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Spatial transcriptomics

Github repo of the original lab that developed Visium

Detection of genes whose expression is highly localized

Mark variogram

A spatial pattern records the locations of events produced by an underlying spatial process in a study region.

spatstat[http://www.spatstat.org/] package

Auxiliary information attached to each point in the point pattern is called a mark and we speak of a marked point pattern.

Variogram:

  • function describing the degree of spatial dependence of a spatial random field
  • how much do the values of two marks differ depending on the distance between those samples (assumption: samples taken far apart will vary more than samples taken close to each other)
  • variogram = variance of the difference between fiedl values at two locations

Application to spatial transcriptomics

Originally introduced by the Sandberg Lab (Edsgard, Johnsson & Sandberg (2018), Nat Methods) in their package trendsceek:

To identify genes for which dependencies exist between the spatial distribution of cells and gene expression in those cells, we modeled data as marked point processes, which we used to rank and assess the significance of the spatial expression trends of each gene.

  • points = spatial locations of cells (or regions)
  • marks on each point = expression levels
  • tests for significant dependency between the spatial distributions of points and their associated marks (expression levels) through pairwise analyses of points as a function of the distance r (radius) between them
  • if marks and the locations of points are independent, the scores obtained should be constant across the different distances r
  • To assess the significance of a gene's spatial expression pattern, we implemented a resampling procedure in which the expression values are permuted, reflecting a null model with no spatial dependency of expression

They also applied their method to the coordinates defined by UMAP/t-SNE

spatial methods have the ability to identify continuous gradients or spatial expression patterns defined by fewer genes that would be hard to identify through clustering of pairwise cellular expression profile correlations

  • only a subset of highly variable genes have significant spatial expression patterns
  • For the distribution of all pairs at a particular radius, a mark segregation is said to be present if the distribution is dependent on r such that it deviates from what would be expected if the marks were randomly distributed
  • Four summary statistics of the pair distribution were calculated for each radius and compared to the null distribution of the summary statistic derived from the permuted expression labels.

SpatialDE

Splotch

Spatial representations in R

sf library

from Jesse Sadler

sf class object = sfg + sfc objects

  • basically a data frame with rows of features, columns of attributes and a special geometry column with the spatial aspects of the features
    • sf object: collection of simple features represented by a data frame
    • sfg object: geometry of a single feature
    • sfc object: geometry column with the spatial attributes of the object printed above the data frame

sfg

Represents the coordinates of the objects.

Geometry types:

Name Represents Created with Function
POINT a single point a vector sf_point()
MULTIPOINT multiple points matrix with each row = point sf_multipoint()
LINESTRING sequence of two or more points connected by straight lines matrix with each row = point sf_linestring()
MULTILINESTRING multiple lines list of matrices sf_multilinestring()
POLYGON closed (!) ring with zero or more interior holes list of matrices sf_polygon()
MULTIPOLYGON multiple polygons list of list of matrices sf_multipolygon()
GEOMETRYCOLLECTION any combination of the above types list that combines any of the above sf_geometrycollection()

sfc

For representing geospatial data, i.e. they are lists of of one ore more sfg objects with attributes that contain the coordinate reference system

Functions for creating sfc objects: st_sfc(multipoint_sfg) (this would create an sfc object with NA's in the epsg and proj4string attributes)

Creating an sf object

The sf objects combine the spatial information with any number of attributes, e.g. names, values etc.

They can be created with the st_sf() function * joins a df to an sfg object

Generating a point pattern (ppp) object for markvariogram function (spatstat package)

## extract coordinates
spatial.coords <- reducedDim(sce.obj, coords_accessor)

## generate ppp object
  x.coord = spatial.coords[, 1]
  y.coord = spatial.coords[, 2]

  pp <- ppp(
    x = x.coord,
    y = y.coord,
    xrange = range(x.coord),
    yrange = range(y.coord)
  )
pp[["marks"]] <- as.data.frame(x = t(x = exprs_data))
mv <- markvario(X = pp, normalise = TRUE, ...)