I will report on a minimal model introduced to describe expansion of a cell colony (Dictyostelium discoideum) in response to aerotaxis. The model is essentially based on the hypothesis that cells may either divide if oxygen is available in a sufficient amount, or move directionaly along its gradient if oxygen concentration is too low. Interestingly, the speed of expansion is explicit, and it reveals a transition between pulled and pushed fronts. This enables discussing the relative importance of the three parameters in the model (rate of division, averaged speed of directional motion, and cell diffusion coefficient) to the dynamics of expansion.