Mechanical feedback controls the emergence of dynamical memory in growing tissue monolayers

The growth of a tissue, which depends on cell-cell interactions and biologically relevant processes such as cell division and apoptosis, is regulated by a mechanical feedback mechanism. We account for these effects in a minimal two-dimensional model in order to investigate the consequences of mechanical feedback, which is controlled by a critical pressure, p_c. A cell can only grow and divide if its pressure, due to interaction with its neighbors, is less than p_c. Because temperature is not a relevant variable, the cell dynamics is driven by self-generated active forces (SGAFs) that arise due to cell division. We show that even in the absence of intercellular interactions, cells undergo diffusive behavior. The SGAF-driven diffusion is indistinguishable from the well-known dynamics of a free Brownian particle at a fixed finite temperature. When intercellular interactions are taken into account, we find persistent temporal correlations in the force-force autocorrelation function (FAF) that extends over a timescale of several cell division times. The time-dependence of the FAF reveals memory effects, which increases as p_c increases. The observed non-Markovian effects emerge due to the interplay of cell division and mechanical feedback and are inherently a non-equilibrium phenomenon.