Chroconet mini-symposium January 12th, 2024 (visio)

1. Racines en haut et feuilles en bas : les arbres en maths
Nathalie Vialaneix
nathalie.vialaneix@inrae.fr
http://www.nathalievialaneix.eu
Mini Symposium ChrocoNet
10 novembre 2023

2. Outline
Clustering based on Hi-C matrices
Differential analysis of Hi-C matrices
Work in progress
Chroconet – 10/11/2023
10 novembre 2023 / Nathalie Vialaneix
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3. Hi-C matrices and hierarchical clustering [Neuvial et al., 2023a]
Idea used in: [Fraser et al., 2015,
Soler-Vila et al., 2020, Zhang et al., 2021]
among others
Chroconet – 10/11/2023
10 novembre 2023 / Nathalie Vialaneix
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4. Clustering based on Hi-C matrices
Summary of the work performed in: Projet CNRS SCALES (with P. Neuvial & S.
Foissac). Thèse INRAE/Inria Nathanaël Randriamihamison (also with M. Chavent)
Chroconet – 10/11/2023
10 novembre 2023 / Nathalie Vialaneix
p. 4

5. Clustering based on Hi-C matrices
Summary of the work performed in: Projet CNRS SCALES (with P. Neuvial & S.
Foissac). Thèse INRAE/Inria Nathanaël Randriamihamison (also with M. Chavent)
How is hierarchical clustering usually performed on Hi-C matrices?
1. a bin =
2. Euclidean distance + HC
Chroconet – 10/11/2023
10 novembre 2023 / Nathalie Vialaneix
p. 4

6. Clustering based on Hi-C matrices
Summary of the work performed in: Projet CNRS SCALES (with P. Neuvial & S.
Foissac). Thèse INRAE/Inria Nathanaël Randriamihamison (also with M. Chavent)
Why is it not satisfactory?
1. Hi-C matrices are already distances!
2. sparse vs full representations
Chroconet – 10/11/2023
10 novembre 2023 / Nathalie Vialaneix
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7. Clustering based on Hi-C matrices
What did we propose?
1. extend Ward’s HC to similarity matrices as Hi-C with adjacency
constraint [Randriamihamison et al., 2021]
2. study of the mathematical properties
[Randriamihamison et al., 2021]
3. study of reversals in practice on Hi-C matrices
[Randriamihamison et al., 2021]
4. fast version using a band computation [Ambroise et al., 2019]
Chroconet – 10/11/2023
10 novembre 2023 / Nathalie Vialaneix
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8. R package adjclust
▶ fully compatible with HiTC format
▶ very flexible (and beautiful!) plots
Chroconet – 10/11/2023
10 novembre 2023 / Nathalie Vialaneix
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9. Outline
Clustering based on Hi-C matrices
Differential analysis of Hi-C matrices
Work in progress
Chroconet – 10/11/2023
10 novembre 2023 / Nathalie Vialaneix
p. 6

10. Pig3D genome project (taken from SF’s slides)
[Marti-Marimon et al., 2018]
Chroconet – 10/11/2023
10 novembre 2023 / Nathalie Vialaneix
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11. Problem of Hi-C differential analysis approaches
Problem of Hi-C differential analysis approaches:
Chroconet – 10/11/2023
10 novembre 2023 / Nathalie Vialaneix
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12. A new differential analysis method: treediff (taken from SF’s
slides)
Chroconet – 10/11/2023
10 novembre 2023 / Nathalie Vialaneix
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13. A new differential analysis method: treediff
τ1 τ2
dwPD(τ1, τ2) = 2 ×
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Chroconet – 10/11/2023
10 novembre 2023 / Nathalie Vialaneix
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14. A new differential analysis method: treediff
▶ Article issu de la thèse Nathanaël [Neuvial et al., 2023b] (en révision)
▶ R package treediff (stage Gwendaëlle)
Chroconet – 10/11/2023
10 novembre 2023 / Nathalie Vialaneix
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15. Outline
Clustering based on Hi-C matrices
Differential analysis of Hi-C matrices
Work in progress
Chroconet – 10/11/2023
10 novembre 2023 / Nathalie Vialaneix
p. 12

