_3.2.1            pillar_1.10.2           htmltools_0.5.8.1      
#> [61] GenomeInfoDbData_1.2.14 R6_2.6.1                evaluate_1.0.3         
#> [64] lattice_0.22-7          backports_1.5.0         bslib_0.9.0            
#> [67] class_7.3-23            Rcpp_1.0.14             SparseArray_1.7.7      
#> [70] checkmate_2.3.2         xfun_0.52               pkgconfig_2.0.3