Skip to contents

Introduction

Spatial transcriptomics allows the spatial profiling of complex tissue architectures. The spatial arrangement and interactions between cells can aid in understanding of complex functions and regulatory mechanisms in various tissue micro environments. Commercially available image-based spatial technologies such as Xenium, CosMX, and MERSCOPSE take advantage of fluorescence-based microscopy to quantify transcripts and focus on a pre-designed panel of genes.

One crucial step in the analysis of spatial transcriptomics data is cell type annotation. There are a number of ways to perform cell type annotation, and marker analysis is one of them. Marker gene analysis to identify genes highly expressed in each cluster compared to the remaining clusters. The identified marker genes are used to annotate clusters with cell types. Computationally tools originally developed for single cell data are used for spatial transcriptomics studies. However, those methods ignore the spatial information for the cells and gene. There is limited literature on developing marker gene detection methods that account for the spatial distribution of gene expression. jazzPanda provides two novel approaches to detect marker genes with transformed spatial information. Our first approach is based on correlation and the second linear modelling approach can account for technical noise and work for studies with multiple samples.

jazzPanda framework

We assume a marker gene will show a significant linear relationship with the target cluster over the tissue space. This suggests that the transcript detection of a marker gene will show similar patterns with the cells from the cluster over tissue space. Given the cluster label of every cell, there are two steps to obtain marker genes for every cluster. We first compute spatial vectors from the spatial coordinates of the genes and the clusters. After that, we can measure the linear relationship between the genes and clusters based on spatial vectors. We develop two approaches for detecting genes that show strong linear relationship with the cluster.

  • Step 1: Create spatial vectors for every gene and every cluster
    get_vectors() can be used to convert the transcript detection and the cell centroids to spatial vectors. You can specify the tile shape and length based on you dataset. The hex bins will generally take longer than the square/rectangle bins to compute. In practice, we find that we can choose the length tiles such that the average cell per tile (# cells per cluster# tiles\frac{\texttt{\#}\text{ cells per cluster} }{\texttt{\#}\text{ tiles}}) is close to one for each cluster.

  • Step 2: Detect marker genes

    • Correlation approach: compute_permp() This approach can detect marker genes for one sample study. We calculate a correlation coefficient between every pair of gene and cluster vector. We perform permutation testing to assess the statistical significance of the calculated correlation and followed by multiple testing adjustment to control the false discovery rate. We keep the genes with significant adjusted p-value and large correlation as marker genes. In practice, we recommend to calculate a correlation threshold value for every cluster based on the data distribution. During our analysis, we use 75% quantile value of all correlations to the given cluster as the cutoff and manage to keep meaningful marker genes.

    • Linear modelling approach: lasso_markers() In this approach, we treat the gene vector as the response variable and the cluster vectors as the explanatory variables. We select the important cluster vectors by lasso regularization first, and fit a linear model to find the cluster that show minimum p-value and largest model coefficient. This approach can account for multi-sample studies and the technical background noise (such as the non-specific binding). We recommend to set a model coefficient cutoff value based on your data. A large cutoff value will result in fewer marker genes whereas a small cutoff value will detect more marker genes. We find a cutoff value at 0.1 or 0.2 work well for our analysis. Marker genes with less than 0.1 model coefficient are generally weak markers.
      Two tables will be returned from this approach:

      1. We record the most significant cluster for each gene as lasso_top_result. This table provides unique marker genes for every cluster. Genes whose top cluster shows a model coefficient smaller than the specified cutoff value will not be labeled as marker genes.

      2. We record all the significant cluster for each gene as lasso_full_result. This table can be used to investigate shared marker genes for different clusters.

Example

The dataset used in this vignette is a selected subset from two replicates of Xenium human breast cancer tissue Sample 1. We select 20 genes for package illustration. This subset was extracted from the raw dataset as described in the R script located at /inst/generate_vignette_data.R.

This subset data is used for package illustration purpose only. The resulting marker genes may not be strong markers for annotating clusters. Please see the full analysis for this dataset for marker genes.

# ggplot style
defined_theme = theme(strip.text = element_text(size = rel(1)),
                        strip.background = element_rect(fill = NA, 
                                                    colour = "black"),
                        axis.line=element_blank(),
                        axis.text.x=element_blank(),
                        axis.text.y=element_blank(),
                        axis.ticks=element_blank(),
                        axis.title.x=element_blank(),
                        axis.title.y=element_blank(),
                        legend.position="none",
                        panel.background=element_blank(),
                        panel.border=element_blank(),
                        panel.grid.major=element_blank(),
                        panel.grid.minor=element_blank(),
                        plot.background=element_blank())

Load data

data(rep1_sub, rep1_clusters, rep1_neg)
rep1_clusters$cluster=factor(rep1_clusters$cluster,
                            levels=paste("c",1:8, sep=""))
# record all real genes in the data
all_real_genes = unique(as.character(rep1_sub$feature_name))
all_celltypes = unique(rep1_clusters[,c("anno","cluster")])
# nc_patterns = "^BLANK_|^NegControlProbe_|^NegControlCodeword_|^antisense_"
# nc_targets = grep(pattern =nc_patterns , x = all_genes,value = TRUE)

The required input data structure for the main function lasso_markers() is a list of matrices. We will illustrate how to simply create the required input data from the raw output of different technologies in the following examples: If you have a Seurat object, you can build the required object as follows. The defined example_vectors_cm/example_vectors_tr can be passed to lasso_markers to identify marker genes.

From a SpatialExperiment object

If you have a SpatialExperiment or SpatialFeatureExperiment object, you can generate the required input for creating the spatial vectors by calling convert_data function. If the transcript coordinates are available, you can use either transcript coordinates or the count matrix to define spatial vectors for genes. The defined example_vectors_cm/example_vectors_tr can be passed to lasso_markers to identify marker genes.

library(SpatialFeatureExperiment)
library(SingleCellExperiment)
library(TENxXeniumData)
library(ExperimentHub)
eh <- ExperimentHub()
q <- query(eh, "TENxXenium")
spe_example <- q[["EH8547"]]

# get the required input list 
example_lst <- convert_data(x=spe_example, sample_names = "sample01")

# -----------------------------------------------------------------------------
# Example clustering 
# get the count matrix 
cm <- spe_example@assays@data$counts
all_genes = row.names(cm)
example_seu <- CreateSeuratObject(counts = cm, 
                            min.cells = 2, min.features = 1)
example_seu <- NormalizeData(example_seu, 
                            normalization.method = "LogNormalize")
all.genes <- rownames(example_seu)
example_seu <- ScaleData(example_seu, features = all.genes)
example_seu <- RunPCA(example_seu, features = all.genes)
ElbowPlot(example_seu)
example_seu <- FindNeighbors(example_seu, dims = 1:15)
example_seu <- FindClusters(example_seu, resolution = 0.1)
seu_clusters <- as.data.frame(example_seu$seurat_clusters,nm="cluster")
seu_clusters$cell_id <- colnames(example_seu)

# -----------------------------------------------------------------------------
# combine cluster labels and the coordinates 
# make sure the cluster information contains column names: 
# cluster, x, y, sample and cell_id
clusters_info <- as.data.frame(spe_example@int_colData$spatialCoords)
colnames(clusters_info) <- c("x","y")
clusters_info$cell_id <- row.names(clusters_info)
clusters_info$sample <- spe_example$sample_id
clusters_info <- merge(clusters_info, seu_clusters, by="cell_id")

w_x <- c(floor(min(clusters_info$x,
                    example_lst$trans_lst$sample01$x)),
        ceiling(max(clusters_info$x, 
                    example_lst$trans_lst$sample01$x)))
w_y <- c(floor(min(clusters_info$y, 
                    example_lst$trans_lst$sample01$y)),
        ceiling(max(clusters_info$y, 
                    example_lst$trans_lst$sample01$y)))

# -----------------------------------------------------------------------------
# build spatial vectors from count matrix and cluster coordinates 
example_vectors_cm <- get_vectors(trans_lst= NULL,
                                cm_lst=example_lst$cm_lst,
                                cluster_info = clusters_info,
                                bin_type="square",
                                bin_param=c(10,10), 
                                all_genes = all_genes,
                                w_x=w_x, w_y=w_y)


