Modeling Cell-Cell Interactions from Spatial Molecular Data with Spatial Variance Component Analysis

Abstract

Technological advances enable assaying multiplexed spatially resolved RNA and protein expression profiling of individual cells, thereby capturing molecular variations in physiological contexts. While these methods are increasingly accessible, computational approaches for studying the interplay of the spatial structure of tissues and cell-cell heterogeneity are only beginning to emerge. Here, we present spatial variance component analysis (SVCA), a computational framework for the analysis of spatial molecular data. SVCA enables quantifying different dimensions of spatial variation and in particular quantifies the effect of cell-cell interactions on gene expression. In a breast cancer Imaging Mass Cytometry dataset, our model yields interpretable spatial variance signatures, which reveal cell-cell interactions as a major driver of protein expression heterogeneity. Applied to high-dimensional imaging-derived RNA data, SVCA identifies plausible gene families that are linked to cell-cell interactions. SVCA is available as a free software tool that can be widely applied to spatial data from different technologies.

Keywords: Gaussian process; multiplexed imaging; random effect model.

Graphical abstract

Figure 1

Spatial Variance Component Analysis (SVCA): A Framework for Decomposing Spatial and Non-spatial Sources of Variation (A) SVCA decomposes the variability of individual genes into (1) cell intrinsic effects (due to differences in intrinsic cell type or state, blue); (2) general environmental effects that capture expression differences due to non-specific local factors (green); and (3) a cell-cell interaction effects that capture differences in expression level attributable to different cellular composition of a cell’s neighborhood (yellow). (B) SVCA builds on the random effect framework to model additive contributions of these components. See Figure S1 and STAR Methods for details on the definition of the corresponding covariance terms. (C) SVCA output: gene-level breakdown of the proportion of variance attributable to different components.

Figure 2

SVCA Is More Conservative and Robust than Alternative Linear Models (A) Simulation approach: the expression profile of a simulated target gene Y is generated as a linear combination of the empirically observed cell expression profile of all genes (X) and a linear combination of the $N_{nn}$ first neighbors expression profiles (X) (here, $N_{nn}$ = 4). The effect of the first neighbors is weighted by the function of their distance to the focal cell. (B) Simulation of cell mis-segmentation effects. Pairs of cells are randomly selected as mis-segmented with probability inversely proportional to the square of their distance (STAR Methods). (C) Inferred cell-cell interactions versus simulated true values for $N_{nn}=4$ and ${\mathit{\epsilon }}_{mis}=0.2$. (D) Error in the inferred cell-cell interactions as a function of the simulated interaction component. (E) Spurious cell-cell interactions as a function of the simulated mis-segmentation effect (as in B). (F) Distribution of the cell-cell interaction error across as a function of the number of neighbors ($N_{nn}$).

Figure 3

Application of SVCA to 46 Breast Cancer Samples Profiled Using IMC (A) Bottom panel: SVCA signatures for 26 proteins. Shown are averages of the fraction of variance explained by intrinsic effects, environmental effects, and cell-cell interactions, across 46 images. Proteins are ordered by the magnitude of the cell-cell interaction component. Top panel: number of images with a cell-cell interaction component greater than 10% variance. (B) Accuracy of SVCA and alternative models for predicting gene expression out of sample (r² assessed using 5-fold cross validation). Shown are average coefficients of determination (r²) between predicted and observed gene expression profiles, averaged across proteins and images. Error bars correspond to ±1 SD across images and proteins. (C) First two principal components for 38 images with clinical annotations, calculated based on the spatial variance signature (variance break down as in A for each protein), with individual images colored by the clinical tumor grade. (D) Loadings of the principal components as in (C), displaying the relevance of individual proteins and types of variance components.

Figure 4

Application of SVCA to 21 Images Profiled Using seqFISH (A) Left: SVCA signatures for the 20 genes with the largest cell-cell interaction component. Shown are averages of the fraction of variance explained by intrinsic effects, environmental effects, and cell-cell interactions, across 21 images. Genes are ordered by the magnitude of the cell-cell interaction component. Right: variance estimate distribution across images and genes for all 249 genes contained in this dataset (violin plots). (B) Spatial organization of the mouse hippocampus with dots corresponding to individual images. Colors and shapes denote regions using the classification as in Shah et al. (2017). (C) First two principal components of the spatial variance signatures for individual images from the DG, the dorsal region, and the ventral region. Color and shape represent the location of the biopsy in the hippocampus. (D) First two principal components of the spatial variance signatures for all 21 images. (E) Enrichment of gene categories for cell-cell interactions (top) and intrinsic effect (bottom) (negative log Benjamini-Hochberg adjusted p values).