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Abstract Shape is data and data is shape. Biologists are accustomed to thinking about how the shape of biomolecules, cells, tissues, and organisms arise from the effects of genetics, development, and the environment. Less often do we consider that data itself has shape and structure, or that it is possible to measure the shape of data and analyze it. Here, we review applications of topological data analysis (TDA) to biology in a way accessible to biologists and applied mathematicians alike. TDA uses principles from algebraic topology to comprehensively measure shape in data sets. Using a function that relates the similarity of data points to each other, we can monitor the evolution of topological features—connected components, loops, and voids. This evolution, a topological signature, concisely summarizes large, complex data sets. We first provide a TDA primer for biologists before exploring the use of TDA across biological sub‐disciplines, spanning structural biology, molecular biology, evolution, and development. We end by comparing and contrasting different TDA approaches and the potential for their use in biology. The vision of TDA, that data are shape and shape is data, will be relevant as biology transitions into a data‐driven era where the meaningful interpretation of large data sets is a limiting factor.
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This content will become publicly available on November 28, 2025
TopoLoop: A new tool for chromatin loop detection in live cells via single-particle tracking
We present a novel method for identifying topological features of chromatin domains in live cells using single-particle tracking and topological data analysis (TDA). By applying TDA to particle trajectories, we can effectively detect complex spatial patterns, such as loops, that are often missed by traditional time series analysis. Using simulations of polymer bead–spring chains, we have validated the accuracy of our method and determined its limitations for detecting loops. Our approach offers a promising avenue for exploring the topological complexity of chromatin in living cells using TDA techniques.
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- Award ID(s):
- 1751339
- PAR ID:
- 10582526
- Publisher / Repository:
- AIP Publishing
- Date Published:
- Journal Name:
- The Journal of Chemical Physics
- Volume:
- 161
- Issue:
- 20
- ISSN:
- 0021-9606
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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