2019-01610 - Post-Doctoral Research Visit F/M Understanding and controlling microbial communities: optimal control of multiscale models

Type de contrat : CDD de la fonction publique

Niveau de diplôme exigé : Thèse ou équivalent

Fonction : Post-Doctorant

A propos du centre ou de la direction fonctionnelle

Located at the heart of the main national research and higher education cluster, member of the Université Paris Saclay, a major actor in the French Investments for the Future Programme (Idex, LabEx, IRT, Equipex) and partner of the main establishments present on the plateau, the centre is particularly active in three major areas: data and knowledge; safety, security and reliability; modelling, simulation and optimisation (with priority given to energy).   

The 450 researchers and engineers from Inria and its partners who work in the research centre's 28 teams, the 60 research support staff members, the high-level equipment at their disposal (image walls, high-performance computing clusters, sensor networks), and the privileged relationships with prestigious industrial partners, all make Inria Saclay Île-de-France a key research centre in the local landscape and one that is oriented towards Europe and the world.

 

Contexte et atouts du poste

For a number of applications of biomedical interest, one has to understand and control the behavior of growing cell populations subjected to killing agents. This is for example the case of pathogenic bacteria subjected to antimicrobial treatments, of tumor cells subjected to anticancer treatments, and of bacteria naturally attacked by phage viruses.

These systems are highly interesting dynamical systems. Firstly, the response of individual cells to treatments is non-trivial to capture. Because of their different past, each cell is different from each other, and because of molecular noise, cell responses are stochastic. Secondly, these heterogeneous and stochastic “agents” are coupled to each other by the fact that they share and act on the same environment. Lastly, the number of interacting agents is evolving through time as a result of birth and death of cells leading  to complex multiscale dynamics of the cell population. Traditionally, problems of this type have been analyzed using mostly agent based simulation tools. Such tools can serve to forward analyze cell population behavior for given model parameters and in a given treatment scenario. For more complex tasks, such as inferring model parameters from experimental data or the optimization of treatments, agent based simulation is computationally too costly.

Problem and approach :

Mathematically, cell fate decisions of individual cells exposed to killing agents can be represented as hitting time problems of a stochastic process (SDE or CTMC) representing biochemical reactions inside the cell to reach a certain set (e.g. an apoptotic protein reaching a level that is sufficiently high to kill the cell). The goal of this project is to develop a tractable multiscale modeling framework for cell populations subjected to killing agents by coupling these hitting time problems to models of growing cell populations: hitting times for individual cells then depend on the state of the environment and the cell population while reversely the environment and population growth are affected by the properties of the hitting times.

This mathematical framework will allow us to quickly fit models to experimental data and to evaluate, and optimize, the effect of different treatments on the cell population.

Regarding the applications mentioned above, the problems of interest include not only predicting systems behavior but also optimizing treatments and fitting parameters given data. To find more efficient solution to the latter problem, optimal experimental approaches could be employed.

In concrete terms, the first task amounts to propose appropriate modeling frameworks for these multiscale systems. One will consider first principle representations, in the form of stochastic individual based models, but also continuous approximations thereof, leading to Fokker-Planck equation models with continuous couplings. The inclusion of cell-to-cell heterogeneity in this framework is non-trivial. The second task is to specify optimal control problems and develop optimal control strategies for this class of systems, and more generally for parabolic partial differential equations. Lastly, one will investigate the possibility to use optimal control tools to design optimally-informative experiments for this class of systems and apply this framework in active learning contexts.

Applications :

These methodological developments will be motivated by experimental work we do on antimicrobial resistance. So far no model has been able to quantitatively capture the complex population dynamics presented by resistant clinical isolates treated multiple times with beta-lactams, a broad class of antibiotics. The optimality of treatment solutions will also be tested experimentally on these clinically-relevant resistant bacteria.  Other applications, using synthetic biology approaches for bioproduction problems, will also be considered.

Scientific environment :

The work will be carried out in the  Commands team at Inria. This team, headed by Frédéric Bonnans, is part of the Centre de Mathématiques Appliquées of Ecole Polytechnique in Palaiseau (south of Paris). Its primary focus is on the development and application of optimal control methods.

The work will also be done in close collaboration with the  InBio team hosted at Institut Pasteur. InBio is a mixed research group between Inria and Institut Pasteur doing interdisciplinary research with experimental and computational biology. Jakob Ruess and Gregory Batt will provide support with stochastic modeling of cell population systems and antimicrobial resistance mechanisms.

Mission confiée

The work will be carried out in the  Commands team at Inria. This team, headed by Frédéric Bonnans, is part of the Centre de Mathématiques Appliquées of Ecole Polytechnique in Palaiseau (south of Paris). Its primary focus is on the development and application of optimal control methods.

The work will also be done in close collaboration with the  InBio team hosted at Institut Pasteur. InBio is a mixed research group between Inria and Institut Pasteur doing interdisciplinary research with experimental and computational biology. Jakob Ruess and Gregory Batt will provide support with stochastic modeling of cell population systems and antimicrobial resistance mechanisms.

Principales activités

The first task amounts to propose appropriate modeling frameworks for these multiscale systems. One will consider first principle representations, in the form of stochastic individual based models, but also continuous approximations thereof, leading to Fokker-Planck equation models with continuous couplings. The inclusion of cell-to-cell heterogeneity in this framework is non-trivial. The second task is to specify optimal control problems and develop optimal control strategies for this class of systems, and more generally for parabolic partial differential equations. Lastly, one will investigate the possibility to use optimal control tools to design optimally-informative experiments for this class of systems and apply this framework in active learning contexts.

 

Compétences

Candidates should ideally have a PhD in partial differential equations or in optimal control. Candidates with a strong background in stochastic model analysis will also be considered. Experience in biological systems modelling will naturally be a significant plus. A strong motivation for interdisciplinary research is essential.

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 : 2.653 euros