Differential Analysis of Gene Spatial Organisation with Minkowski Functionals and Tensors

Abstract

Spatial transcriptomics measures gene expression together with transcript coordinates in tissues. To date, comparing spatial gene expression patterns within and across samples remains challenging. We present here minkiPy, a geometric framework that computes, for each gene, a compact profile of morphological and topological descriptors based on Minkowski functionals and tensors. These profiles are defined in a shared feature space, enabling direct comparison of spatial organisation across genes, samples, and conditions, and the ranking of genes by the magnitude of their spatial reorganisation. We applied minkiPy to a MERFISH dataset of control and facioscapulohumeral muscular dystrophy myoblast cultures and to a Visium HD dataset of colorectal cancer and normal adjacent tissues, illustrating its utility across tissue types and spatial transcriptomics platforms. minkiPy is an open-source Python library available at https://github.com/BAUDOTlab/minkiPy.