C-SIDE for Cell-type-specific Spatial DE

Posted on Nov 12, 2024 (Update: Nov 23, 2024)

Tags: Spatial Transcriptomics, Differential Expression, Poisson

This note is for Cable, D. M., Murray, E., Shanmugam, V., Zhang, S., Zou, L. S., Diao, M., Chen, H., Macosko, E. Z., Irizarry, R. A., & Chen, F. (2022). Cell type-specific inference of differential expression in spatial transcriptomics. Nature Methods, 19(9), 1076–1087. https://doi.org/10.1038/s41592-022-01575-3

cell type-specific inference of differential expression in spatial transcriptomics

a central problem: detect DE genes within cell types across tissue context

Challenges to learn DE:

changing cell type composition across space and measurement pixels detecting transcripts from multiple cell types

C-SIDE: identifies cell type-specific DE in spatial transcriptomics, accounting for localization of other cell types

model gene expression as an additive mixture across cell types of log-linear cell type-specific expression functions

current methods for DE in spatial transcriptomics fall into two categories

• nonparametric: not use constrained hypotheses about gene expression patterns, but rather fit general smooth spatial patterns of gene expression
  • some not consider cell types, others operate on individual cell types
• parametric
  • no general parametric framework is currently available

an important challenge unaddressed by current spatial transcriptomics DE methods:

• observations from cell type mixtures

sequencing-based, RNA-capture spatial transcriptomics technologies, such as Visium, GeoMx and Slide-seq, can capture multiple cell types on individual measurement pixels

imaging-based spatial transcriptomics technologies, such as MERFISH, ExSeq, and STARmap, have the potential to achieve single-cell resolution, these technologies may encounter mixing across cell types due to diffusion or imperfect cellular segmentation

the paper introduce cell type-specific inference of DE (C-SIDE), a general parametric statistical method that estimates cell type-specific DE in the context of cell type mixtures

1. estimate cell type proportions on each pixel using a cell type-annotated scRNA-seq reference
2. fit a parametric model, using predefined covariates such as spatial location or cellular microenvironment, that accounts for cell type differences to obtain cell type-specific DE estimates and corresponding standard errors
   1. the model accounts for sampling noise, gene-specific overdispersion, multiple hypothesis testing and platform effects between the scRNA-seq reference and the spatial data
   2. permits statistical inference across multiple experimental samples and/or replicates

C-SIDE inputs one or more experimental samples of spatial transcriptomics data, consisting of $Y_{i,j,g}$ as the observed RNA counts for pixel $i$, gene $j$ and experimental sample $g$

assume Poisson sampling

\[Y_{i,j,g}\mid \lambda_{i,j,g} \approx \text{Poisson}(N_{ig}\lambda_{i,j,g})\]

• $\lambda_{ijg}$: expected count
• $N_{ig}$: total transcript count (e.g., total unique molecular identifiers, UMIs)

accounting for platform effects and other sources of technical and natural variability, assume $\lambda_{ijg}$ is a mixture of $K$ cell type expression profiles, defined by

\[\log (\lambda_{ijg}) = \log\left( \sum_{k=1}^K \beta_{ikg}\mu_{ikjg} \right) + \gamma_{jg} + \epsilon_{ijg}\]

• $\mu_{ikjg}$: cell type-specific expected gene expression rate
• $\beta_{ikg}$: proportion of cell type
• $\gamma_{jg}$: gene-specific random effect that accounts for platform variability
• $\epsilon_{ijg}$: random effect to account for gene-specific overdispersion

account for cell type-specific DE, model across pixel locations the log of the cell type-specific profiles $\mu_{ikjg}$ as a linear combination of $L$ covariates used to explain DE:

\[\log(\mu_{ikjg}) = \alpha_{0kjg} + \sum_{\ell=1}^Lx_{ilg}\alpha_{\ell kjg}\]

• $x$: predefined covariates that explain DE
• $\alpha$: DE effect size of covariate $\ell$ for gene $j$ in cell type $k$ for sample $g$