Mathematical modelling of cell migration in confined domains

Scientific background

On a 2D substrate, cells migrate by combining protrusive forces to deploy a strongly adhering lamellipodium at their front which is very thin (around 200-400 nm). In contrast, when the same cells migrate through the constrictions of a 3D medium, the lamellipodium thickens to occupy the whole section of the constrictions (up to 3x3 µm2). We will construct a mathematical and numerical model of the actin gel dynamics in the lamellipodium to reproduce the structural transition from 2D to 3D. This model will be compared with novel experimental data on the lamellipodium structural transition using advanced light-sheet microscopy in microfluidics, the internal actin dynamics by FRAP and the forces developped by lamellipodium using pressure control systems and traction force microscopy.

PhD Objectives

  • To identify biological scenarios that could account for the behavior of the migrating cell in confined environment and to formulate mathematical models coherent with these scenarios.
  • To study these models theoretically and to implement numerical approximations of the models so as to be able to reproduce experimental setting. To compare the numerical experiments to real-life ones
  • To interact with experimentalist that will perform light-sheet microscopy experiments of cells exhibiting 2D/3D transition in microfluidic devices and eventually help in the design of new experiments.

PhD student’s expected profile

Applicants are expected to have a strong background in mathematical modeling or numerical methods for  PDEs or in computational fluid mechanics and  expertise in development of numerical codes, and of course an interest in biology, biophysics or cell modeling.