REVIEW article
Front. Immunol.
Sec. Systems Immunology
Volume 16 - 2025 | doi: 10.3389/fimmu.2025.1615278
This article is part of the Research TopicComputational Modeling and Applications of Systems Immunology in Hispanic AmericaView all articles
Topological data analysis in single cell biology
Provisionally accepted- Computational Genomics, National Institute of Genomic Medicine (INMEGEN), Mexico City, Mexico
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Single-cell technologies have revolutionized our ability to interrogate biological systems at unprecedented resolution, revealing complex cellular heterogeneity and dynamic processes that underlie development, disease, and immune responses. However, the high dimensionality and nonlinear structure of single-cell data present substantial analytical challenges. Topological data analysis offers a powerful mathematical framework for capturing the intrinsic shape of data, providing novel insights that complement and extend traditional statistical and machine learning methods. By leveraging tools such as persistent homology and the Mapper algorithm, TDA enables the detection of subtle, multiscale patterns -including rare cell populations, transitional states, and branching trajectories -that are often obscured by conventional approaches. In this review, we explore the theoretical foundations of topological data analysis and examine its emerging applications across single-cell transcriptomics, proteomics, and spatial biology. We highlight how this approach can unveil previously unrecognized biological phenomena, from alternative differentiation paths to complex tissue architectures, and discuss the growing ecosystem of computational tools that support its use. As single-cell datasets become increasingly large and multimodal, topological data analysis stands out as a uniquely robust and interpretable approach, with the potential to deepen our understanding of cellular identity and function in health and disease. TDA is specially suited for fields such as systems immunology since it can capture the complex, nonlinear structures inherent in high-dimensional immune data helping to identify distinct immune cell states, differentiation pathways, and dynamic responses to infection or therapy. This topological perspective complements traditional statistical approaches, providing a robust, scale-invariant framework for uncovering hidden organization within the immune system's complexity.
Keywords: topological data analysis, Single cell biology, persistence homology, Simplicial complexes, Cell type assignment, Systems immunology
Received: 21 Apr 2025; Accepted: 05 Aug 2025.
Copyright: © 2025 Hernandez-Lemus. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence: Enrique Hernandez-Lemus, Computational Genomics, National Institute of Genomic Medicine (INMEGEN), Mexico City, Mexico
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