Modelling cancer cell budding in-vitro as a self-organised, non-equilibrium growth process.

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. We further propose a theoretical model and its finite element implementation to characterize such a topological transition, that is modelled as 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.