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Charting cellular differentiation trajectories with Ricci flow

Author

Listed:
  • Anthony Baptista

    (The British Library
    Queen Mary University of London)

  • Ben D. MacArthur

    (The British Library
    University of Southampton
    University of Southampton)

  • Christopher R. S. Banerji

    (The British Library
    University College London)

Abstract

Complex biological processes, such as cellular differentiation, require intricate rewiring of intra-cellular signalling networks. Previous characterisations revealed a raised network entropy underlies less differentiated and malignant cell states. A connection between entropy and Ricci curvature led to applications of discrete curvatures to biological networks. However, predicting dynamic biological network rewiring remains an open problem. Here we apply Ricci curvature and Ricci flow to biological network rewiring. By investigating the relationship between network entropy and Forman-Ricci curvature, theoretically and empirically on single-cell RNA-sequencing data, we demonstrate that the two measures do not always positively correlate, as previously suggested, and provide complementary rather than interchangeable information. We next employ Ricci flow to derive network rewiring trajectories from stem cells to differentiated cells, accurately predicting true intermediate time points in gene expression time courses. In summary, we present a differential geometry toolkit for understanding dynamic network rewiring during cellular differentiation and cancer.

Suggested Citation

  • Anthony Baptista & Ben D. MacArthur & Christopher R. S. Banerji, 2024. "Charting cellular differentiation trajectories with Ricci flow," Nature Communications, Nature, vol. 15(1), pages 1-14, December.
    • Handle: RePEc:nat:natcom:v:15:y:2024:i:1:d:10.1038_s41467-024-45889-6
    DOI: 10.1038/s41467-024-45889-6
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    References listed on IDEAS

    as
    1. Christopher R S Banerji & Simone Severini & Carlos Caldas & Andrew E Teschendorff, 2015. "Intra-Tumour Signalling Entropy Determines Clinical Outcome in Breast and Lung Cancer," PLOS Computational Biology, Public Library of Science, vol. 11(3), pages 1-23, March.
    2. Andrew E. Teschendorff & Tariq Enver, 2017. "Single-cell entropy for accurate estimation of differentiation potency from a cell’s transcriptome," Nature Communications, Nature, vol. 8(1), pages 1-15, August.
    Full references (including those not matched with items on IDEAS)

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