Persistence diagrams as morphological signatures of cells: A method to measure and compare cells within a population
Yossi Bokor Bleile, Pooja Yadav, Patrice Koehl, Florian Rehfeldt
Abstract
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.
Introduction
Cells are the basic unit of life. Understanding how they grow, divide, die, and change shape is of central importance in virtually all fields of cell biology, including immunology, cancer biology, pathology, tissue, and organ morphogenesis during development, as well as in many other areas of the life sciences.
Materials and Methods
3.1 Human Mesenchymal stem cells
Adult human mesenchymal stem cells (hMSCs) were purchased from Lonza ( Basel, Switzerland) and cultured in low glucose DMEM (Gibco, ) supplemented with 10% FBS (Sigma-Aldrich, Ref. F7524), and 1% penicillin/streptomycin (Gibco, #15140122) in regular tissue culture treated flasks (greiner Bio-One, 75cm2, at C and 5.0% CO2.
Results and Discussion
The result section serves three purposes:
- a) Identification of subpopulations in a set of cells. We report how our method PH for comparing the shapes of cells can be used to identify unusual cells (i.e., outliers) and subpopulations within a cell population.
- b) Assessing the performance of PH for clustering cells. We check how PH can distinguish two different cell types when the true partitioning is known.
- c) Comparing PH with existing methods for comparing cell contours. We compare PH with an aspect ratio distance, a Fourier descriptor distance, and a elastic distance.
Acknowledgments
We thank Stephan Huckemann, Katharine Turner, Benjamin Eltzner, Stephan Tillmann, Fariza Rashid, Vanessa Robins, and Lamiae Azizi for many useful discussions at various stages of this project. FR and PY gratefully acknowledge Matthias Weiss (Experimental Physics I, University of Bayreuth, Germany) for granting access to cell culture and laboratories, as well as funding consumables and the fruitful discussion that contributed to this work.
Citation: Bokor Bleile Y, Yadav P, Koehl P, Rehfeldt F (2026) Persistence diagrams as morphological signatures of cells: A method to measure and compare cells within a population. PLoS Comput Biol 22(1): e1013890. https://doi.org/10.1371/journal.pcbi.1013890
Editor: Anna Grosberg, UCI BME: University of California Irvine Department of Biomedical Engineering, UNITED STATES OF AMERICA
Received: September 2, 2025; Accepted: January 6, 2026; Published: January 28, 2026
Copyright: © 2026 Bleile et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Data Availability: The code for PH is available on Github https://github.com/yossibokorbleile/correa as well as an archive on Zenodo (https://doi.org/10.5281/zenodo.17968765). All images used in this paper, as well as the code to analyse them, are available on GitHub PDaMSoC-data, which is also archived on Zenodo (10.5281/zenodo.17709489. In the repository, there are 4 directories (X1, X2, X3, Y1) containing data sets, with X1, X2, X3 consisting of populations of hMSCs and Y1 a population of HeLa cells. In this paper, we presented analysis of the datasets X1 and Y1. We did analyse X2 and X3, but did not obtain results that were distinctly different from X1.
Funding: This research was funded in whole or in part by the Austrian Science Fund (FWF) (ESP9584724 to YBB). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing interests: The authors have declared that no competing interests exist.