# -----------------------------------------------------------------------------
# build spatial vectors from transcript coordinates and cluster coordinates 
example_vectors_tr <- get_vectors(trans_lst= example_lst$trans_lst,
                                cluster_info = clusters_info,
                                bin_type="square",
                                bin_param=c(10,10), 
                                all_genes = all_genes,
                                w_x=w_x, w_y=w_y)

From a SpatialFeatureExperiment object

sfe_example <- toSpatialFeatureExperiment(spe_example)
example_sfe_lst <- convert_data(x=sfe_example,sample_names = "sample01")
# -----------------------------------------------------------------------------
# build spatial vectors from count matrix and cluster coordinates 
# make sure the cluster information contains column names: 
# cluster, x, y, sample and cell_id
example_vectors_cm <- get_vectors(trans_lst= NULL,
                                cm_lst=example_sfe_lst$cm_lst,
                                cluster_info = clusters_info,
                                bin_type="square",
                                bin_param=c(10,10), 
                                all_genes = all_genes,
                                w_x=w_x, w_y=w_y)

# -----------------------------------------------------------------------------
# build spatial vectors from transcript coordinates and cluster coordinates 
example_vectors_tr <- get_vectors(trans_lst= example_sfe_lst$trans_lst,
                                cluster_info = clusters_info,
                                bin_type="square",
                                bin_param=c(10,10), 
                                all_genes = all_genes,
                                w_x=w_x, w_y=w_y)

From a SingleCellExperiment object

sce_example <- SingleCellExperiment(list(sample01 = cm))
example_sce_lst <- convert_data(x=sce_example,sample_names = "sample01")
# -----------------------------------------------------------------------------
# build spatial vectors from count matrix and cluster coordinates 
# make sure the cluster information contains column names: 
# cluster, x, y, sample and cell_id
example_vectors_cm <- get_vectors(trans_lst= NULL,
                                cm_lst=example_sce_lst$cm_lst,
                                cluster_info = clusters_info,
                                bin_type="square",
                                bin_param=c(10,10), 
                                all_genes = all_genes,
                                w_x=w_x, w_y=w_y)

From a Seurat object

# cm is the count matrix
seu_obj =Seurat::CreateSeuratObject(counts = cm)
# make sure the clusters information contains column names: 
# cluster, x, y and sample
clusters_info = rep1_clusters
# make sure the transcript information contains column names: 
# feature_name, x, y
transcript_coords = rep1_sub$trans_info
data_example = list(cm=seu_obj@assays$RNA$counts,
                    trans_info =transcript_coords)

w_x =  c(min(floor(min(data$x)), floor(min(clusters_info$x))), 
        max(ceiling(max(data$x)), ceiling(max(clusters_info$x))))
w_y =  c(min(floor(min(data$y)), floor(min(clusters_info$y))), 
        max(ceiling(max(data$y)), ceiling(max(clusters_info$y))))

# build spatial vectors from transcript coordinates and cluster coordinates 
example_vectors_tr = get_vectors(trans_lst= list("rep1"=transcript_coords),
                                cluster_info = clusters_info,
                                bin_type="square",
                                bin_param=c(10,10), 
                                all_genes = row.names(cm), 
                                w_x=w_x, w_y=w_y)
# -----------------------------------------------------------------------------
# build spatial vectors from count matrix and cluster coordinates 
# make sure the cluster information contains column names: 
# cluster, x, y, sample and cell_id
colnames(clusters_info)[5] = "cell_id"
example_vectors_cm = get_vectors(trans_lst= NULL,
                                cm_lst=list(rep1=seu_obj@assays$RNA$counts),
                                cluster_info = clusters_info,
                                bin_type="square",
                                bin_param=c(10,10), 
                                all_genes = row.names(cm), 
                                w_x=w_x, w_y=w_y)

From direct platform output

10x Xenium data

The constructed xenium_data can be used in function get_vectors(). The defined nc_lst can be used in functioncreate_genesets().

path <- 'path/to/data/directory'
mtx_name="cell_feature_matrix"
trans_name="transcripts.csv.gz"

transcript_info <- as.data.frame(fread(paste(path, trans_name,sep="")))
transcript_info$x <- as.numeric(transcript_info$x_location)
transcript_info$y <- as.numeric(transcript_info$y_location)
data <- Read10X(data.dir = paste(path,mtx_name, sep=""))
# count matrix 
cm <- as.matrix(data$`Gene Expression`)

# negative control targets
r_codeword <- as.matrix(data$`Negative Control Codeword`)
r_probe <- as.matrix(data$`Negative Control Probe`)

xenium_data = list("sample1" = transcript_info )

# -----------------------------------------------------------------------------
# cell label and coordinates 
clusters_info <-  read.csv("./cells_meta.csv")
# the cluster label, sample label and coordinates for each cell 
cl_req_cols <- c("x","y","cluster","sample")
clusters_df <- clusters_info[,cl_req_cols]

# -----------------------------------------------------------------------------
# define negative control objects if available, need to repeat for each sample
# load coordinates for each detection, must contain following columns 
# - "x": x coordinate
# - "y": y coordinate 
# - "target": negative control names 
# - "sample": sample label 
probe_target <- row.names(r_probe)
codeword <- row.names(r_codeword)

nc_coords = read.csv("./negative_controls_detections.csv")
nc_names = unique(nc_coords$feature_name)
kpt_cols = c("x","y","feature_name","sample")
transcript_neg = transcript_info[transcript_info$feature_name %in% 
                                c(probe_target, codeword_target),
                                c("x_location","y_location","feature_name")]
colnames(transcript_neg)[1:3]= c("x","y","feature_name")
transcript_neg$sample = "sample1"
nc_lst = list("sample1" = transcript_neg)
MERSCOPE data

The constructed merscope_data can be used in function get_vectors(). The defined nc_lst can be used in functioncreate_genesets().

# count matrix
# rows as genes and columns as cells
# gene name as row names 
data_p = "path/to/merscope/output/data/"
cm = qread("./counts.qs")
# cell label and coordinates 
clusters_info =  read.csv("./cells_meta.csv")

# -----------------------------------------------------------------------------
# if transcript coordinates are available, need to repeat for each sample
# load transcript data, transcripts must contain follwing columns 
# - "x": x coordinate
# - "y": y coordinate 
# - "feature_name": gene name 
tr_req_cols = c("x", "y", "feature_name")
transcript_df =  read.csv("./transcripts.csv")
merscope_data = list("sample1" = transcript_df[,req_cols])
# the defined merscope_data can be used in function get_vectors() 

# the cluster label, sample label and coordinates for each cell 
cl_req_cols = c("x","y","cluster","sample")
clusters_df = clusters_info[,cl_req_cols]

# -----------------------------------------------------------------------------
# define negative control objects if available, need to repeat for each sample
# load coordinates for each detection, must contain following columns 
# - "x": x coordinate
# - "y": y coordinate 
# - "target": negative control names 
# - "sample": sample label 
nc_coords = read.csv("./negative_controls_detections.csv")
nc_names = unique(nc_coords$feature_name)
kpt_cols = c("x","y","feature_name","sample")
nc_lst = list("sample1"= nc_coords[,kpt_cols])
CosMx data

The constructed cosmx_data can be used in function get_vectors(). The defined nc_lst can be used in functioncreate_genesets().

tiledbURI <- "file/path/to/TileDB/array/on/local/machine"

# read in SOMACollection
tiledb_scdataset <- tiledbsc::SOMACollection$new(uri = tiledbURI, 
                                                verbose = FALSE)
cm <- tiledb_scdataset$somas$RNA$X$members$counts$to_matrix(batch_mode = TRUE)

# the cluster label, sample label and coordinates for each cell 
clusters_info <- tiledb_scdataset$somas$RNA$obs$to_dataframe()

