ERC SINGER - Stochastic dynamics of sINgle cells : Growth, Emergence and Resistance

Themes

Applied Mathematics
Stochastic Processes
Bacterial Evolution
Modeling in Hematology
Biology
Research
Medical

About

The ERC SINGER project aims to introduce new stochastic and deterministic models for biological and medical applications. This is an interdisciplinary societal challenge that seeks to develop scenarios of resistance evolution as well as better strategies for antibiotics or chemotherapy related to them.

The primary objective is to study new multi-scale mathematical problems, inspired by the biological challenges posed by unicellular organisms. By working closely with biology experts, we seek to understand and model the complexity of evolving populations while contributing to the development of new mathematical theories to address these exciting challenges.

The Project

The project focuses on the eco-evolutionary biology of asexual populations of bacteria or cells, exploring how survival and reproduction depend on phenotypic or genetic traits. The evolution of these traits results from various mechanisms, and the major challenge is to predict evolution scenarios considering these mechanisms. The project takes advantage of recent measurements of individual cells, where small populations and high variability are observed, with a significant impact from the environment.

The main objective is to develop stochastic models to control these fluctuations and predict their behavior in response to environmental changes.

The mathematical approach adopted encompasses a class of models and characteristics aimed at medical and biological applications for populations evolving, reproducing, growing, and emerging. Close collaboration with biologists will solve biological problems by posing new mathematical questions. The project follows a tradition of developing new mathematical concepts from biological discoveries, using structured population and growth-fragmentation models.

The methodology involves structured stochastic processes with measure-valued traits generating a diversity of macroscopic behaviors. The main tools include limit theorems, stochastic differential equations, branching processes with interactions, and nonlinear partial differential equations.

The project represents a mathematical challenge by seeking to reconcile stochastic and Hamilton-Jacobi approaches in eco-evolutionary modeling, exploring new time and size scales, and controlling extinction events. It also addresses medical problems, particularly understanding leukemic mutations and response times in multi-scale systems, with potential implications for medical treatments.

Key Research Themes :

Transition from stochastic processes to Hamilton-Jacobi equations,
Modeling leukemic mutations and response times in multi-scale systems,
Tracing lineages and reverse paths in nonlinear situations,
Modeling the growth and fragmentation of multi-type bacteria in response to antibiotics.

In summary, this project relies on mathematical models to explore the mechanisms of biological population evolution at different scales, focusing on mathematical challenges and potential applications in biology and medicine.

The Two Main Axes of the Project

Axis 1 : Development of a mathematical framework to track very small subpopulations in large population approximations to explain and quantify surprising long-term behaviors in population evolutionary dynamics, such as the emergence of "extinct populations".
Axis 2 : Modeling and mathematical understanding of resistance evolution scenarions in close collaboration with biologists to propose new strategies considering these scenarios.

The project is supported by :

“Funded by the European Union (ERC, acronym, project number). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council Executive Agency. Neither the European Union nor the granting authority can be held responsible for them.”

Related Projects Link

Permanent Members

Project Leader

Sylvie Méléard, Professor, Ecole polytechnique, France.

Mathematicians

Vincent Bansaye, Professor, Ecole polytechnique, France.
Nicolas Champagnat, Research Director, INRIA Nancy - Grand est, France.
Marie Doumic, Research Director, INRIA Paris, France.
Sepideh Mirrahimi, Research Director, CNRS Montpellier, France.
Chi Viet Tran, Professor, Université Gustave Eiffel, France.
Anita Winter, Professor, Universität Duisburg - Essen, Allemagne.

Biologists and Doctors

Sylvain Billiard, Professor, Université de Lille, France.
Meriem El Karoui, Professor, Université d'Edimbourg, Ecosse.
Stéphane Giraudier, Professor, Hôpital Saint - Louis, France.
Raphaël Itzykson, Professor, Hôpital Saint - Louis, France.
Evelyne Lauret, Researcher, CNRS, INSERM, Institut Cochin, France.

Temporary Members

Clément Foucart (01/09/2023 - 31/08/2025)-Associate Reseacher
Pierre Gabriel (01/02/2023 – 30/07/2023)-Delegation
Sarah Kaakai - Collaborator
Jaime San Martin (Mai-June 2023/2024)

Post doc students

Laetitia Colombani, Ecole polytechnique, France.

Phd students

Anouar Jeddi, Ecole polytechnique, France.
Alexandre Perrin, Ecole polytechnique, France.

Public Events

Seminars
Summer Schools

Internal Events

Working Groups

Project References

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To be appointed

Sylvie Méléard :

• Invited Speaker to ICM 2022 : London 2022.

• IMS Medallion Lecture: INFORMS Applied Probability Conference, Nancy 2023.

• Plenary Speaker. Mathematics Panorama, Hausdorff Center, Bonn 2023.

Members