Zoo guide to network embedding

Baptista, A; Sánchez-García, R J; Baudot, A; Bianconi, G

doi:10.1088/2632-072x/ad0e23

Cited by 4 publications

(1 citation statement)

References 198 publications

(236 reference statements)

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“…However, at the genome-wide scale, we do not have this deep understanding of intra-cellular interactions and instead rely on sparse graphical representations, known as biological networks, which can be weighted by biological samples to describe relevant dynamics 9 . The notion that a (weighted) network has an underlying geometry is well-studied and there are numerous methodologies for network embedding 14 , with application to biological networks 15 , 16 . Recently, discrete analogues of tools from differential geometry 17 , 18 , a rich mathematical field for studying manifolds and their curvatures, have been applied to the study of biological networks 19 – 23 .…”

Section: Introductionmentioning

confidence: 99%

Charting cellular differentiation trajectories with Ricci flow

Baptista,

MacArthur,

Banerji

2024

Nat Commun

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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.

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Section: Introductionmentioning

confidence: 99%

Charting cellular differentiation trajectories with Ricci flow

Baptista,

MacArthur,

Banerji

2024

Nat Commun

Self Cite

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Charting cellular differentiation trajectories with Ricci flow

Baptista¹,

MacArthur²,

Banerji³

2023

Preprint

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

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Network science: Ising states of matter

Sun,

Panda,

Verdel

et al. 2024

Phys. Rev. E

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Network science provides very powerful tools for extracting information from interacting data. Although recently the unsupervised detection of phases of matter using machine learning has raised significant interest, the full prediction power of network science has not yet been systematically explored in this context. Here we fill this gap by providing an in-depth statistical, combinatorial, geometrical, and topological characterization of 2D Ising snapshot networks (IsingNets) extracted from Monte Carlo simulations of the 2D Ising model at different temperatures, going across the phase transition. Our analysis reveals the complex organization properties of IsingNets in both the ferromagnetic and paramagnetic phases and demonstrates the significant deviations of the IsingNets with respect to randomized null models. In particular percolation properties of the IsingNets reflect the existence of the symmetry between configurations with opposite magnetization below the critical temperature and the very compact nature of the two emerging giant clusters revealed by our persistent homology analysis of the IsingNets. Moreover, the IsingNets display a very broad degree distribution and significant degree-degree correlations and weight-degree correlations demonstrating that they encode relevant information present in the configuration space of the 2D Ising model. The geometrical organization of the critical IsingNets is reflected in their spectral properties deviating from the one of the null model. This work reveals the important insights that network science can bring to the characterization of phases of matter. The set of tools described hereby can be applied as well to numerical and experimental data. Published by the American Physical Society 2024

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Zoo guide to network embedding

Cited by 4 publications

References 198 publications

Charting cellular differentiation trajectories with Ricci flow

Charting cellular differentiation trajectories with Ricci flow

Charting cellular differentiation trajectories with Ricci flow

Network science: Ising states of matter

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