# GASTON-Mix: a unified model of spatial gradients and domains using spatial mixture-of-experts

## TL;DR

GASTON-Mix is a new machine learning method that identifies both discrete tissue regions and continuous gene expression gradients within them from spatial transcriptomics data.

## Contribution

GASTON-Mix introduces a spatial mixture-of-experts model that jointly identifies spatial domains and continuous gradients without restrictive geometric assumptions.

## Key findings

- GASTON-Mix outperforms existing methods in identifying spatial domains and gradients in simulated and real data.
- The method reveals spatial gradients in brain regions linked to social behavior and in tumor microenvironments involving hypoxia and TNF-α signaling.

## Abstract

Gene expression varies across a tissue due to both the organization of the tissue into spatial domains, i.e. discrete regions of a tissue with distinct cell type composition, and continuous spatial gradients of gene expression within different spatial domains. Spatially resolved transcriptomics (SRT) technologies provide high-throughput measurements of gene expression in a tissue slice, enabling the characterization of spatial gradients and domains. However, existing computational methods for quantifying spatial variation in gene expression either model only spatial domains—and do not account for continuous gradients of expression—or require restrictive geometric assumptions on the spatial domains and spatial gradients that do not hold for many complex tissues.

We introduce GASTON-Mix, a machine learning algorithm to identify both spatial domains and spatial gradients within each domain from SRT data. GASTON-Mix extends the mixture-of-experts (MoE) deep learning framework to a spatial MoE model, combining the clustering component of the MoE model with a neural field model that learns a separate 1D coordinate (“isodepth”) within each domain. The spatial MoE is capable of representing any geometric arrangement of spatial domains in a tissue, and the isodepth coordinates define continuous gradients of gene expression within each domain. We show using simulations and real data that GASTON-Mix identifies spatial domains and spatial gradients of gene expression more accurately than existing methods. GASTON-Mix reveals spatial gradients in the striatum and lateral septum that regulate complex social behavior, and GASTON-Mix reveals localized spatial gradients of hypoxia and TNF-α signaling in the tumor microenvironment.

GASTON-Mix is available at https://github.com/raphael-group/GASTON-Mix.