Using a self-generated hypoxic assay, it is shown that Dictyostelium discoideum displays a remarkable collective aerotactic behavior: when a cell colony is covered, cells quickly consume the available oxygen and form a dense ring moving outwards at constant speed and density.
We propose a simple, yet original PDE model with the hypothesis that cells have two distinct behaviors depending on the surrounding oxygen levels : either they undergo cell division, or they move upwards the oxygen gradient. This leads to a system of parabolic PDEs, with one having coefficients constant by piece. The approach is very fruitful as it leads to an explicit characterization of traveling wave solutions, a qualitative analysis of the phenomenon, as well as an explicit and novel formula of the collective migration speed of cells that encapsulates a surprising combination of expansion by cell divison, such as described by the Fisher/KPP equation, and aerotaxis. Furthermore, the model exhibits a remarkable dichotomy between pulled waves and pushed waves as a function of the parameters of the model.
The analysis shows that collective migration is caused by the interaction between cell division and the modulation of aerotaxis. The modeling approach and its conclusions complement and are in turn confirmed by an experimental study of the collective behavior of cells.
This is joint work with Christophe ANJARD Vincent CALVEZ, Jean-Paul RIEU, Olivier COCHET-ESCARTIN and is a subpart of the work presented in article DOI: 10.7554/eLife.6473.