# -----------------------------------------------------------------------------
# if transcript coordinates are available, need to repeat for each sample
# load transcript data, transcripts must contain follwing columns 
# - "x": x coordinate
# - "y": y coordinate 
# - "feature_name": gene name 
req_cols = c("x","y","feature_name")
cosmx_data = list("sample1"= transcript_df[,c(req_cols)])
# 

# clusters and cell locations 
cl_req_cols = c("x","y","cluster","sample")
clusters_df = clusters_info[,cl_req_cols]

# -----------------------------------------------------------------------------
# if available
# define negative control objects if available
# need to repeat for each background category and each sample
# load coordinates for each detection, must contain following columns 
# - "x": x coordinate
# - "y": y coordinate 
# - "target": negative control names 
# - "sample": sample label 
nc_coords = read.csv("./negative_controls_detections.csv")
nc_names = unique(nc_coords$feature_name)
kpt_cols = c("x","y","feature_name","sample")
nc_lst = list("sample1"=nc_coords[,kpt_cols])

Visualise the clusters over the tissue space

We can plot the cells coordinates for each cluster of Replicate 1 subset

p1<-ggplot(data = rep1_clusters,
        aes(x = x, y = y, color=cluster))+
        geom_point(position=position_jitterdodge(jitter.width=0,
                                        jitter.height=0), size=0.1)+
        scale_y_reverse()+
        theme_classic()+
        facet_wrap(~sample)+
        scale_color_manual(values = c("#FC8D62","#66C2A5" ,"#8DA0CB","#E78AC3",
                        "#A6D854","skyblue","purple3","#E5C498"))+
        guides(color=guide_legend(title="cluster", nrow = 2,
                        override.aes=list(alpha=1, size=2)))+
        
        theme(axis.text.x=element_blank(),
                axis.text.y=element_blank(),
                axis.ticks=element_blank(),
                axis.title.x=element_blank(),
                axis.title.y=element_blank(),
                panel.spacing = unit(0.5, "lines"),
                legend.position="none",
                strip.text = element_text(size = rel(1)))+
        xlab("")+
        ylab("")
p2<-ggplot(data = rep1_clusters,
        aes(x = x, y = y, color=cluster))+
        geom_point(position=position_jitterdodge(jitter.width=0, 
                                    jitter.height=0), size=0.1)+
        facet_wrap(~cluster, nrow = 2)+
        scale_y_reverse()+
        theme_classic()+
        scale_color_manual(values = c("#FC8D62","#66C2A5" ,"#8DA0CB","#E78AC3",
                        "#A6D854","skyblue","purple3","#E5C498"))+
        guides(color=guide_legend(title="cluster", nrow = 1,
        override.aes=list(alpha=1, size=4)))+
        theme(axis.text.x=element_blank(),
            axis.text.y=element_blank(),
            axis.ticks=element_blank(),
            axis.title.x=element_blank(),
            axis.title.y=element_blank(),
            panel.spacing = unit(0.5, "lines"), 
            legend.text = element_text(size=10),
            legend.position="none",
            legend.title = element_text(size=10),
            strip.text = element_text(size = rel(1)))+
        xlab("")+
        ylab("")

spacer <- patchwork::plot_spacer()
layout_design <- (p1 / spacer) | p2

layout_design <- layout_design + 
                    patchwork::plot_layout(widths = c(1, 4), heights = c(1, 1)) 

print(layout_design)

Spatial vectors

We can visualize the spatial vectors for clusters and genes as follows. As an example for creating spatial vectors for genes, we plot the transcript detections for the gene EPCAM over tissue space, along with the square and hex binning result. Similarly, we plot the cell coordinates in cluster c1, as well as the square and hex bin values over the space as an example. We can see that with the square and hex bins capture the key patterns of the original coordinates. Hex bins can capture more details than square bins.

Example of gene vectors

w_x =  c(min(floor(min(rep1_sub$x)),
        floor(min(rep1_clusters$x))), 
        max(ceiling(max(rep1_sub$x)),
        ceiling(max(rep1_clusters$x))))
w_y =  c(min(floor(min(rep1_sub$y)),
        floor(min(rep1_clusters$y))), 
        max(ceiling(max(rep1_sub$y)),
        ceiling(max(rep1_clusters$y))))

# plot transcript detection coordinates
selected_genes = rep1_sub$feature_name == "EPCAM"
loc_mt = as.data.frame(rep1_sub[selected_genes,
                        c("x","y","feature_name")]%>%distinct())
colnames(loc_mt)=c("x","y","feature_name")
layout(matrix(c(1, 2, 3), 1, 3, byrow = TRUE))
par(mar=c(5,3,6,3))
plot(loc_mt$x, loc_mt$y, main = "", xlab = "", ylab = "", 
        pch = 20, col = "maroon4", cex = 0.1,xaxt='n', yaxt='n')   
title(main = "EPCAM transcript detection", line = 3)
box() 

# plot square binning 
curr<-loc_mt[loc_mt[,"feature_name"]=="EPCAM",c("x","y")] %>% distinct()
curr_ppp <- ppp(curr$x,curr$y,w_x, w_y)
vec_quadrat <- quadratcount(curr_ppp, 10,10)
vec_its <- intensity(vec_quadrat, image=TRUE)
par(mar=c(0.01,1, 1, 2))
plot(vec_its, main = "")
title(main = "square binning", line = -2)

# plot hex binning 
w <- owin(xrange=w_x, yrange=w_y)
H <- hextess(W=w, 20)
bin_length <- length(H$tiles)
curr<-loc_mt[loc_mt[,"feature_name"]=="EPCAM",c("x","y")] %>% distinct()
curr_ppp <- ppp(curr$x,curr$y,w_x, w_y)
vec_quadrat <- quadratcount(curr_ppp, tess=H)
vec_its <- intensity(vec_quadrat, image=TRUE)
par(mar=c(0.1,1, 1, 2))
plot(vec_its, main = "")
title(main = "hex binning", line = -2)

Example of cluster vectors

w_x =  c(min(floor(min(rep1_sub$x)),
            floor(min(rep1_clusters$x))), 
        max(ceiling(max(rep1_sub$x)),
            ceiling(max(rep1_clusters$x))))
w_y =  c(min(floor(min(rep1_sub$y)),
            floor(min(rep1_clusters$y))), 
        max(ceiling(max(rep1_sub$y)),
            ceiling(max(rep1_clusters$y))))

# plot cell coordinates
loc_mt = as.data.frame(rep1_clusters[rep1_clusters$cluster=="c1",
            c("x","y","cluster")])
colnames(loc_mt)=c("x","y","cluster")
layout(matrix(c(1, 2, 3), 1, 3, byrow = TRUE))
par(mar=c(5,3,6,3))
plot(loc_mt$x, loc_mt$y, main = "", xlab = "", ylab = "", 
        pch = 20, col = "maroon4", cex = 0.1,xaxt='n', yaxt='n')   
title(main = "cell coordinates in cluster c1", line = 3)
box() 

# plot square binning 
curr<-loc_mt[loc_mt[,"cluster"]=="c1", c("x","y")]%>%distinct()
curr_ppp <- ppp(curr$x,curr$y,w_x, w_y)
vec_quadrat <- quadratcount(curr_ppp, 10,10)
vec_its <- intensity(vec_quadrat, image=TRUE)
par(mar=c(0.1,1, 1, 2))
plot(vec_its, main = "")
title(main = "square binning", line = -2)

# plot hex binning 
w <- owin(xrange=w_x, yrange=w_y)
H <- hextess(W=w, 20)
bin_length <- length(H$tiles)
curr<-loc_mt[loc_mt[,"cluster"]=="c1",c("x","y")] %>%distinct()
curr_ppp <- ppp(curr$x,curr$y,w_x, w_y)
vec_quadrat <- quadratcount(curr_ppp, tess=H)
vec_its <- intensity(vec_quadrat, image=TRUE)
par(mar=c(0.1,1, 1, 2))
plot(vec_its, main = "")
title(main = "hex binning", line = -2)

The function get_vectors() can be used to create spatial vectors for all the genes and clusters. These spatial vectors may take the form of squares, rectangles, or hexagons specified by the bin_type parameter.

