Recherche

Synthèse des années 2014-2017

Pour voir une présentation de l’activité de Mamba (en anglais): Mamba presentation – 2014 to 2017

et télécharger la fiche de synthèse (en anglais): MAMBA synthesis report – 2014 to 2017

Overall objectives

MUSCLEES is the evolution of the MAMBA Inria project-team, headed by Marie Doumic (now head of the Inria project-team MERGE in Saclay) during 9 years (2014-2022); which was in turn a continuation of the BANG Inria project-team, headed by Benoît Perthame during 11 years (2003-2013). Just as its scientific ascendants, this new project-team aims at developing, analyzing, controlling, observing, identifying and simulating models involving dynamics of phenomena encountered in various biological systems.

The nature of the corresponding populations involved is very diverse, as well as the nature of the interactions between their members. They may contain chemical species, cells, molecules, neurons, bacteria, (human or animal) individuals. We are interested for example in cell motion, (physiological or tumor) cell development, binding/unbinding of macro-molecules, bacteria micro-colony growth, tissue development, repair and ageing, epidemic spread, vector control, together with methodological questions related to these questions.

In accordance with the context, we will use stochastic or deterministic models, systems of ordinary (possibly defined on graphs) or partial differential equations, and agent-based approaches. We will also consider the link between models of different types, exploring the behavior across different scales, and will appeal to tools from control theory to treat issues of (optimal or non-optimal) control, state observation or parametric identification.

An overview of the different research axes of the MUSCLEES team is given in the Figure. The horizontal axis distinguishes schematically between the stochastic and deterministic descriptions, while the vertical axis indicates the description scale. At the heart of our research lie the different applications that drive our mathematical studies: living tissues/cell populations, reaction networks and epidemiology (in green in the Figure). All our efforts, even the most theoretical ones, will be motivated by biological questions/challenges with applications in these different fields. The MUSCLEES team proposes to tackle these challenges from different and complementary angles, attempting to provide generalizations and unified points of view in the study of biological systems: Axis 2 (in dark red in the Figure) is devoted to the understanding of the role of stochasticity in biological systems through the development and analysis of Stochastic Differential Equations (SDE) for reaction networks; Axes 3 and 4 (in blue) aim to provide a theoretical understanding of continuum models widely used to describe biological systems at the population scale, essentially by use of Ordinary Differential Equations (ODE) for the applications to mathematical epidemiology (dark blue), or of Partial Differential Equations (PDE) for various applications (in light blue); and Axis 5, the most interdisciplinary axis of our research team, is entirely devoted to the development of valid agent-based models directly confronted to in vitro/in vivo data for bacterial growth and tissue development and ageing (orange). Lastly, Axis 1 (in red arrows) represents one of the fundamental perspectives to link all our research activities. It is devoted to establishing the link between the various modelling viewpoints taken in the other research axes, by deriving, as rigorously as possible, the continuum (ODE, SDE, PDE) models from microscopic agent-based descriptions.

The MUSCLEES project-team gathers researchers with complementary skills and interests in applied mathematics (partial differential equations, stochastic processes, control theory). Our goal is to incorporate the different knowledges present in the team as well as expertise obtained from first hand collaborators specialists of the considered applications, in order to provide firm mathematical ground to the representation, understanding, numerical assessment and control of the biological systems of interest. As a peculiarity, we also intend to locate these questions in the larger framework of analysis methods. We will always attempt to unify as much as possible the specific application domains within a common formalism, with scales ranging from individual decision to collective behaviour: this vision and methodology go far beyond the specific applications we have listed. Altogether, the team ambitions to provide a deep Mathematical Understanding across Scales of Complex Living Ecosystems with Emerging Structures, whence the acronym: MUSCLEES. Our planned activities are exposed below. As a rule, they are activities already currently in progress or whose realisation will be undertaken soon. Longer-term actions or perspectives are mentioned specifically, whenever needed.

Last activity report : 2023