Motility-induced mixing transition in exponentially growing multicellular spheroids

Abstract Growth drives cellular dynamics in dense aggregates, including bacterial colonies, developing tissues, and tumors. However, its effects on other relevant activities have not received sufficient attention. Here, we investigate the underlying physical principles emerging from the interplay of unconstrained growth, steric repulsion, and motility in a minimal agent-based model of exponentially growing, three-dimensional spheroids. Our results reveal a motility-induced mixing transition: Despite cell-scale diffusion, cell lineages remain confined to their local environment until a certain motility threshold is reached, after which the system transitions to tangential superdiffusivity and global cell mixing, with a diverging timescale near the transition, reminiscent of glassy dynamics. Using a phenomenological model, we identify two effects governing this transition: Steric interactions that suppress active motion below a threshold, and the expanding nature of the system, which inhibits complete mixing. The results provide a baseline for identifying additional biological mechanisms in experiments and could be relevant for competition and heterogeneous tumor evolution.