Spatial vectors for all genes and clusters

seed_number= 589

w_x =  c(min(floor(min(rep1_sub$x)),
            floor(min(rep1_clusters$x))), 
        max(ceiling(max(rep1_sub$x)),
            ceiling(max(rep1_clusters$x))))
w_y =  c(min(floor(min(rep1_sub$y)),
            floor(min(rep1_clusters$y))), 
        max(ceiling(max(rep1_sub$y)),
            ceiling(max(rep1_clusters$y))))

grid_length = 10
# get spatial vectors
rep1_sq10_vectors = get_vectors(trans_lst= list(rep1_sub),
                                cluster_info = rep1_clusters,
                                bin_type="square",
                                bin_param=c(grid_length,grid_length), 
                                all_genes = all_real_genes , 
                                w_x=w_x, w_y=w_y)

The constructed spatial vectors can be used to quantify cluster-cluster and gene-gene correlation.

Cluster-Cluster correlation
exp_ord = paste("c", 1:8, sep="")
rep1_sq10_vectors$cluster_mt = rep1_sq10_vectors$cluster_mt[,exp_ord]
cor_cluster_mt = cor(rep1_sq10_vectors$cluster_mt,
                rep1_sq10_vectors$cluster_mt, method = "pearson")
# Calculate pairwise correlations
cor_gene_mt = cor(rep1_sq10_vectors$gene_mt, rep1_sq10_vectors$gene_mt,
                    method = "pearson")

col <- grDevices::colorRampPalette(c("#4477AA", "#77AADD", 
                                    "#FFFFFF","#EE9988", "#BB4444"))

corrplot::corrplot(cor_cluster_mt, method="color", col=col(200), diag=TRUE,
                addCoef.col = "black",type="upper",
                tl.col="black", tl.srt=45, mar=c(0,0,5,0),sig.level = 0.05, 
                insig = "blank", 
                title = "cluster-cluster correlation (square bin = 40x40)"
                )

Gene-Cluster correlation
cor_genecluster_mt = cor(x=rep1_sq10_vectors$gene_mt, 
                        y=rep1_sq10_vectors$cluster_mt, method = "pearson")

gg_correlation = as.data.frame(cbind(apply(cor_gene_mt, MARGIN=1, 
                                            FUN = mean, na.rm=TRUE),
                                        apply(cor_genecluster_mt, MARGIN=1, 
                                            FUN = mean, na.rm=TRUE)))
colnames(gg_correlation) = c("mean_correlation","mean_cluster")  
gg_correlation$gene=row.names(gg_correlation)

plot(ggplot(data = gg_correlation, 
    aes(x= mean_correlation, y=mean_cluster))+
        geom_point()+
        geom_text_repel(aes(label=gg_correlation$gene), size=1.8, hjust=1)+
    theme_bw()+
    theme(legend.title=element_blank(),
            axis.text.y = element_text(size=20),
            axis.text.x = element_text(size=20),
            axis.title.x=element_text(size=20),
            axis.title.y=element_text(size=20), 
            panel.spacing = unit(0.5, "lines"), 
            legend.position="none",
            legend.text=element_blank())+
    xlab("Average gene-gene correlation")+
    ylab("Average gene-cluster correlation"))

We can also construct a gene network based on the spatial vector for the genes.

Gene network
vector_graph= igraph::graph_from_adjacency_matrix(cor_gene_mt,
                                                mode = "undirected", 
                                                weighted = TRUE, 
                                                diag = FALSE)

vector_graph=igraph::simplify(igraph::delete_edges(vector_graph, 
                        E(vector_graph)[abs(E(vector_graph)$weight) <= 0.7]))

layout=igraph::layout_with_kk(vector_graph)

# Plot the graph
ggraph::ggraph(vector_graph, layout = layout) +
    geom_edge_link(aes(edge_alpha = weight), show.legend = FALSE) +
    geom_node_point(color = "lightblue", size = 5) +
    geom_node_text(aes(label = name), 
                    vjust = 1, hjust = 1,size=2,color="orange", repel = TRUE) 

Linear relationship between markers and clusters

We assume that the relationship between a marker gene vector its cluster spatial vector is linear.

Here are several genes and their annotation from the panel.

Gene Annotation
ERBB2 Breast cancer cells
IL7R T cells
MZB1 B cells
AQP1 Endothelial
LUM Fibroblasts
genes_lst = c("ERBB2","AQP1","LUM","IL7R","MZB1")

for (i_cluster in c("c1","c8","c3","c6","c7")){
    cluster_vector=rep1_sq10_vectors$cluster_mt[,i_cluster]
    
    data_vis=as.data.frame(cbind("cluster", cluster_vector,
                            rep1_sq10_vectors$gene_mt[, genes_lst]))
    
    colnames(data_vis)=c("cluster","cluster_vector",genes_lst)
    data_vis=reshape2::melt(data_vis,variable.name = "genes",
                            value.name = "gene_vector",
                            id= c("cluster","cluster_vector" ))
    data_vis$cluster_vector=as.numeric(data_vis$cluster_vector)
    data_vis$genes=factor(data_vis$genes)
    data_vis$gene_vector=as.numeric(data_vis$gene_vector)
    
    plot(ggplot(data = data_vis, 
            aes(x= cluster_vector, y=gene_vector))+
            geom_point(size=0.1)+
            facet_wrap(~genes,scales = "free_y", ncol=10)+
            theme_bw()+
            theme(legend.title=element_blank(),
                axis.text.y = element_text(size=6),
                axis.text.x = element_text(size=6,angle=0),
                axis.title.x=element_text(size=10),
                axis.title.y=element_text(size=10), 
                panel.spacing = unit(0.5, "lines"), 
                legend.position="none",
                legend.text=element_blank(),
                strip.text = element_text(size = rel(1)))+
                xlab(paste(i_cluster," - cluster vector", sep=""))+
                ylab("gene vector"))
}

Scenario 1: one sample

A straightforward approach to identifying genes that exhibit a linear correlation with cluster vectors involves computing the Pearson correlation for each gene with every cluster. To assess the statistical significance of these correlations, the compute_permp() function can be used to perform permutation testing, generating a p-value for every pair of gene cluster and cluster vector.

Correlation-based method to detect marker genes

w_x =  c(min(floor(min(rep1_sub$x)),
            floor(min(rep1_clusters$x))), 
        max(ceiling(max(rep1_sub$x)),
            ceiling(max(rep1_clusters$x))))
w_y =  c(min(floor(min(rep1_sub$y)),
            floor(min(rep1_clusters$y))), 
        max(ceiling(max(rep1_sub$y)),
            ceiling(max(rep1_clusters$y))))
set.seed(seed_number)
perm_p = compute_permp(data=list(rep1_sub),
                        cluster_info=rep1_clusters, 
                        perm.size=1000,
                        bin_type="square",
                        bin_param=c(10,10),
                        all_genes= all_real_genes,
                        correlation_method = "pearson", 
                        n.cores=1, 
                        correction_method="BH",
                        w_x=w_x ,
                        w_y=w_y)

