Persistence diagrams as morphological signatures of cells: A method to measure and compare cells within a population

Quantifying cell morphology is central to understanding cellular regulation, fate, and heterogeneity, yet conventional image-based analyses often struggle with diverse or irregular shapes. We present a computational framework that uses topological data analysis to characterise and compare single-cell morphologies from fluorescence microscopy. Each cell is represented by its contour together with the position of its nucleus, from which we construct a filtration based on a radial distance function and derive a persistence diagram encoding the shape’s topological evolution. The similarity between two cells is quantified using the 2-Wasserstein distance between their diagrams, yielding a shape distance we call the PH distance. We apply this method to two representative experimental systems—primary human mesenchymal stem cells (hMSCs) and HeLa cells—and show that PH distances enable the detection of outliers in those systems, the identification of sub-populations, and the quantification of shape heterogeneity. We benchmark PH against three established contour-based distances (aspect ratio, Fourier descriptors, and elastic shape analysis) and show that PH offers better separation between cell types and greater robustness when clustering heterogeneous populations. Together, these results demonstrate that persistent-homology-based signatures provide a principled and sensitive approach for analysing cell morphology in settings where traditional geometric or image-based descriptors are insufficient.Author summary: Cell shape carries important information about how cells grow, respond to their environment, and differ from one another. However, cell populations often contain substantial natural variability, which makes it difficult for traditional image-analysis methods to reliably compare their shapes. In this study, we introduce a new way to measure and compare cell morphology using a mathematical approach known as topological data analysis. Our method describes each cell by the outline of its membrane together with the position of its nucleus, and converts this information into a compact shape signature that can be compared across thousands of cells. We apply this approach to two widely studied systems—human mesenchymal stem cells and HeLa cells—and show that it can detect unusual cell shapes, reveal sub-populations within heterogeneous samples, and quantify how variable a cell population truly is. We also compare our method with several commonly used shape-comparison techniques and find that it provides clearer separation between distinct cell types and more reliable clustering. Overall, this framework offers a robust and interpretable way to analyse cell morphology and may help researchers better understand the diversity and behaviour of cells in biological experiments.