48-1 Biomechanical properties of the cell

Cellular mechanics plays a fundamental role in a number of mechanobiological phenomena such as bone remodelling, cancer, embryogenesis and immune response.  Over the last few decades, biologists have begun to explore the role of mechanics and, more specifically, the forces and stresses undergone or exerted by cells on their environment. In this course, we will review the basic principles of continuum mechanics in order to approach the mathematical modelling of several biological processes such as adhesion, migration, invasion and cell-cell interactions. Various mathematical approaches based on ODEs, PDEs, in particular reaction-diffusion equations or others, will be presented in order to highlight how these phenomena can be modelled and coupled, while taking into account the multi-scale aspects in their modelling. Particular emphasis will be placed on cell migration, both individual and collective, and on the mechanics of the cell nucleus.