A minimal mathematical model of cytoplasmic mixing in large motile cells

The cytoplasm of cells is a dynamic fluid with continuous mixing of cellular components. This mixing is vital for cell functions but is complicated by the cell's motion, shape changes, and crowding due to organelles and other sub cellular structures. The giant amoeba chaos carolinensis is an excellent model experimental system for studying cytoplasmic mixing thanks to its large size. While diffusion is sufficient for cytoplasmic mixing in relatively small cells, large cells rely on active mechanisms to facilitate cytoplasmic mixing. Motivated by this, we carry out agent-based simulations of a minimal mathematical model of the dynamics of tracer particles in a large motile cell with low to moderate internal crowding and deformable boundaries. We investigate the emergent cytoplasmic flow and mixing in this model system by characterizing the motion of the tracer particles in terms of their trajectories, mean squared displacements, and velocity correlations. We compare our results with experimental data and estimates of mixing timescales in various fluid flows, and discuss potential mechanisms for mixing in large cells.