miloR 2.0.0

```
library(miloR)
library(SingleCellExperiment)
library(scater)
library(scran)
library(dplyr)
library(patchwork)
library(MouseGastrulationData)
```

For this vignette we will use the mouse gastrulation single-cell data from Pijuan-Sala et al.Â 2019. The dataset can be downloaded as a `SingleCellExperiment`

object from the `MouseGastrulationData`

package on Bioconductor. To make computations faster, here we will download just a subset of samples, 4 samples at stage E7 and 4 samples at stage E7.5.

This dataset has already been pre-processed and contains a `pca.corrected`

dimensionality reduction, which was built after batch correction using `fastMNN`

.

```
select_samples <- c(2, 3, 6, 4, #15,
# 19,
10, 14#, 20 #30
#31, 32
)
embryo_data = EmbryoAtlasData(samples = select_samples)
embryo_data
```

```
## class: SingleCellExperiment
## dim: 29452 7558
## metadata(0):
## assays(1): counts
## rownames(29452): ENSMUSG00000051951 ENSMUSG00000089699 ...
## ENSMUSG00000096730 ENSMUSG00000095742
## rowData names(2): ENSEMBL SYMBOL
## colnames(7558): cell_361 cell_362 ... cell_29013 cell_29014
## colData names(17): cell barcode ... colour sizeFactor
## reducedDimNames(2): pca.corrected umap
## mainExpName: NULL
## altExpNames(0):
```

We recompute the UMAP embedding for this subset of cells to visualize the data.

```
embryo_data <- embryo_data[,apply(reducedDim(embryo_data, "pca.corrected"), 1, function(x) !all(is.na(x)))]
embryo_data <- runUMAP(embryo_data, dimred = "pca.corrected", name = 'umap')
plotReducedDim(embryo_data, colour_by="stage", dimred = "umap")
```

We will test for significant differences in abundance of cells between these stages of development, and the associated gene signatures.

For differential abundance analysis on graph neighbourhoods we first construct a `Milo`

object. This extends the `SingleCellExperiment`

class to store information about neighbourhoods on the KNN graph.

```
embryo_milo <- Milo(embryo_data)
embryo_milo
```

```
## class: Milo
## dim: 29452 6875
## metadata(0):
## assays(1): counts
## rownames(29452): ENSMUSG00000051951 ENSMUSG00000089699 ...
## ENSMUSG00000096730 ENSMUSG00000095742
## rowData names(2): ENSEMBL SYMBOL
## colnames(6875): cell_361 cell_362 ... cell_29013 cell_29014
## colData names(17): cell barcode ... colour sizeFactor
## reducedDimNames(2): pca.corrected umap
## mainExpName: NULL
## altExpNames(0):
## nhoods dimensions(2): 1 1
## nhoodCounts dimensions(2): 1 1
## nhoodDistances dimension(1): 0
## graph names(0):
## nhoodIndex names(1): 0
## nhoodExpression dimension(2): 1 1
## nhoodReducedDim names(0):
## nhoodGraph names(0):
## nhoodAdjacency dimension(2): 1 1
```

We need to add the KNN graph to the Milo object. This is stored in the `graph`

slot, in `igraph`

format. The `miloR`

package includes functionality to build and store the graph from the PCA dimensions stored in the `reducedDim`

slot. In this case, we specify that we want to build the graph from the MNN corrected PCA dimensions.

For graph building you need to define a few parameters:

`d`

: the number of reduced dimensions to use for KNN refinement. We recommend using the same \(d\) used for KNN graph building, or to select PCs by inspecting the scree plot.`k`

: this affects the power of DA testing, since we need to have enough cells from each sample represented in a neighbourhood to estimate the variance between replicates. On the other side, increasing \(k\) too much might lead to over-smoothing. We suggest to start by using the same value for \(k\) used for KNN graph building for clustering and UMAP visualization. We will later use some heuristics to evaluate whether the value of \(k\) should be increased.

`embryo_milo <- buildGraph(embryo_milo, k = 30, d = 30, reduced.dim = "pca.corrected")`

Alternatively, one can add a precomputed KNN graph (for example constructed with Seurat or scanpy) to the `graph`

slot using the adjacency matrix, through the helper function `buildFromAdjacency`

.

We define the neighbourhood of a cell, the index, as the group of cells connected by an edge in the KNN graph to the index cell. For efficiency, we donâ€™t test for DA in the neighbourhood of every cell, but we sample as indices a subset of representative cells, using a KNN sampling algorithm used by Gut et al.Â 2015.

As well as \(d\) and \(k\), for sampling we need to define a few additional parameters:

`prop`

: the proportion of cells to randomly sample to start with. We suggest using`prop=0.1`

for datasets of less than 30k cells. For bigger datasets using`prop=0.05`

should be sufficient (and makes computation faster).`refined`

: indicates whether you want to use the sampling refinement algorithm, or just pick cells at random. The default and recommended way to go is to use refinement. The only situation in which you might consider using`random`

instead, is if you have batch corrected your data with a graph based correction algorithm, such as BBKNN, but the results of DA testing will be suboptimal.

`embryo_milo <- makeNhoods(embryo_milo, prop = 0.1, k = 30, d=30, refined = TRUE, reduced_dims = "pca.corrected")`

Once we have defined neighbourhoods, we plot the distribution of neighbourhood sizes (i.e.Â how many cells form each neighbourhood) to evaluate whether the value of \(k\) used for graph building was appropriate. We can check this out using the `plotNhoodSizeHist`

function.

