Dynamical correlation lengths in shape-based models of confluent tissue

It has become increasingly clear that the rheology of densely packed cells in confluent tissue helps control processes ranging from multicellular development to wound healing to cancer tumor development. However, the impact on tissue rheology of cell-autonomous active processes, such as active alignment of cell motility and cell proliferation, remains unclear. Moreover, our recent observations of cell monolayers that undergo extensive cell division indicate that tissue rheology changes dramatically as cells proliferate, with interesting dynamical correlation length scales that depend on the mechanical environment. To understand these observations, we extend shape-based models of confluent tissues to include both cell alignment and proliferation. We find that shape-based models quite naturally generate the time-varying trends in cell density, cell shape, and cell motility observed in our monolayers, and that a coupling mechanism like cell-cell alignment is necessary to generate the observed correlation length scales. In this context, we additionally investigate the effects of using metric vs topological alignment rules in active matter systems where the interaction potential is itself explicitly topological.