Description of the thesis topic

Adult tissue self-renewal relies on the activity of stem cells (SCs), which are characterised by properties such as stemness, quiescence, and the ability to differentiate to varying degrees (Tai et al, 2019).
A major challenge in this field is understanding how SC production and differentiation are spatiotemporally coordinated.
The Notch signalling pathway (NSP) plays a significant role in regulating SC fate decisions.
This pathway involves communication between adjacent cells to activate target genes promoting quiescence or differenciation (Sprinzak & Blacklow, 2021).
However, in vivo Notch signalling is complex, and models have yet integrated experimental and statistical approaches to account for the full complexity of the NSP.

Spatial and spatio-temporal point processes are well-suited to study the organisation of tissues like the zebrafish pallium (Dray et al, 2021).
Specifically, multivariate Hawkes processes (Hawkes, 1971) have already shown their potential in modelling interacting cell networks, both the signalling process within the cells and the spatial couplings between the cells (Verma et al, 2021).

This PhD thesis aims to develop new methods for the inference of non-linear Hawkes processes, in order to study how stem cells coordinate their behaviours to maintain tissue homeostasis.
The objectives are two-fold:
• Aim 1: Explore non-parametric estimation methods for non-linear Hawkes processes, inspired by random forests.
• Aim 2: Infer NSP from experimental data, using the models and estimation methods derived in Aim 1.

References:
- Tai, K., Cockburn, K., & Greco, V. (2019). Flexibility sustains epithelial tissue homeostasis. Current Opinion in Cell Biology, 60, 84–91.
- Sprinzak, D., & Blacklow, S. C. (2021). Biophysics of Notch Signaling. Annual Review of Biophysics, 50(1), 157–189.
- Dray, N., Mancini, L., Binshtok, U., Cheysson, F., Supatto, W., Mahou, P., Bedu, S., Ortica, S., Than-Trong, E., Krecsmarik, M., Herbert, S., Masson, J.-B., Tinevez, J.-Y., Lang, G., Beaurepaire, E., Sprinzak, D., & Bally-Cuif, L. (2021). Dynamic spatiotemporal coordination of neural stem cell fate decisions occurs through local feedback in the adult vertebrate brain. Cell Stem Cell, 28(8), 1457-1472.e12.
- Hawkes, A. G. (1971). Spectra of Some Self-Exciting and Mutually Exciting Point Processes. Biometrika, 58(1), 83–90.
- Verma, A., Jena, S. G., Isakov, D. R., Aoki, K., Toettcher, J. E., & Engelhardt, B. E. (2021). A self-exciting point process to study multicellular spatial signaling patterns. Proceedings of the National Academy of Sciences of the United States of America, 118(32).

Work Context

The "Laboratoire d'analyse et de mathématiques appliquées" (LAMA) is a joint research center between CNRS, Université Paris-Est Créteil (UPEC) and Université Gustave Eiffel (UGE).
The laboratory is split between two locations: one at Champs-sur-Marne inside UGE, one at Créteil inside UPEC.
More than 70 permanent researchers and teachers are affiliated to the laboratory, within 5 teams.

The PhD will be funded through a grant from PEPR Maths-Vives, and will take place at Champs-sur-Marne, within the Probability and Statistics team.
The PhD student will also interact with biologists at Institut Pasteur.

The position is located in a sector under the protection of scientific and technical potential (PPST), and therefore requires, in accordance with the regulations, that your arrival is authorized by the competent authority of the MESR.