Collective motion of cells crawling on a substrate: roles of cell shape and contact inhibition

Simon K Schnyder,Yuki Tanaka,John J Molina,Ryoichi Yamamoto

doi:10.1038/s41598-017-05321-0

Abstract

Contact inhibition plays a crucial role in cell motility, wound healing, and tumour formation. By mimicking the mechanical motion of cells crawling on a substrate, we constructed a minimal model of migrating cells that naturally gives rise to contact inhibition of locomotion (CIL). The model cell consists of two disks, a front disk (a pseudopod) and a back disk (cell body), which are connected by a finite extensible spring. Despite the simplicity of the model, the collective behaviour of the cells is highly non-trivial and depends on both the shape of the cells and whether CIL is enabled. Cells with a small front disk (i.e., a narrow pseudopod) form immobile colonies. In contrast, cells with a large front disk (e.g., a lamellipodium) exhibit coherent migration without any explicit alignment mechanism in the model. This result suggests that crawling cells often exhibit broad fronts because this helps facilitate alignment. After increasing the density, the cells develop density waves that propagate against the direction of cell migration and finally stop at higher densities.

Highlights

In the first stage of the crawling cycle 0 < t < ΔT/2, the pseudopod is pushed forward against friction with the substrate by an extensional force, Ffene + Fmig, which acts between the two disks of opposite signs, while the cell body adheres to the substrate with ζb = ∞, vb(t) = 0, vf (t)
In the second stage of the crawling cycle, ΔT/2 < t →< ΔT, the pseudopod adheres to the substrate with ζf = ∞ and the cell body is drawn in with a contraction force Ffene, vb(t)

Summary

Discussion

CIL cells with small fronts cluster because their migration force tends to stay pointed toward the other cells after a collision, which compresses and inhibits them. Unlike most models, the alignment mechanism is not explicitly included in the model While such a transition as a function of cell shape has not been observed in experiments, it may explain why crawling cells often exhibit a broad front: It improves alignment. Keratocytes exhibit a different transition from disordered to coherent motion that is driven by an increase in density[35] At first, this behaviour is not found in our model because the alignment of cells is mostly independent of density. Because our CIL mechanism links the velocity waves to corresponding density waves, it makes them distinct from heterogeneous velocity fields occurring without corresponding heterogeneous density[47]

Summary and conclusion

Methods