Mathematical Modeling in Biology

The objective of our team, created in 2014, is to analyze, from a theoretical point of view, or in collaboration with experimenters, certain biological processes or systems derived from biology through mathematical models. In the approach that we adopt, the models obtained use, in the vast majority, tools from the field of partial differential equations and dynamical systems.

Our current work focuses on three main themes:

  • Neuroscience
  • Mechanisms of cell polarization
  • Cancerology

Lear more :

  • Neuroscience:

 A large part of our work, in the field of neuroscience, consists of the analysis of neural network models of the average field type where we consider networks where each neuron perceives the average activity of the entire network. We develop new mathematical methods allowing to describe from a theoretical point of view the qualitative dynamics of the network according to the forces of interconnections between the neurons and the intrinsic nature of the neurons considered in the network. On the other hand, we are interested in learning type models where it is a question of understanding how a network learns a given signal. This work is carried out in collaboration with K. Pakdaman (IJM, Paris Diderot), B. Perthame and D. Smets (LJLL, UPMC), J.-A. Carrillo (Imperial college of London) and G. Wainrib (ENS, Univ Paris 13)

  • Cell polarization:

In collaboration with the team of N. Minc (IJM, Paris Diderot), it is a question of better understanding the mechanisms underlying the phenomena of cell polarization according to the geometry of the cell. Indeed, in work in progress with the team of N. Minc, experiments have highlighted the fact that, the flatter the local geometry of the cell, the more the cluster of Cdc42 proteins, during polarization, is spread out. . Moreover, the experiments carried out by this team show that it is the actin filaments which are mainly responsible for this correlation. The question of why and how the dynamics of actin filaments allows a recognition of the geometry of the cell is thus fundamental in the understanding of these experiments and the appropriate mathematical models make it possible to bring conjectures to these questions.

  • Cancerology:

New projects focus on the study of biological systems linked to cancer. In particular, in an ongoing collaboration with J.-.M. Camadro (IJM, Paris Diderot), we seek to better understand the mechanisms involved in the evolution of cirrhosis to liver cancer and to describe the impact of these mechanisms on the ubiquitin proteasome system.

Collaborations :

  • Laboratoire Jacques-Louis Lions, UPMC
  • Ecole Normale Supérieure
  • Université Paris XIII
  • Imperial College of London
  • Institut Jacques Monod
  • Université d’Orsay
  • Université de Nantes