Master's internship in Lyon (M1 or M2): Stochastic modeling of the cellular dynamics underlying oral cancers.

The Inria Lyon centre is Inria's ninth research centre. Created in January 2022, it brings together around 320 people in 19 research teams and research support services.

Its teams are located in Villeurbanne, Lyon Gerland and Saint-Etienne.

The Lyon centre is active in the fields of software, distributed and high-performance computing, embedded systems, quantum computing and privacy in the digital world, as well as digital health and biology.

The master’s student will be based at the Unité de Mathématiques Pures et Appliquées (UMPA), integrated within the Inria/Inserm team Casting. Throughout the internship, the student will benefit from the scientific environment of UMPA’s probability team, as well as the interdisciplinary exchanges fostered by team Casting. A priory, there are no plans for a thesis to follow this internship.

For any questions, do not hesitate to ask questions by mail: 

• helene.leman at inria.fr
• celine.bonnet at inria.fr

The recruited student will be supervised by Hélène Leman and Céline Bonnet. Regular meetings with both supervisors will ensure continuous guidance and support for the student’s research progress.

Cancer represents a substantial challenge to society, with current treatments being both physically taxing and financially costly. Despite these efforts, treatments can be ineffective, in part due to rescue events.  A rescue event occurs when cells initially respond to a treatment but, over time, some undergo mutations that confer resistance, allowing a subpopulation to survive and proliferate despite ongoing therapy. During this internship, we therefore propose to investigate the composition and behavior of a cell population undergoing a rescue event, by developing and analyzing stochastic models that represent these dynamics.

Advances in DNA sequencing technologies have revolutionized our ability to gather detailed, high-resolution genetic data from cell populations. This technology makes it possible to track the genetic composition of a population at some times. To analyze this data, one often relies on the Site Frequency Spectrum (SFS), a statistical tool that captures the distribution of mutations across a population. More precisely, for any i, it counts the number of mutations carried by exactly i cells at a positive time. The SFS is a useful summary of how a population’s genetic diversity changes over time and can be used to infer evolutionary history from genomic data.

This project aims to explore the Site Frequency Spectrum (SFS) of stochastic processes that model the dynamics of cell populations experiencing a rescue event and frequent neutral mutations, based on the article [BL24]. Neutral mutations are those that do not affect the individual growth rate, but nonetheless provide useful information on the overall evolutionary dynamics. The aim of this internship will be first to well understand the paper [BL24], then try to generalize or explore new results studying age-structured population or competitive population.

[BL24] Céline Bonnet and Hélène Leman. Site frequency spectrum of a rescued population under rare resistant mutations. Stochastic Processes and their Applications, 176:104421, 2024.

This internship is designed for candidates with a strong mathematical background, ideally at the M1 or M2 level, particularly in probability, stochastic processes, or Markov chains.

While not mandatory, programming skills—especially in languages such as Python, R, or MATLAB—will be highly valued for implementing algorithms and conducting simulations.

Additionally, a keen interest in applying mathematical concepts to biological systems will be a significant asset, as the internship may involve interdisciplinary projects at the intersection of mathematics and biology.

• 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

Gratification