Amoeboid movement utilizes the shape coupled bifurcation of an active droplet to boost ballistic motion

One of the essential functions of living organisms is spontaneous migration through the deformation of their body, such as crawling, swimming, and walking. Depending on the size of the object, the efficient migratory mode should be altered because the contribution from the inertial and frictional forces acting on the object switches. Although the self-propelling motion characterizing active matter has been extensively studied, it is still elusive how a living cell utilizes the mode switching of the self-propulsion. Here, we studied the migration dynamics of amoeboid movement of free-living amoeba, Amoeba proteus, for starved and vegetative phases, as typified by dynamic and stationary states, respectively. Fourier-mode analysis on the cell shape and migration velocity extracted two characteristic migration modes, which makes a coexistence of amoeboid-swimmer like random motion and the active-droplet like ballistic motion. While the amoeboid-swimmer mode governs random motion, the active-droplet mode performs non-negligible contribution on the migration strength. By employing the symmetry argument of the active-droplet, we discover the supercritical pitchfork bifurcation of the migration velocity due to the symmetry breaking of the cell shape represents the switching manner from the motionless state to the random and the ballistic motions. Our results suggest that sub-mm sized A. proteus utilizes both shape oscillatory migration of deformed-swimmer driven by surface wave and convection based mass transfer, called blebbing, as like as cm-sized active droplet to optimize the movement efficiency.