As a rule of thumb we want to have an average neighbourhood size over 5 x N_samples. If the mean is lower, or if the distribution is

`plotNhoodSizeHist(embryo_milo)`

*Milo* leverages the variation in cell numbers between replicates for the same experimental condition to test for differential abundance. Therefore we have to count how many cells from each sample are in each neighbourhood. We need to use the cell metadata and specify which column contains the sample information.

`embryo_milo <- countCells(embryo_milo, meta.data = as.data.frame(colData(embryo_milo)), sample="sample")`

This adds to the `Milo`

object a \(n \times m\) matrix, where \(n\) is the number of neighbourhoods and \(m\) is the number of experimental samples. Values indicate the number of cells from each sample counted in a neighbourhood. This count matrix will be used for DA testing.

`head(nhoodCounts(embryo_milo))`

```
## 6 x 6 sparse Matrix of class "dgCMatrix"
## 2 3 6 4 10 14
## 1 . . 19 2 62 13
## 2 1 . 21 . 64 15
## 3 . . 17 1 60 13
## 4 . . 22 3 83 11
## 5 . . 6 . 99 6
## 6 2 3 26 4 . .
```

Now we are all set to test for differential abundance in neighbourhoods. We implement this hypothesis testing in a generalized linear model (GLM) framework, specifically using the Negative Binomial GLM implementation in `edgeR`

.

We first need to think about our experimental design. The design matrix should match each sample to the experimental condition of interest for DA testing. In this case, we want to detect DA between embryonic stages, stored in the `stage`

column of the dataset `colData`

. We also include the `sequencing.batch`

column in the design matrix. This represents a known technical covariate that we want to account for in DA testing.

```
embryo_design <- data.frame(colData(embryo_milo))[,c("sample", "stage", "sequencing.batch")]
## Convert batch info from integer to factor
embryo_design$sequencing.batch <- as.factor(embryo_design$sequencing.batch)
embryo_design <- distinct(embryo_design)
rownames(embryo_design) <- embryo_design$sample
embryo_design
```

```
## sample stage sequencing.batch
## 2 2 E7.5 1
## 3 3 E7.5 1
## 6 6 E7.5 1
## 4 4 E7.5 1
## 10 10 E7.0 1
## 14 14 E7.0 2
```

Milo uses an adaptation of the Spatial FDR correction introduced by cydar, where we correct p-values accounting for the amount of overlap between neighbourhoods. Specifically, each hypothesis test P-value is weighted by the reciprocal of the kth nearest neighbour distance. To use this statistic we first need to store the distances between nearest neighbors in the Milo object. This is done by the `calcNhoodDistance`

function
(N.B. this step is the most time consuming of the analysis workflow and might take a couple of minutes for large datasets).

`embryo_milo <- calcNhoodDistance(embryo_milo, d=30, reduced.dim = "pca.corrected")`

Now we can do the DA test, explicitly defining our experimental design. In this case, we want to test for differences between experimental stages, while accounting for the variability between technical batches (You can find more info on how to use formulas to define a testing design in R here)

```
da_results <- testNhoods(embryo_milo, design = ~ sequencing.batch + stage, design.df = embryo_design, reduced.dim="pca.corrected")
head(da_results)
```

```
## logFC logCPM F PValue FDR Nhood SpatialFDR
## 1 -4.287998 11.99046 26.237254 3.456984e-07 1.143855e-06 1 1.030733e-06
## 2 -4.387249 12.04024 27.711410 1.636710e-07 6.037044e-07 2 5.336860e-07
## 3 -4.508896 11.92637 28.648719 1.018505e-07 3.996949e-07 3 3.522620e-07
## 4 -4.434757 12.25008 29.026918 8.412736e-08 3.350205e-07 4 2.955593e-07
## 5 -6.610287 12.22163 50.545907 1.881002e-12 8.464509e-11 5 6.587006e-11
## 6 5.976495 10.35138 7.739349 5.478230e-03 9.409173e-03 6 9.438189e-03
```

This calculates a Fold-change and corrected P-value for each neighbourhood, which indicates whether there is significant differential abundance between developmental stages. The main statistics we consider here are:

`logFC`

: indicates the log-Fold change in cell numbers between samples from E7.5 and samples from E7.0`PValue`

: reports P-values before FDR correction`SpatialFDR`

: reports P-values corrected for multiple testing accounting for overlap between neighbourhoods

```
da_results %>%
arrange(SpatialFDR) %>%
head()
```

```
## logFC logCPM F PValue FDR Nhood SpatialFDR
## 15 -7.803126 12.22317 56.69822 9.254034e-14 1.590661e-11 15 1.232394e-11
## 105 -8.455623 12.51775 56.41245 1.063918e-13 1.590661e-11 105 1.232394e-11
## 337 -9.233096 11.72111 57.05201 7.786822e-14 1.590661e-11 337 1.232394e-11
## 35 -9.321762 12.04151 55.37327 1.767401e-13 1.590661e-11 35 1.271931e-11
## 146 -9.138621 11.75762 55.82790 1.415380e-13 1.590661e-11 146 1.271931e-11
## 166 -9.484251 12.71392 54.27300 3.026729e-13 2.270047e-11 166 1.831519e-11
```

We can start inspecting the results of our DA analysis from a couple of standard diagnostic plots. We first inspect the distribution of uncorrected P values, to verify that the test was balanced.

`ggplot(da_results, aes(PValue)) + geom_histogram(bins=50)`

Then we visualize the test results with a volcano plot (remember that each point here represents a neighbourhood, *not* a cell).

```
ggplot(da_results, aes(logFC, -log10(SpatialFDR))) +
geom_point() +
geom_hline(yintercept = 1) ## Mark significance threshold (10% FDR)
```