16. Current and future work on Hi-C and Hi-C differential analysis
▶ Chrocodiff: review of the different methods/tools for the differential analysis of
Hi-C data
▶ Élise’s PhD thesis: minimum and maximum differential subtrees (challenges:
multiple testing control in a hierarchical setting, very large computational
problems, ...)
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17. Credits for the images
▶ slide 3: Hi-C matrices hierarchically organized are taken from [Rao et al., 2014]
▶ slide 4: chromatine organization taken from [Jansen and Verstrepen, 2011]
The rest is my own work (or Sylvain’s work).
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18. References
Ambroise, C., Dehman, A., Neuvial, P., Rigaill, G., and Vialaneix, N. (2019).
Adjacency-constrained hierarchical clustering of a band similarity matrix with application to genomics.
Algorithms for Molecular Biology, 14:22.
Fraser, J., Ferrai, C., Chiariello, A. M., Schueler, M., Rito, T., Laudanno, G., Barbieri, M., Moore, B. L., Kraemer, D. C., Aitken, S., Xie,
S. Q., Morris, K. J., Itoh, M., Kawaji, H., Jaeger, I., Hayashizaki, Y., Carninci, P., Forrest, A. R., The FANTOM Consortium, Semple, C. A.,
Dostie, J., Pombo, A., and Nicodemi, M. (2015).
Hierarchical folding and reorganization of chromosomes are linked to transcriptional changes in cellular differentiation.
Molecular Systems Biology, 11:852.
Jansen, A. and Verstrepen, K. J. (2011).
Nucleosome positioning in Saccharomyces cerevisiae.
Microbiology and Molecular Biology Reviews, 75(2):301–320.
Marti-Marimon, M., Vialaneix, N., Voillet, V., Yerle-Bouissou, M., Lahbib-Mansais, Y., and Liaubet, L. (2018).
A new approach of gene co-expression network inference reveals significant biological processes involved in porcine muscle development in late
gestation.
Scientific Report, 8:10150.
Neuvial, P., Foissac, S., and Vialaneix, N. (2023a).
Comprendre l’organisation spatiale de l’ADN à l’aide de la statistique.
In Knoop, M., Blanc, S., and Bouzeghoub, M., editors, L’Interdisciplinarité. Voyage au-del‘a des Disciplines, pages 172–176. CNRS.
Neuvial, P., Randriamihamison, N., Chavent, M., Foissac, S., and Vialaneix, N. (2023b).
A two-sample tree-based test for hierarchically organized genomic signals.
Preprint submitted for publication. In revision.
Randriamihamison, N., Vialaneix, N., and Neuvial, P. (2021).
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19. Applicability and interpretability of Ward’s hierarchical agglomerative clustering with or without contiguity constraints.
Journal of Classification, 38:363–389.
Rao, S. S., Huntley, M. H., Durand, N. C., Stamenova, E. K., Bochkov, I. D., Robinson, J. T., Sanborn, A. L., Machol, I., Omer, A. D.,
Lander, E. S., and Lieberman-Aiden, E. (2014).
A 3D map of the human genome at kilobase resolution reveals principle of chromatin looping.
Cell, 159(7):1665–1680.
Soler-Vila, P., Cuscó, P., Farabella, I., Di Stefano, M., and Marti-Renon, M. A. (2020).
Hierarchical chromatin organization detected by TADpole.
Nucleic Acids Research, 45(7):e39.
Zhang, Y. W., Wang, M. B., and Li, S. C. (2021).
SuperTAD: robust detection of hierarchical topologically associated domains with optimized structural information.
Genome Biology, 22:45.
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