Spatially varying graph estimation for spatial transcriptomics cancer data

Modern spatial transcriptomic profiling techniques facilitate spatially resolved, high-dimensional assessment of cellular gene transcription across the tumor domain. The characterization of spatially varying gene networks enables the discovery of heterogeneous regulatory patterns and biological mechanisms underlying cancer etiology. We propose a spatial Graphical Regression (sGR) model to infer spatially varying graphs for high-resolution multivariate spatial data. Unlike existing graphical models, sGR explicitly incorporates spatial information to infer non-linear conditional dependencies through Gaussian processes. It conducts sparse estimation and selection of spatially varying edges, at both spatial and sub-spatial levels. Extensive simulation studies illustrate the profitability of sGR for spatial graph structural recovery and estimation accuracy. Our methods are motivated by and applied to two spatial transcriptomics data sets in breast and prostate cancer, to investigate spatially varying gene connectivity patterns across the tumor micro-environment. Our findings reveal several novel spatial interactions between genes related to immune activation and carcinogenesis regulation such as CD19 in breast cancer and ARHGAP family in prostate cancer. We also provide a modular software package for fitting and visualization of spatially varying graphs.