A network regularized linear model to infer spatial expression pattern for singlecells

Spatial gene-expression is a crucial determinant of cell fate and behavior. Recent imaging and sequencing-technology advancements have enabled scientists to develop new tools that use spatial information to measure gene-expression at close to single-cell levels. Yet, while Fluorescence In-situ Hybridization (FISH) can quantify transcript numbers at single-cell resolution, it is limited to a small number of genes. Similarly, slide-seq was designed to measure spatial-expression profiles at the single-cell level but has a relatively low gene-capture rate. And although single-cell RNA-seq enables deep cellular gene-expression profiling, it loses spatial information during sample-collection. These major limitations have stymied these methods broader application in the field. To overcome spatio-omics technologys limitations and better understand spatial patterns at single-cell resolution, we designed a computation algorithm that uses glmSMA to predict cell locations by integrating scRNA-seq data with a spatialomics reference atlas. We treated cell-mapping as a convex optimization problem by minimizing the differences between cellular-expression profiles and location-expression profiles with a L1 regularization and graph Laplacian based L2 regularization to ensure a sparse and smooth mapping. We validated the mapping results by reconstructing spatial-expression patterns of well-known marker genes in complex tissues, like the mouse cerebellum and hippocampus. We used the biological literature to verify that the reconstructed patterns can recapitulate cell-type and anatomy structures. Our work thus far shows that, together, we can use glmSMA to accurately assign single cells to their original reference-atlas locations.