Title: Proliferation-driven mechanical feedback regulates cell dynamics in growing tissues

Abstract: Local stresses in a tissue, a collective property, regulate cell division and apoptosis. In turn, cell growth and division induce active stresses in the tissue. As a consequence, there is a feedback between cell growth and local stresses. However, how the cell dynamics depend on local stress-dependent cell division and the feedback strength is not fully understood. Here, we probe the consequences of stress-mediated growth and cell division on cell dynamics using agent-based simulations of a two-dimensional growing tissue. We discover a rich dynamical behavior of individual cells, ranging from jamming (mean square displacement, $\Delta (t) \sim t^{\alpha}$ with $\alpha$ less than unity), to hyperdiffusion ($\alpha > 2$) depending on cell division rate and the strength of the mechanical feedback. Strikingly, $\Delta (t)$ is determined by the tissue growth law, which quantifies cell proliferation (number of cells $N(t)$ as a function of time). The growth law ($N(t) \sim t^{\lambda}$ at long times) is regulated by the critical pressure that controls the strength of the mechanical feedback and the ratio between cell division-apoptosis rates. We show that $\lambda \sim \alpha$, which implies that higher growth rate leads to a greater degree of cell migration. The variations in cell motility are linked to the emergence of highly persistent forces extending over several cell cycle times. Our predictions are testable using cell-tracking imaging techniques.