stTrace: Detecting Spatial-Temporal Domains from spatial transcriptome to Trace Developmental Path

Development is essential for the growth and functional maintenance of organisms. Investigating the development process is vital for uncovering the formation of complex biological systems. However, current approaches to studying development from gene expression rely primarily on single-cell gene expression data to infer developmental trajectories, neglecting the spatial distribution of cells within tissues and their interactions. Although spatial transcriptomics provides spatial context for gene expression, existing algorithms focus mainly on identifying spatial regions without further exploring their developmental connections. In this study, we propose an algorithm for detecting spatial-temporal domains in tissue to trace developmental path (stTrace) using spatial transcriptomics. stTrace integrates the degree of cell development, gene expression, and spatial location to identify "spatial-temporal domains", regions where cells share similar functions and developmental stages within the tissue. Moreover, hierarchical relationships exist among these regions, reflecting developmental connections between cells in the tissue. Our experiments on mouse embryo and human breast cancer data revealed that stTrace can detect more refined regions than traditional spatial domain identification algorithms. Furthermore, the directions of developmental paths inferred from hierarchical relationships are consistent with the dynamic trajectories derived from single-cell velocity. Key pointsO_LIWe proposed spatial-temporal domain, which refers to spatially continuous regions where cells exhibit similar gene expression patterns, related functions, and close developmental levels. C_LIO_LIWe present stTrace, a computational framework for identifying spatial-temporal domains by iteratively optimizing two objectives: minimizing Structure Entropy to capture functional similarity and hierarchy, and maximizing the Silhouette Coefficient to ensure temporal compactness. C_LIO_LIIn both mouse embryo and human breast cancer datasets, spatial-temporal domains align better with H&E-stained images and and have better compactness in developmental level. C_LIO_LIstTrace detected developmental paths that are well-mapped with cells temporal information like single-cell velocity and trajectories and application show the usage in studying embryo development and cancer invasion. C_LI