Harmonic representations of regions and interactions in spatial transcriptomics

Abstract

Spatial transcriptomics technologies enable unbiased measurement of the cell-cell interactions underlying tissue structure and function. However, most unsupervised methods instead focus on identifying tissue regions, representing them as positively covarying low-frequency spatial patterns of gene expression over the tissue. Here, we extend this frequency-based (i.e. harmonic) approach to show that negatively covarying high frequencies represent interactions. Similarly, combinations of low and high frequencies represent interactions along large length scales, or, equivalently, region boundaries. The resulting equations further reveal a duality in which regions and interactions are complementary representations of the same underlying information, each with unique strengths and weaknesses. We demonstrate these concepts in multiple datasets from human lymph node, human tonsil, and mouse models of Alzheimers disease. Altogether, this work offers a conceptually consistent quantitative framework for spatial transcriptomics.