Cell Growth Rate Dictates the Onset of Glass to Fluidlike Transition and Long Time Superdiffusion in an Evolving Cell Colony

Collective migration dominates many phenomena, from cell movement in living systems to abiotic selfpropelling particles. Focusing on the early stages of tumor evolution, we enunciate the principles involved in cell dynamics and highlight their implications in understanding similar behavior in seemingly unrelated soft glassy materials and possibly chemokine-induced migration of CD8(+)T cells. We performed simulations of tumor invasion using a minimal three-dimensional model, accounting for cell elasticity and adhesive cell-cell interactions, as well as cell birth and death, to establish that cell-growth-rate-dependent tumor expansion results in the emergence of distinct topological niches. Cells at the periphery move with higher velocity perpendicular to the tumor boundary, while the motion of interior cells is slower and isotropic. The mean-square displacement (Delta t) of cells exhibits glassy behavior at times comparable to the cell cycle time, while exhibiting superdiffusive behavior, Delta(t) approximate to t(alpha) (alpha > 1), at longer times. We derive the value of alpha approximate to 1.33 using a field theoretic approach based on stochastic quantization. In the process, we establish the universality of superdiffusion in a class of seemingly unrelated nonequilibrium systems. Superdiffusion at long times arises only if there is an imbalance between cell birth and death rates. Our findings for the collective migration, which also suggest that tumor evolution occurs in a polarized manner, are in quantitative agreement with in vitro experiments. Although set in the context of tumor invasion, the findings should also hold in describing the collective motion in growing cells and in active systems, where creation and annihilation of particles play a role.