# observed correlation for every pair of gene and cluster vector
obs_corr = as.data.frame(perm_p$obs.stat)
head(obs_corr)
##                c5          c8         c3         c2          c1         c4
## LUM   -0.08301696  0.13734641  0.8724430 -0.4389799 -0.46034377  0.1823640
## CD68  -0.26037887  0.06259766  0.2360819 -0.4126090 -0.02885842  0.5951329
## ERBB2  0.08159437 -0.34437593 -0.5542681  0.6259111  0.69027586 -0.3613350
## MZB1  -0.13221192  0.11731624  0.1781597 -0.1148358 -0.25954267  0.4160637
## EPCAM -0.11473423 -0.35287011 -0.5724549  0.3454557  0.86438353 -0.3496045
## PTPRC -0.15420177  0.23596298  0.2773785 -0.2801968 -0.37755016  0.8048566
##               c6         c7
## LUM    0.2118598  0.1531026
## CD68   0.2343318  0.1504930
## ERBB2 -0.4587071 -0.4455121
## MZB1   0.5952111  0.8168198
## EPCAM -0.4591613 -0.4444322
## PTPRC  0.9455237  0.7628466
# permutation adjusted p-value for every pair of gene and cluster vector
perm_res = as.data.frame(perm_p$perm.pval.adj)
head(perm_res)
##       c5         c8          c3         c2          c1          c4          c6
## LUM    1 0.04329004 0.006660007 1.00000000 1.000000000 0.004995005 0.003996004
## CD68   1 0.72261072 0.167832168 1.00000000 1.000000000 0.003330003 0.061476985
## ERBB2  1 1.00000000 1.000000000 0.00999001 0.003996004 1.000000000 1.000000000
## MZB1   1 0.78492936 0.773073081 1.00000000 1.000000000 0.007992008 0.002497502
## EPCAM  1 1.00000000 1.000000000 0.09990010 0.003996004 1.000000000 1.000000000
## PTPRC  1 0.61338661 0.773073081 1.00000000 1.000000000 0.003330003 0.002497502
##                c7
## LUM   0.054945055
## CD68  0.267005722
## ERBB2 1.000000000
## MZB1  0.002854289
## EPCAM 1.000000000
## PTPRC 0.002854289
Visualise top marker genes detected by correlation approach

Genes with a significant adjusted p-value are considered as marker genes for the corresponding cluster. We can rank the marker genes by the observed correlationand plot the transcript detection coordinates for the top three marker genes for every cluster.

res_df_1000=as.data.frame(perm_p$perm.pval.adj)
res_df_1000$gene=row.names(res_df_1000)
cluster_names = unique(as.character(rep1_clusters$cluster))
for (cl in cluster_names){
    perm_sig = res_df_1000[res_df_1000[,cl]<0.05,]
    # define a cutoff value based on 75% quantile 
    obs_cutoff = quantile(obs_corr[, cl], 0.75)
    perm_cl=intersect(row.names(perm_res[perm_res[,cl]<0.05,]),
                        row.names(obs_corr[obs_corr[, cl]>obs_cutoff,]))
    inters=perm_cl
    rounded_val=signif(as.numeric(obs_corr[inters,cl]), digits = 3)
    inters_df = as.data.frame(cbind(gene=inters, value=rounded_val))
    inters_df$value = as.numeric(inters_df$value)
    inters_df=inters_df[order(inters_df$value, decreasing = TRUE),]
    inters_df = inters_df[1:min(nrow(inters_df),2),]
    inters_df$text= paste(inters_df$gene,inters_df$value,sep=": ")
    curr_genes = rep1_sub$feature_name %in% inters_df$gene
    data_vis =rep1_sub[curr_genes, c("x","y","feature_name")]
    data_vis$text = inters_df[match(data_vis$feature_name,inters_df$gene),
                                "text"]
    data_vis$text = factor(data_vis$text, levels=inters_df$text)
    p1<-ggplot(data = data_vis,
                aes(x = x, y = y))+
                geom_point(size=0.01,color="maroon4")+
                facet_wrap(~text,ncol=10, scales="free")+
                scale_y_reverse()+
                guides(fill = guide_colorbar(height= unit(5, "cm")))+
                defined_theme
    cl_pt<-ggplot(data = rep1_clusters[rep1_clusters$cluster==cl, ],
                    aes(x = x, y = y, color=cluster))+
                    geom_point(position=position_jitterdodge(jitter.width=0, 
                                            jitter.height=0), size=0.2)+
                    facet_wrap(~cluster)+
                    scale_y_reverse()+
                    theme_classic()+
                    scale_color_manual(values = "black")+
                    defined_theme
    lyt <- cl_pt | p1
    layout_design <- lyt + patchwork::plot_layout(widths = c(1,3)) 
    print(layout_design)
}

Visualise cluster vector and the top marker genes at spatial vector level

To check the linear relationship between the cluster vector and the marker gene vectors, we can plot the cluster vector on x-axis, and the marker gene vector on y-axis. The figure below shows the relationship between the cluster vector and the top marker gene vectors detected by correlation approach.

cluster_names = paste("c", 1:8, sep="")
plot_lst=list()
for (cl in cluster_names){
    perm_sig = res_df_1000[res_df_1000[,cl]<0.05,]
    curr_cell_type = all_celltypes[all_celltypes$cluster==cl,"anno"]
    obs_cutoff = quantile(obs_corr[, cl], 0.75)
    perm_cl=intersect(row.names(perm_res[perm_res[,cl]<0.05,]),
                        row.names(obs_corr[obs_corr[, cl]>obs_cutoff,]))
    inters=perm_cl
    rounded_val=signif(as.numeric(obs_corr[inters,cl]), digits = 3)
    inters_df = as.data.frame(cbind(gene=inters, value=rounded_val))
    inters_df$value = as.numeric(inters_df$value)
    inters_df=inters_df[order(inters_df$value, decreasing = TRUE),]
    inters_df$text= paste(inters_df$gene,inters_df$value,sep=": ")
    mk_gene = inters_df[1:min(2, nrow(inters_df)),"gene"]
    if (length(mk_gene > 0)){
        dff = as.data.frame(cbind(rep1_sq10_vectors$cluster_mt[,cl],
                                    rep1_sq10_vectors$gene_mt[,mk_gene]))
        colnames(dff) = c("cluster", mk_gene)
        
        dff$vector_id = c(1:(grid_length * grid_length))
        long_df <- dff %>% 
        pivot_longer(cols = -c(cluster, vector_id), names_to = "gene", 
                                values_to = "vector_count")
        long_df$gene = factor(long_df$gene, levels=mk_gene)
        
        p=ggplot(long_df, aes(x = cluster, y = vector_count )) +
            geom_point( size=0.01) +
            facet_wrap(~gene, scales = "free_y", nrow=1) +
            labs(x = paste("cluster vector ", curr_cell_type, sep=""), 
                    y = "marker gene vectors") +
            theme_minimal()+
            guides(color=guide_legend(nrow = 1,
                        override.aes=list(alpha=1, size=2)))+
            theme(panel.grid = element_blank(),legend.position = "none",
                    strip.text = element_text(size = rel(1)),
                    axis.line=element_blank(),
                    legend.title = element_blank(),
                    legend.key.size = unit(0.5, "cm"),
                    legend.text = element_text(size=10),
                    axis.text=element_blank(),
                    axis.ticks=element_blank(),
                    axis.title=element_text(size = 10),
                    panel.border =element_rect(colour = "black", 
                                                fill=NA, linewidth=0.5)
            )
        plot_lst[[cl]] = p
    }
}
combined_plot <- ggarrange(plotlist = plot_lst, 
                            ncol = 2, nrow = 4,
                            common.legend = FALSE, legend = "none")

combined_plot 

The other method to identify linearly correlated genes for each cluster is to construct a linear model for each gene. We can use the lasso_markers function to get the most relevant cluster label for every gene.

