Usually, mathematical models dealing with the formation of patterns by cells in the extracellular matrix do not take into account the chemical environmental cues involved in chemotaxis (movement of a motile cell in a direction corresponding to the gradient of concentration of a particular substance).
Here, the teams of Michèle Sabbah and Benoît Perthame studied a Keller-Segel partial differential equation system in order to model the chemotactical auto-organization of the cells in the matrix. They proved that it was subject to Turing instabilities under a time-dependent condition. This work has implications in understanding how cancer cells move as clusters rather than individual cells in the frame of metastasis formation.
Congratulations for their work! They prove that biologists and mathematicians can join their efforts for the modeling of complex biological questions like cancer dissemination.