Maxspin (maximization of spatial information) is an information theoretic approach to quantifying the degree of spatial organization in spatial transcriptomics (or other spatial omics) data.

Our paper describing and benchmarking this method is out now in Cell Reports Methods:

Jones, D.C., Danaher, P., Kim, Y., Beechem, J.M., Gottardo, R. and Newell, E.W. (2023) An information theoretic approach to detecting spatially varying genes. Cell Reports Methods.

Installation

The python package can be installed with:

pip install maxspin

Basic Usage

This package operates on AnnData objects from the anndata package.

We assume the existence of a spatial neighborhood graph. A simple and effective way of doing this is Delaunay triangulation, for example using squidpy.

import squidpy as sq

sq.gr.spatial_neighbors(adata, delaunay=True, coord_type="generic")

Spatial information can then be measured using the spatial_information function.

from maxspin import spatial_information

spatial_information(adata, prior=None)

This adds a spatial_information column to the var metadata.

Similarly, pairwise spatial information can be computed with pairwise_spatial_information. This function will test every pair of genes, which is pretty impractical for large numbers of genes, so it's a good idea to subset the AnnData object before calling this.

from maxspin import pairwise_spatial_information

pairwise_spatial_information(adata, prior=None)

For a more detailed example, check out the tutorial.

Interpreting the spatial information score

The method compute a score for every cell/spot that's in [0,1], like a correlation but typically much smaller, and sums them to arrive at a spatial information score that is then in [0, ncells]. It's possible to normalize for the number of cells by just dividing, but by default a pattern involving more cells is considered more spatially coherent, hence the sum.

Normalization

There are different ways spatial information can be computed. By default, no normalization is done and spatial information is computed on absolute counts. Uncertainty is incorporated using a Gamma-Poisson model.

If prior=None is used, the method makes no attempt to account for estimation uncertainty and computes spatial information directly on whatever is in adata.X.

The recommended way to run spatial_information is with some kind of normalized estimate of expression with some uncertainty estimation. There are two recommended ways of doing this: SCVI and Vanity.

SCVI

SCVI is a convenient and versatile probabilistic model of sequencing experiments, from which we can sample from the posterior to get normalized point estimates with uncertainty.

Using Maxspin with SCVI looks something like this:

import scvi
import numpy as np
from maxspin import spatial_information

scvi.model.SCVI.setup_anndata(adata)
model = scvi.model.SCVI(adata, n_latent=20)

# Sample log-expression values from the posterior.
posterior_samples = np.log(model.get_normalized_expression(return_numpy=True, return_mean=False, n_samples=20, library_size="latent"))
adata_scvi = adata.copy()
adata_scvi.X = np.mean(posterior_samples, axis=0)
adata_scvi.layers["std"] = np.std(posterior_samples, axis=0)

spatial_information(adata_scvi, prior="gaussian")

The tutorial has a more in depth example of using SCVI.

Vanity

I developed the normalization method vanity in part as convenient way to normalize spatial transcriptomics data in a way that provides uncertainty estimates. The preferred way of running vanity + maxspin is then:

from maxspin import spatial_information
from vanity import normalize_vanity

normalize_vanity(adata)
spatial_information(adata, prior="gaussian")

Compared to SCVI, this model more aggressively shrinks low expression genes, which might cause it to miss something very subtle, but is less likely to detect spurious patterns.