Linear modeling approach to detect marker genes

We can create spatial vectors for negative control genes and include them as background noise “clusters”.

probe_nm = unique(rep1_neg[rep1_neg$category=="probe","feature_name"])
codeword_nm = unique(rep1_neg[rep1_neg$category=="codeword","feature_name"])
rep1_nc_vectors = create_genesets(data_lst=list("rep1"= rep1_neg),
                                    name_lst=list(probe=probe_nm, 
                                                codeword=codeword_nm), 
                                    bin_type="square",
                                    bin_param=c(10, 10), 
                                    w_x=w_x, w_y=w_y,
                                    cluster_info = NULL)

set.seed(seed_number)

rep1_lasso_with_nc = lasso_markers(gene_mt=rep1_sq10_vectors$gene_mt,
                                    cluster_mt = rep1_sq10_vectors$cluster_mt,
                                    sample_names=c("rep1"),
                                    keep_positive=TRUE, 
                                    coef_cutoff=0.2,
                                    background=rep1_nc_vectors)

rep1_top_df_nc = rep1_lasso_with_nc$lasso_top_result
# the top result table 
head(rep1_top_df_nc)
##        gene top_cluster  glm_coef   pearson max_gg_corr max_gc_corr
## LUM     LUM          c3 15.181040 0.8724430   0.9115601   0.8724430
## CD68   CD68          c4  4.468619 0.5951329   0.5143408   0.5951329
## ERBB2 ERBB2          c1 14.508203 0.6902759   0.8864028   0.6902759
## MZB1   MZB1          c7  3.020872 0.8168198   0.7963419   0.8168198
## EPCAM EPCAM          c1 10.590911 0.8643835   0.9547929   0.8643835
## PTPRC PTPRC          c6  3.620975 0.9455237   0.8794803   0.9455237
# the full result table 
rep1_full_df = rep1_lasso_with_nc$lasso_full_result
head(rep1_full_df)
##      gene cluster glm_coef      p_value   pearson max_gg_corr max_gc_corr
## 50   AQP1      c8 6.998951 3.650999e-25 0.8270796   0.8442294   0.8270796
## 51   AQP1      c6 1.702569 9.317924e-05 0.3209543   0.8442294   0.8270796
## 52   AQP1      c3 1.013530 2.956703e-03 0.2099349   0.8442294   0.8270796
## 57 CCDC80      c3 3.920877 2.448703e-21 0.7163637   0.8086714   0.7163637
## 58 CCDC80      c7 1.583871 2.963857e-02 0.2349379   0.8086714   0.7163637
## 2    CD68      c4 4.468619 2.344267e-11 0.5951329   0.5143408   0.5951329
Visualise top marker genes detected by linear modelling approach

We can rank the marker genes by its linear model coefficient to the cluster ans plot the transcript detection coordinates for the top three marker genes for every cluster.

cluster_names = paste("c", 1:8, sep="")
for (cl in setdiff(cluster_names,"NoSig")){
    inters=rep1_top_df_nc[rep1_top_df_nc$top_cluster==cl,"gene"]
    rounded_val=signif(as.numeric(rep1_top_df_nc[inters,"glm_coef"]),
                                    digits = 3)
    inters_df = as.data.frame(cbind(gene=inters, value=rounded_val))
    inters_df$value = as.numeric(inters_df$value)
    inters_df=inters_df[order(inters_df$value, decreasing = TRUE),]
    inters_df$text= paste(inters_df$gene,inters_df$value,sep=": ")
    
    if (length(inters > 0)){
        inters_df = inters_df[1:min(2, nrow(inters_df)),]
        inters = inters_df$gene
        iters_rep1= rep1_sub$feature_name %in% inters
        vis_r1 =rep1_sub[iters_rep1,
                                c("x","y","feature_name")]
        vis_r1$value = inters_df[match(vis_r1$feature_name,inters_df$gene),
                                "value"]
        #vis_r1=vis_r1[order(vis_r1$value,decreasing = TRUE),]
        vis_r1$text_label= paste(vis_r1$feature_name,
                                    vis_r1$value,sep=": ")
        vis_r1$text_label=factor(vis_r1$text_label, levels = inters_df$text)
        vis_r1$sample="rep1"
        p1<- ggplot(data = vis_r1,
                    aes(x = x, y = y))+ 
                    geom_point(size=0.01,color="maroon4")+
                    facet_wrap(~text_label,ncol=10, scales="free")+
                    scale_y_reverse()+
                    guides(fill = guide_colorbar(height= unit(5, "cm")))+
                    defined_theme
        cl_pt<-ggplot(data = rep1_clusters[rep1_clusters$cluster==cl, ],
                    aes(x = x, y = y, color=cluster))+
                    geom_point(position=position_jitterdodge(jitter.width=0, 
                                            jitter.height=0), size=0.2)+
                    facet_wrap(~cluster)+
                    scale_y_reverse()+
                    theme_classic()+
                    scale_color_manual(values = "black")+
                    defined_theme
        lyt <- cl_pt | p1
        layout_design <- lyt + patchwork::plot_layout(widths = c(1,3)) 
        print(layout_design)
}}

Visualise cluster vector and the top marker genes at spatial vector level

We can plot the cluster vector on x-axis, and the marker gene vectors (detected by the linear modelling approach) on y-axis to validate the linear relationship assumption between the cluster vector and the marker gene vectors.

cluster_names = paste("c", 1:8, sep="")
plot_lst=list()
for (cl in cluster_names){
    curr_cell_type = all_celltypes[all_celltypes$cluster==cl,"anno"]
    inters=rep1_top_df_nc[rep1_top_df_nc$top_cluster==cl,"gene"]
    if (length(inters > 0)){
        rounded_val=signif(as.numeric(rep1_top_df_nc[inters,"glm_coef"]),
                                digits = 3)
        inters_df = as.data.frame(cbind(gene=inters, value=rounded_val))
        inters_df$value = as.numeric(inters_df$value)
        inters_df=inters_df[order(inters_df$value, decreasing = TRUE),]
        inters_df$text= paste(inters_df$gene,inters_df$value,sep=": ")
    
        inters_df = inters_df[1:min(2, nrow(inters_df)),]
        mk_gene = inters_df$gene

        dff = as.data.frame(cbind(rep1_sq10_vectors$cluster_mt[,cl],
                                rep1_sq10_vectors$gene_mt[,mk_gene]))
        colnames(dff) = c("cluster", mk_gene)
        dff$vector_id = c(1:(grid_length * grid_length))
        long_df <- dff %>% 
        pivot_longer(cols = -c(cluster, vector_id), names_to = "gene", 
                        values_to = "vector_count")
        long_df$gene = factor(long_df$gene, levels=mk_gene)
        p=ggplot(long_df, aes(x = cluster, y = vector_count )) +
            geom_point( size=0.01) +
            facet_wrap(~gene, scales = "free_y", nrow=1) +
            labs(x = paste("cluster vector ", curr_cell_type, sep=""), 
                    y = "marker gene vectors") +
            theme_minimal()+
            guides(color=guide_legend(nrow = 1,
                        override.aes=list(alpha=1, size=2)))+
            theme(panel.grid = element_blank(),legend.position = "none",
                    strip.text = element_text(size = rel(1)),
                    axis.line=element_blank(),
                    legend.title = element_blank(),
                    legend.key.size = unit(0.5, "cm"),
                    legend.text = element_text(size=10),
                    axis.text=element_blank(),
                    axis.ticks=element_blank(),
                    axis.title=element_text(size = 10),
                    panel.border =element_rect(colour = "black", 
                                                fill=NA, linewidth=0.5)
        )
        plot_lst[[cl]] = p
    }
}
combined_plot <- ggarrange(plotlist = plot_lst, 
                            ncol = 2, nrow = 4,
                            common.legend = FALSE, legend = "none")

combined_plot 

Scenario 2: multiple samples

Load the replicate 2 from sample 1.

data(rep2_sub, rep2_clusters, rep2_neg)
rep2_clusters$cluster=factor(rep2_clusters$cluster,
                            levels=paste("c",1:8, sep=""))
rep1_clusters$cells = paste(row.names(rep1_clusters),"_1",sep="")
rep2_clusters$cells =paste(row.names(rep2_clusters),"_2",sep="")
rep_clusters = rbind(rep1_clusters,rep2_clusters)
rep_clusters$cluster=factor(rep_clusters$cluster,
                            levels=paste("c",1:8, sep=""))
table(rep_clusters$sample, rep_clusters$cluster)
##       
##         c1  c2  c3  c4  c5  c6  c7  c8
##   rep1 745 205 221 127  87 176  45  99
##   rep2  27 476 313 190 360 256  99  94
Visualise the clusters

We can plot the coordinates of cells for every cluster in every replicate

ggplot(data = rep_clusters,
        aes(x = x, y = y, color=cluster))+
        geom_point(position=position_jitterdodge(jitter.width=0, 
                                                jitter.height=0),size=0.1)+
        facet_grid(sample~cluster)+
        scale_y_reverse()+
        theme_classic()+
        scale_color_manual(values = c("#FC8D62","#66C2A5" ,"#8DA0CB","#E78AC3",
                                "#A6D854","skyblue","purple3","#E5C498"))+
        guides(color=guide_legend(title="cluster", nrow = 1,
        override.aes=list(alpha=1, size=7)))+
        theme(
            axis.line=element_blank(),
            axis.text.x=element_blank(),
            axis.text.y=element_blank(),
            axis.ticks=element_blank(),
            axis.title.x=element_blank(),
            axis.title.y=element_blank(),
            panel.background=element_blank(),
            panel.border=element_blank(),
            panel.grid.major=element_blank(),
            panel.grid.minor=element_blank(),
            plot.background=element_blank(),
            legend.text = element_text(size=10),
            legend.position="none",
            legend.title = element_text(size=10),
            strip.text = element_text(size = rel(1)))+
        xlab("")+
        ylab("")

When we have multiple replicates in the dataset, we can find marker genes by providing additional sample information as the input for the function lasso_markers.

