  We study the dynamics of proliferating cell collectives whose microscopic
constituents' growth is inhibited by macroscopic growth-induced stress.
Discrete particle simulations of a growing collective show the emergence of
concentric-ring patterns in cell size whose spatio-temporal structure is
closely tied to the individual cell's stress response. Motivated by these
observations, we derive a multiscale continuum theory whose parameters map
directly to the discrete model. Analytical solutions of this theory show the
concentric patterns arise from anisotropically accumulated resistance to growth
over many cell cycles. This work shows how purely mechanical processes can
affect the internal patterning and morphology of cell collectives, and provides
a concise theoretical framework for connecting the micro- to macroscopic
dynamics of proliferating matter.
