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Amoeboid migration requires cells to undergo large shape changes, and to apply highly coordinated mechanical forces on the extracellular matrix by means of transient cell-matrix adhesions. Despite the recent intense study of amoeboid movement, the mechanisms of rapid shape changes and how they lead to migration are still unclear. One striking observation is that the strength of the traction forces exerted by these migrating cells is much larger than needed to overcome friction from the underlying fluid. We hypothesized that both the in-plane and out-of-plane traction stresses exerted by motile cells are key to understanding the mechanisms of what causes cell shape changes and the underlying dynamics of cell-matrix interaction.

We have developed a computational model to study the interplay of cellular mechanics, cell geometry dynamics, cell-substrate interaction, and the resulting migration. Under high cortical tension and axial actomyosin contraction, the model produced in-plane and out-of-plane traction stress patterns similar to those measured experimentally. Using our model we investigated what adhesion dynamics are required to give the signature seen in the exerted traction stresses. A few models for the adhesion bond dynamics are considered and the resulting traction stresses are compared with those measured experimentally. This work shows that the motility coordination observed in Dictyostelium discoideum amoeba emerges from the properties of these main components: actin polymerization, cortical tension, and a catch/slip force-dependent response of adhesive bonds.