Julia Brettschneider (University of Warwick) – Geometry-Aware Permutation Tests for Spatial and Spatiotemporal Point-Process Data in Microscopy

In many real-world settings, spatial point processes provide a natural framework for modelling data such as molecular locations, structural features within cells or materials, or dead pixels on X-ray detectors. Comparing the empirical distributions of these point patterns across populations can give insight into the underlying generative mechanisms.

We employ geometry-aware nonparametric methods and illustrate them through two applications to confocal microscopy data.

Firstly, we analyse the spatial locations or microtubules within K-fibers in cells with an overexpressed protein (TACC3) versus control. This sheds light on the interplay between the structures and chemicals involved in cell division (mitosis), a fundamental process for most biological organisms and highly relevant for cancer research.

Second, we study the spatiotemporal dependencies between protein species. We construct an estimator of their bulk movement using the earth mover’s distance and propose a test statistic that aggregates local movement differences across a spatial partition. Our method is built on a novel null-hypothesis framework combining between- and within-sample independence of bulk movement patterns with distributional invariance under a geometrically defined subgroup of permutations. We apply this to EB3–TACC3 experiments in microtubules, providing evidence for the colocalisation of these proteins.