Post-Doctoral Research Visit F - M Bifurcation And Robustness Analysis In Structured Population Models Application To Female Reproductive Cycles H/F INRIA

Post-Doctoral Research Visit F/M Bifurcation and robustness analysis in structured population models: Application to female reproductive cycles
Le descriptif de l'offre ci-dessous est en Anglais
Type de contrat : CDD

Niveau de diplôme exigé : Thèse ou équivalent

Fonction : Post-Doctorant

A propos du centre ou de la direction fonctionnelle

The Inria Saclay-Île-de-France Research Centre was established in 2008. It has developed as part of the Saclay site in partnership with Paris-Saclay University and with the Institut Polytechnique de Paris .

The centre has 40, 27 of which operate jointly with Paris-Saclay University and the Institut Polytechnique de Paris; Its activities occupy over 600 people, scientists and research and innovation support staff, including 44 different nationalities.

Contexte et atouts du poste

The postdoc position is open in the framework of the ANR project OVOPAUSE led by MUSCA, gathering researchers from different institutions and scientific background (applied mathematics, developmental and reproductive biology).

The position is an opportunity to be involved in a strongly interdisciplinary consortium, and to strengthen experience in mathematical and computational biology by working on the analysis of coupled ODE-PDE models.

Mission confiée

The detailed subject is avalaible at:

There are major societal challenges associated with maintaining the reproductive fitness of female individuals, whether in a clinical, breeding, or ecological context. Understanding female reproductive (germ) cell population dynamics is instrumental for maintaining women health and fertility, managing ovarian aging, developing sustainable breeding practices, and monitoring the effects of micro-pollutants in humans, livestock and wild species.

Up to now, most available mathematical models dedicated to reproductive biology have been designed either to represent the whole oogenesis, without accounting for cyclicity [4], or to mimic the oscillatory hormonal patterns along the ovarian cycle, without accounting for oogenesis [5]. The objective of the postdoc is to extend previous models developed in the MUSCA team to couple, in a mechanistic manner, oogenesis with ovarian cyclicity, to get insight into their reciprocal interactions on both the short and long term.

The work will be based on population dynamics models of the whole oogenesis, formulated either as discrete compartmental models [1,2] or as continuous structured population models [3].

The first objective will be to extend the existing size-structured PDE model [3] to account for the hormonally-controlled and population-dependent recruitment of the cyclic cohort, and for the (neuro-)endocrine conditions needed to trigger ovulation. A detailed bifurcation analysis will then be performed to understand how the coupling between oogenesis and hormonal feedback shapes the properties of the ovarian cycle (e.g. one or several germ cell waves, number of germ cells per wave, ovarian cycle length and regularity).

The second objective will be to analyze the robustness of these properties with respect to the number and distribution of germ cells (e.g. stochastic fluctuations, inter-individual variability), as well as the effect of aging (e.g. diminishing quiescent pool, altered neuro-endocrine control).

From these studies, theoretical results on the longtime analysis of coupled PDE/ODE systems are expected, as well as outcomes in comparative physiology highlighting the shared mechanisms and species-specific differences in germ cell dynamics among vertebrate species (e.g. in mammals compared to fish).

References

[1] G. Ballif, F. Clément, and R. Yvinec. Averaging of a stochastic slow-fast model for population dynamics: application to the development of ovarian follicles. SIAM J. Appl. Math., 82(1):359-380, 2022.
[2] G. Ballif, F. Clément, and R. Yvinec. Nonlinear compartmental modeling to monitor ovarian follicle popu- lation dynamics on the whole lifespan. J. Math. Biol., 89(1):9, 2024.
[3] F. Clément, L. Fostier, and R. Yvinec. Bifurcation analysis of a size-structured population model: application to oocyte dynamics and ovarian cycle. SIAM J. Appl. Dyn. Syst. (in press), 2025.
[4] F. Clément and D. Monniaux. Mathematical modeling of ovarian follicle development: A population dynamics viewpoint. Curr. Opin. Endocr. Metab. Res., 18:54-61, 2021.
[5] R. Yvinec, P. Crépieux, E. Reiter, A. Poupon, and F. Clément. Advances in computational modeling approaches of pituitary gonadotropin signaling. Expert Opin. Drug Discov., 13(9):799-813, 2018

Principales activités

- Extend and couple existing models
- Perform extensive bifurcation analysis on the coupled model
- Develop and implement numerical schemes suited for the coupled model
- Characterize the properties of the oscillatory solutions
- Perform a sensitivity/robustness analysis applied to the oscillatory solutions
- Position the results with respect to the mathematical and biological literature in the field
- Write and disseminate the results to the scientific community

Compétences

Ph.D in applied Mathematics, with expert knowledge in analysis and numerical simulation of ODEs and PDEs. Experience with either sensitivity/identifiability analysis or parameter estimation will be greatly appreciated.
Strong motivation for biological applications and work in an interdisciplinary context.

Avantages

- Subsidized meals
- Partial reimbursement of public transport costs
- Leave: 7 weeks of annual leave + 10 extra days off due to RTT (statutory reduction in working hours) + possibility of exceptional leave (sick children, moving home, etc.)
- Possibility of teleworking (after 6 months of employment) and flexible organization of working hours
- Professional equipment available (videoconferencing, loan of computer equipment, etc.)
- Social, cultural and sports events and activities
- Access to vocational training
- Social security coverage

Rémunération

Monthly gross salary : 2.788 euros