Motility-induced mixing transition in exponentially growing multicellular spheroids

Abstract

Growth drives cellular dynamics in dense aggregates including bacterial colonies, developing tissues, and tumors. We investigate the underlying physical principles emerging from the interplay of 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: Without motility, deterministic radial motion from volume expansion dominates, while growth and division cause tangential, cellular-scale diffusion, largely independent of expansion velocity. Despite this small-scale diffusion, cell lineages remain confined to their local environment. This confinement persists at weak motility and is overcome only above a threshold, leading 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 motility-induced velocity below a threshold, and the expanding nature of the system which inhibits complete mixing. Our study highlights the complex interaction of local cell division and motility with global expansion, mediated exclusively by mechanics. The results provide a baseline for identifying additional biological mechanisms in experiments, for example in tissue spheroids. The mixing dynamics might also be relevant for competition or tumor progression by interacting with genetic heterogeneity.