  We study colonies of non-motile, rod-shaped bacteria growing on solid
substrates. In our model, bacteria interact purely mechanically, by pushing
each other away as they grow, and consume a diffusing nutrient. We show that
mechanical interactions control the velocity and shape of the advancing front,
which leads to features that cannot be captured by established
Fisher-Kolmogorov models. In particular, we find that the velocity depends on
the elastic modulus of bacteria or their stickiness to the surface.
Interestingly, we predict that the radius of an incompressible, strictly
two-dimensional colony cannot grow linearly in time. Importantly, mechanical
interactions can also account for the nonequilibrium transition between
circular and branching colonies, often observed in the lab.
