  Tissue self-organization into defined and well-controlled three-dimensional
structures is essential during development for the generation of organs. A
similar, but highly deranged process might also occur during the aberrant
growth of cancers, which frequently display a loss of the orderly structures of
the tissue of origin, but retain a multicellular organization in the form of
spheroids, strands, and buds. The latter structures are often seen when tumors
masses switch to an invasive behavior into surrounding tissues. However, the
general physical principles governing the self-organized architectures of tumor
cell populations remain by and large unclear. In this work, we perform in-vitro
experiments to characterize the growth properties of glioblastoma budding
emerging from monolayers. Using a theoretical model and numerical tools here we
find that such a topological transition is a self-organised, non-equilibrium
phenomenon driven by the trade--off of mechanical forces and physical
interactions exerted at cell-cell and cell-substrate adhesions. Notably, the
unstable disorder states of uncontrolled cellular proliferation macroscopically
emerge as complex spatio--temporal patterns that evolve statistically
correlated by a universal law.
