Speaker
Description
Spatial relationships in multi-species data can shape biological system behaviors, from cancer progression in pathology to coral reef resilience in ecology. We propose a topological data analysis framework to quantify higher-order spatial relationships in multi-species point cloud data \cite{Natarajan2026}.
Our approach is applicable to the analysis of interactions between three or even more species, capturing both (i) the presence of topological features in the data---such as connected components, loops and voids---and (ii) the combinatorial arrangement of these features across multiple subsets of species.
The method leverages recent developments in chromatic topological data analysis \cite{Montesano2026}, introducing a new construction called the \emph{$k$-chromatic gluing map}, and providing interpretable descriptors.
We validate our framework on two datasets: (1) synthetic data from an agent-based model of the tumor micro-environment \cite{bull2023}, where our results are consistent with existing analysis by Stolz et al.~\cite{stolz2024}; and (2) a colorectal cancer dataset, where the method recovers biologically reasonable patterns, including the importance of periostin--macrophage spatial interactions (consistent with existing literature \cite{zhou2015}), as well as potentially important three-way interactions among macrophages, neutrophils, periostin, and SMA (interactions that are not directly captured by pairwise analysis).
Bibliography
@article{Natarajan2026,
title={Topology of Multi-species Localization},
author={Natarajan, Abhinav and Chaplin, Thomas and Bull, Joshua A and Mulholland-Illingworth, Eoghan J and Leedham, Simon J and Byrne, Helen M and Jimenez, Maria-Jose and Harrington, Heather A},
journal={arXiv preprint arXiv:2603.03237},
year={2026}
}
@article{Montesano2026,
title = {Chromatic Alpha Complexes},
author = {Cultrera di Montesano, Sebastiano and Draganov, Ond\v{r}ej and Edelsbrunner, Herbert and Saghafian, Morteza},
journal = {Foundations of Data Science},
year = {2026},
volume = {8},
pages = {30--62},
doi = {10.3934/fods.2025003},
publisher = {American Institute of Mathematical Sciences}
}
@article{bull2023,
title = {Quantification of spatial and phenotypic heterogeneity in an agent-based model of tumour-macrophage interactions},
author = {Bull, Joshua A and Byrne, Helen M},
journal = {PLOS Computational Biology},
volume = {19},
number = {3},
pages = {e1010994},
year = {2023},
publisher = {Public Library of Science San Francisco, CA USA}
}
@article{zhou2015,
title = {Periostin secreted by glioblastoma stem cells recruits M2 tumour-associated macrophages and promotes malignant growth},
volume = {17},
rights = {2014 Springer Nature Limited},
issn = {1476-4679},
doi = {10.1038/ncb3090},
pages = {170--182},
number = {2},
journal = {Nature Cell Biology},
shortjournal = {Nat Cell Biol},
publisher = {Nature Publishing Group},
author = {Zhou, Wenchao and Ke, Susan Q. and Huang, Zhi and Flavahan, William and Fang, Xiaoguang and Paul, Jeremy and Wu, Ling and Sloan, Andrew E. and {McLendon}, Roger E. and Li, Xiaoxia and Rich, Jeremy N. and Bao, Shideng},
urldate = {2026-02-11},
date = {2015-02},
year = {2015}
}
@article{stolz2024,
title = {Relational persistent homology for multispecies data with application to the tumor microenvironment},
author = {Stolz, Bernadette J and Dhesi, Jagdeep and Bull, Joshua A and Harrington, Heather A and Byrne, Helen M and Yoon, Iris HR},
journal = {Bulletin of Mathematical Biology},
volume = {86},
number = {11},
pages = {128},
year = {2024},
publisher = {Springer}
}
