sepal: identifying transcript profiles with spatial patterns by diffusion-based modeling

Abstract

Motivation Collection of spatial signals in large numbers has become a routine task in multiple omicsfields, but parsing of these rich data sets still pose certain challenges. In whole or near-full transcriptome spatial techniques, spurious expression profiles are intermixed with those exhibiting an organized structure. To distinguish profiles with spatial patterns from the background noise, a metric that enables quantification of spatial structure is desirable. Current methods designed for similar purposes tend to be built around a framework of statistical hypothesis testing, hence we were compelled to explore a fundamentally different strategy. Results We propose an unexplored approach to analyze spatial transcriptomics data, simulating diffusion of individual transcripts to extract genes with spatial patterns. The method performed as expected when presented with synthetic data. When applied to real data, it identified genes with distinct spatial profiles, involved in key biological processes or characteristic for certain cell types. Compared to existing methods, ours seemed to be less informed by the genes’ expression levels and showed better time performance when run with multiple cores. Availability Open-source Python package with a command line interface (CLI), freely available at https://github.com/almaan/sepal under a MIT licence. A mirror of the GitHub repository can be found at Zenodo, doi: 10.5281/zenodo.4573237. Supplementary information Supplementary data are available at Bioinformatics online.

SpatialCorr: Identifying Gene Sets with Spatially Varying Correlation Structure

“…A fundamental task in ST experiments is identifying genes with expression levels that vary across a tissue sample, and a number of differential expression (DE) methods have been developed toward this end (Andersson and Lundeberg, 2021; Edsgärd et al, 2018; Li et al, 2021; Sun et al, 2020; Svensson et al, 2018). Although a critical first step, DE measures do not capture many important types of differential regulation.…”

“…A first step in ST data analysis is identifying genes with expression that varies spatially, so-called spatially variable (SV) genes, and robust statistical methods exist to address this challenge (Andersson and Lundeberg, 2021; Edsgärd et al, 2018; Li et al, 2021; Sun et al, 2020; Svensson et al, 2018). While useful, SV genes alone do not fully describe, and in many cases cannot capture, important signals present in ST data.…”

Squidpy: a scalable framework for spatial omics analysis

“…4d; 'Fiber tract' and 'Hypothalamus 2' for Mobp and 'Pyramidal layers' and 'Pyramidal layers/Dentate gyrus' for Nrgn). An orthogonal method for the same task, Sepal 42 ranks Krt18 as a top spatially variable gene, which shows a distinct expression in a subset of the 'Lateral ventricle' cluster (Fig. 4d and Supplementary Fig.…”

“…Test statistics and P values (computed from a permutation-based test or via analytic formulation, similar to libpysal 58 sq.gr.spatial_autocorr(adata, cluster_key="<cluster_key>",mode="<moran|geary>") Sepal. Sepal is a recently developed method for spatially variable genes identification 42 . It simulates a diffusion process and evaluates the time it takes to reach a uniform state (convergence).…”

“…It is a formulation of Fick's second law to a regular graph (grid). It is defined as: u (x, y, t + dt) = u (x, y, t) + DΔu (x, y, t) dt (7) Where u(x,y,t) is the concentration (for example gene expression on a node in x,y coordinates), D is the diffusion coefficient, t is the update time and ∆(u(x,y,t)dt) is the laplacian on the graph (see elsewhere 42 for an extended formulation).…”