Inertia of amoebic cell locomotion as an emergent collective property of the cellular dynamics.

Amoebic cells are ubiquitous in many species and have been used as model systems to study the eukaryotic cellular locomotion. We construct a model of amoebic cells on two-dimensional grids, which describes sensing, cell status, and locomotion in a unified way. We show that the averaged position of simulated cells is described by a second-order differential equation of motion and that the mechanical pushing at the initial moment boosts the cell movement, which continues after the cell is released from the pushing. These "inertialike" features suggest the possibility of Newtonian-type motions in chemical distributions of the signaling molecule. We show, as an example, the possibility of rotating motion in a "centripetal" distribution. The observed inertial motion is an emergent collective dynamics, which is controlled by diffusive and chemical processes in the cell.