Linear modeling approach to detect marker genes

w_x =  c(min(floor(min(rep1_sub$x)),
            floor(min(rep2_sub$x)),
            floor(min(rep_clusters$x))), 
        max(ceiling(max(rep1_sub$x)),
            ceiling(max(rep2_sub$x)),
            ceiling(max(rep_clusters$x))))
w_y =  c(min(floor(min(rep1_sub$y)),
            floor(min(rep2_sub$y)),
            floor(min(rep_clusters$y))), 
        max(ceiling(max(rep1_sub$y)),
            ceiling(max(rep2_sub$y)),
            ceiling(max(rep_clusters$y))))
grid_length=10
# get spatial vectors
two_rep_vectors = get_vectors(trans_lst= list("rep1"=rep1_sub, 
                                            "rep2" = rep2_sub),
                            cluster_info = rep_clusters, bin_type="square",
                            bin_param=c(grid_length, grid_length),
                            all_genes = all_real_genes , 
                            w_x=w_x, w_y=w_y)
probe_nm = unique(rep1_neg[rep1_neg$category=="probe","feature_name"])
codeword_nm = unique(rep1_neg[rep1_neg$category=="probe","feature_name"])

two_rep_nc_vectors = create_genesets(data_lst=list("rep1" = rep1_neg, 
                                                    "rep2" = rep2_neg),
                                        name_lst=list(probe=probe_nm, 
                                                    codeword=codeword_nm),
                                        bin_type="square",
                                        bin_param=c(10,10), 
                                        w_x=w_x, w_y=w_y,
                                        cluster_info = NULL)
set.seed(seed_number)
two_rep_lasso_with_nc = lasso_markers(gene_mt=two_rep_vectors$gene_mt,
                                    cluster_mt = two_rep_vectors$cluster_mt,
                                    sample_names=c("rep1","rep2"),
                                    keep_positive=TRUE, 
                                    coef_cutoff=0.2,
                                    background=two_rep_nc_vectors,n_fold = 5)
tworep_res=two_rep_lasso_with_nc$lasso_top_result
tworep_res$celltype = rep_clusters[match(tworep_res$top_cluster,
                                            rep_clusters$cluster),"anno"]
table(tworep_res$top_cluster)
## 
## c1 c2 c3 c4 c5 c6 c7 c8 
##  3  2  3  3  2  2  2  3
head(tworep_res)
##        gene top_cluster  glm_coef   pearson max_gg_corr max_gc_corr    celltype
## LUM     LUM          c3 12.252136 0.8838826   0.9150385   0.8838826     Stromal
## CD68   CD68          c4  2.820226 0.6902781   0.6540004   0.6902781 Macrophages
## ERBB2 ERBB2          c2 21.723376 0.7811584   0.9072989   0.7811584        DCIS
## MZB1   MZB1          c7  2.806131 0.7500983   0.7879303   0.7500983     B_Cells
## EPCAM EPCAM          c1  9.271843 0.6247635   0.9398823   0.6247635       Tumor
## PTPRC PTPRC          c6  3.446430 0.9170205   0.8945435   0.9170205     T_Cells
Visualise the top marker genes for each cluster
for (cl in all_celltypes$anno){
    inters=tworep_res[tworep_res$celltype==cl,"gene"]
    rounded_val=signif(as.numeric(tworep_res[inters,"glm_coef"]),
                        digits = 3)
    inters_df = as.data.frame(cbind(gene=inters, value=rounded_val))
    inters_df$value = as.numeric(inters_df$value)
    inters_df=inters_df[order(inters_df$value, decreasing = TRUE),]
    inters_df$text= paste(inters_df$gene,inters_df$value,sep=": ")
    if (length(inters > 0)){
        inters_df = inters_df[1:min(2, nrow(inters_df)),]
        inters = inters_df$gene
        iters_rep1= rep1_sub$feature_name %in% inters
        vis_r1 =rep1_sub[iters_rep1,
                                c("x","y","feature_name")]
        vis_r1$value = inters_df[match(vis_r1$feature_name,inters_df$gene),
                                "value"]
        vis_r1=vis_r1[order(vis_r1$value,decreasing = TRUE),]
        vis_r1$text_label= paste(vis_r1$feature_name,
                                    vis_r1$value,sep=": ")
        vis_r1$text_label=factor(vis_r1$text_label)
        vis_r1$sample="rep1"
        iters_rep2= rep2_sub$feature_name %in% inters
        vis_r2 =rep2_sub[iters_rep2,
                                c("x","y","feature_name")]
        vis_r2$value = inters_df[match(vis_r2$feature_name,inters_df$gene),
                                "value"]
        vis_r2=vis_r2[order(vis_r2$value, decreasing = TRUE),]
        vis_r2$text_label= paste(vis_r2$feature_name,
                                vis_r2$value,sep=": ")
        vis_r2$text_label=factor(vis_r2$text_label)
        vis_r2$sample="rep2"
        p1<- ggplot(data = vis_r1,
                    aes(x = x, y = y))+ 
                    geom_point(size=0.01,color="maroon4")+
                    facet_grid(sample~text_label, scales="free")+
                    scale_y_reverse()+
                    guides(fill = guide_colorbar(height= unit(5, "cm")))+
                    defined_theme
        p2<- ggplot(data = vis_r2,
                    aes(x = x, y = y))+ 
                    geom_point(size=0.01,color="maroon4")+
                    facet_grid(sample~text_label,scales="free")+
                    scale_y_reverse()+
                    guides(fill = guide_colorbar(height= unit(5, "cm")))+
                    defined_theme
        
        cl_pt<-ggplot(data = rep_clusters[rep_clusters$anno==cl, ],
                    aes(x = x, y = y, color=cluster))+
                    geom_point(position=position_jitterdodge(jitter.width=0, 
                                            jitter.height=0), size=0.2)+
                    facet_grid(sample~cluster)+
                    scale_y_reverse()+
                    theme_classic()+
                    scale_color_manual(values = "black")+
                    defined_theme
        lyt <- cl_pt | (p1 / p2) 
        if (cl %in% c("c6","c7")){
            lyt <- cl_pt | ((p1 / p2) | patchwork::plot_spacer())   
        }
        layout_design <- lyt + patchwork::plot_layout(widths = c(1,3)) 

        print(layout_design)
}}

Visualise cluster vector and the top marker genes at spatial vector level

The figure below shows the relationship between the cluster vector and the top marker gene vectors detected by linear modelling approach by accounting for multiple samples and background noise

cluster_names = paste("c", 1:8, sep="")
plot_lst=list()
for (cl in cluster_names){
    inters=tworep_res[tworep_res$top_cluster==cl,"gene"]
    curr_cell_type = all_celltypes[all_celltypes$cluster==cl,"anno"]
    rounded_val=signif(as.numeric(tworep_res[inters,"glm_coef"]),
                            digits = 3)
    inters_df = as.data.frame(cbind(gene=inters, value=rounded_val))
    inters_df$value = as.numeric(inters_df$value)
    inters_df=inters_df[order(inters_df$value, decreasing = TRUE),]
    inters_df$text= paste(inters_df$gene,inters_df$value,sep=": ")
        
