  The transition from monolayers to multilayered structures in bacterial
colonies is a fundamental step in biofilm development. Observed across
different morphotypes and species, this transition is triggered within freely
growing bacterial microcolonies comprising a few hundred cells. Using a
combination of numerical simulations and analytical modeling, here we
demonstrate that this transition originates from the competition between
growth-induced in-plane active stresses and vertical restoring forces, due to
the cell-substrate interactions. Using a simple chainlike colony of laterally
confined cells, we show that the transition sets when individual cells become
unstable to rotations, thus it is localized and mechanically deterministic.
Asynchronous cell division renders the process stochastic, so that all the
critical parameters that control the onset of the transition are continuously
distributed random variables. Here we demonstrate that the occurrence of the
first division in the colony can be approximated as a Poisson process in the
limit of large cells numbers. This allows us to approximately calculate the
probability distribution function of the position and time associated with the
first extrusion. The rate of such a Poisson process can be identified as the
order parameter of the transition, thus highlighting its mixed
deterministic-stochastic nature.
