Abstract
Amoeboid cells propel by generating pseudopods that are finger-like protrusions of the cell body that continually grow, bifurcate, and retract. Pseudopod-driven motility of amoeboid cells represents a complex and multiscale process that involves bio-molecular reactions, cell deformation, and cytoplasmic and extracellular fluid motion. Here we present a 3D model of pseudopod-driven swimming of an amoeba suspended in a fluid without any adhesion and in the absence of any chemoattractant. Our model is based on front-tracking/immersed-boundary methods, and it combines large deformation of the cell, a coarse-grain model for molecular reactions, and cytoplasmic and extracellular fluid flow. The predicted shapes of the swimming cell from our model show similarity with experimental observations. We predict that the swimming behavior changes from random-like to persistent unidirectional motion, and that the swimming speed increases, with increasing cell deformability and protein diffusivity. The unidirectionality in cell swimming is observed without any external cues and as a direct result of a change in pseudopod dynamics. We find that pseudopods become preferentially focused near the front of the cell and appear in greater numbers with increasing cell deformability and protein diffusivity, thereby increasing the swimming speed and making the cell shape more elongated. We find that the swimming speed is minimum when the cytoplasm viscosity is close to the extracellular fluid viscosity. We further find that the speed increases significantly as the cytoplasm becomes less viscous compared with the extracellular fluid, resembling the viscous fingering phenomenon observed in interfacial flows. While these results support the notion that softer cells migrate more aggressively, they also suggest a strong coupling between membrane elasticity, membrane protein diffusivity, and fluid viscosity.