    mk_gene = inters_df[1:min(2, nrow(inters_df)),"gene"]
    if (length(inters > 0)){
        dff = as.data.frame(cbind(two_rep_vectors$cluster_mt[,cl],
                                    two_rep_vectors$gene_mt[,mk_gene]))
        colnames(dff) = c("cluster", mk_gene)
        total_tiles = grid_length * grid_length
        dff$vector_id = c(1:total_tiles)
        dff$sample= "Replicate1"
        dff[(total_tiles+1):(total_tiles*2),"sample"] = "Replicate2"
        dff$vector_id = c(1:total_tiles, 1:total_tiles)
        long_df <- dff %>% 
        pivot_longer(cols = -c(cluster, sample, vector_id), names_to = "gene", 
                        values_to = "vector_count")
        long_df$gene = factor(long_df$gene, levels=mk_gene)
        p=ggplot(long_df, 
                        aes(x = cluster, y = vector_count, color =sample)) +
            geom_point( size=0.01) +
            facet_wrap(~gene, scales = "free_y", nrow=1) +
            labs(x = paste("cluster vector ", curr_cell_type, sep=""), 
                    y = "marker gene vectors") +
            theme_minimal()+
            guides(color=guide_legend(nrow = 1,
                        override.aes=list(alpha=1, size=2)))+
            theme(panel.grid = element_blank(),legend.position = "bottom",
                    strip.text = element_text(size = rel(1)),
                    axis.line=element_blank(),
                    legend.title = element_blank(),
                    legend.key.size = unit(0.5, "cm"),
                    legend.text = element_text(size=10),
                    axis.text=element_blank(),
                    axis.ticks=element_blank(),
                    axis.title=element_text(size = 10),
                    panel.border =element_rect(colour = "black", 
                                                fill=NA, linewidth=0.5)
            )
        plot_lst[[cl]] = p
    }
}
combined_plot <- ggarrange(plotlist = plot_lst, 
                            ncol = 2, nrow = 4,
                            common.legend = TRUE, legend = "top")

combined_plot 

## R version 4.4.2 (2024-10-31)
## Platform: x86_64-pc-linux-gnu
## Running under: Ubuntu 22.04.5 LTS
## 
## Matrix products: default
## BLAS:   /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3 
## LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.20.so;  LAPACK version 3.10.0
## 
## locale:
##  [1] LC_CTYPE=C.UTF-8       LC_NUMERIC=C           LC_TIME=C.UTF-8       
##  [4] LC_COLLATE=C.UTF-8     LC_MONETARY=C.UTF-8    LC_MESSAGES=C.UTF-8   
##  [7] LC_PAPER=C.UTF-8       LC_NAME=C              LC_ADDRESS=C          
## [10] LC_TELEPHONE=C         LC_MEASUREMENT=C.UTF-8 LC_IDENTIFICATION=C   
## 
## time zone: UTC
## tzcode source: system (glibc)
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] ggpubr_0.6.0           tidyr_1.3.1            spatstat_3.2-1        
##  [4] spatstat.linnet_3.2-2  spatstat.model_3.3-2   rpart_4.1.23          
##  [7] spatstat.explore_3.3-3 nlme_3.1-166           spatstat.random_3.3-2 
## [10] spatstat.geom_3.3-3    spatstat.univar_3.1-1  spatstat.data_3.1-2   
## [13] gridExtra_2.3          ggrepel_0.9.6          ggraph_2.2.1          
## [16] igraph_2.1.1           corrplot_0.95          caret_6.0-94          
## [19] lattice_0.22-6         glmnet_4.1-8           Matrix_1.7-1          
## [22] dplyr_1.1.4            data.table_1.16.2      jazzPanda_0.99.0      
## [25] ggplot2_3.5.1          Seurat_5.1.0           SeuratObject_5.0.2    
## [28] sp_2.1-4              
## 
## loaded via a namespace (and not attached):
##   [1] RcppAnnoy_0.0.22      splines_4.4.2         later_1.3.2          
##   [4] tibble_3.2.1          polyclip_1.10-7       hardhat_1.4.0        
##   [7] pROC_1.18.5           fastDummies_1.7.4     lifecycle_1.0.4      
##  [10] rstatix_0.7.2         doParallel_1.0.17     globals_0.16.3       
##  [13] MASS_7.3-61           backports_1.5.0       magrittr_2.0.3       
##  [16] plotly_4.10.4         sass_0.4.9            rmarkdown_2.29       
##  [19] jquerylib_0.1.4       yaml_2.3.10           httpuv_1.6.15        
##  [22] sctransform_0.4.1     spam_2.11-0           spatstat.sparse_3.1-0
##  [25] reticulate_1.39.0     cowplot_1.1.3         pbapply_1.7-2        
##  [28] RColorBrewer_1.1-3    lubridate_1.9.3       abind_1.4-8          
##  [31] Rtsne_0.17            purrr_1.0.2           nnet_7.3-19          
##  [34] tweenr_2.0.3          ipred_0.9-15          lava_1.8.0           
##  [37] irlba_2.3.5.1         listenv_0.9.1         spatstat.utils_3.1-1 
##  [40] goftest_1.2-3         RSpectra_0.16-2       fitdistrplus_1.2-1   
##  [43] parallelly_1.39.0     pkgdown_2.1.1         leiden_0.4.3.1       
##  [46] codetools_0.2-20      ggforce_0.4.2         tidyselect_1.2.1     
##  [49] shape_1.4.6.1         farver_2.1.2          viridis_0.6.5        
##  [52] matrixStats_1.4.1     stats4_4.4.2          jsonlite_1.8.9       
##  [55] Formula_1.2-5         tidygraph_1.3.1       progressr_0.15.0     
##  [58] ggridges_0.5.6        survival_3.7-0        iterators_1.0.14     
##  [61] systemfonts_1.1.0     foreach_1.5.2         tools_4.4.2          
##  [64] ragg_1.3.3            ica_1.0-3             Rcpp_1.0.13-1        
##  [67] glue_1.8.0            prodlim_2024.06.25    xfun_0.49            
##  [70] mgcv_1.9-1            withr_3.0.2           fastmap_1.2.0        
##  [73] fansi_1.0.6           digest_0.6.37         timechange_0.3.0     
##  [76] R6_2.5.1              mime_0.12             textshaping_0.4.0    
##  [79] colorspace_2.1-1      scattermore_1.2       tensor_1.5           
##  [82] utf8_1.2.4            generics_0.1.3        recipes_1.1.0        
##  [85] class_7.3-22          graphlayouts_1.2.0    httr_1.4.7           
##  [88] htmlwidgets_1.6.4     uwot_0.2.2            ModelMetrics_1.2.2.2 
##  [91] pkgconfig_2.0.3       gtable_0.3.6          timeDate_4041.110    
##  [94] lmtest_0.9-40         htmltools_0.5.8.1     carData_3.0-5        
##  [97] dotCall64_1.2         scales_1.3.0          png_0.1-8            
## [100] gower_1.0.1           knitr_1.48            reshape2_1.4.4       
## [103] cachem_1.1.0          zoo_1.8-12            stringr_1.5.1        
## [106] KernSmooth_2.23-24    parallel_4.4.2        miniUI_0.1.1.1       
## [109] desc_1.4.3            pillar_1.9.0          grid_4.4.2           
## [112] vctrs_0.6.5           RANN_2.6.2            promises_1.3.0       
## [115] car_3.1-3             xtable_1.8-4          cluster_2.1.6        
## [118] evaluate_1.0.1        cli_3.6.3             compiler_4.4.2       
## [121] rlang_1.1.4           ggsignif_0.6.4        future.apply_1.11.3  
## [124] labeling_0.4.3        plyr_1.8.9            fs_1.6.5             
## [127] stringi_1.8.4         viridisLite_0.4.2     deldir_2.0-4         
## [130] BiocParallel_1.40.0   munsell_0.5.1         lazyeval_0.2.2       
## [133] RcppHNSW_0.6.0        patchwork_1.3.0       future_1.34.0        
## [136] shiny_1.9.1           highr_0.11            ROCR_1.0-11          
## [139] broom_1.0.7           memoise_2.0.1         bslib_0.8.0