Cell sorting based on motility differences

Self-propelled particles are used to simulate cell aggregates in a model considering homogeneous adhesion forces between cells and using only motility differences as segregation drivers. The tendency of cells to follow their neighbors is also included in the formulation. Three model variants are explored, and the conditions on which motility differences may produce segregation are mapped in parameter diagrams. The evolution of the order parameter measuring cell segregation is similar to those found by models based on differential adhesion. It is also found that, considering only velocity differences, the faster cells envelope the slower ones, which is opposite to the ordering observed in early experiments by Jones and co-workers [Jones, Evans, and Lee, Exp. Cell. Res. 180, 287 (1989)].

Figure 1

Snapshot of the asymptotic configuration of cells for three different proportions of slower to faster cells: (a) 1:3; (b) 1:1; (c) 3:1. In all cases, $N=2000$, $\delta =4$, $\alpha =0$.

Figure 2

Evolution of the segregation order parameter. The ratio between cell speeds is $\delta =4$. The straight line indicates a power law with exponent $\lambda \sim -0.22(\pm 0.02).$

Figure 3

System snapshots at $t=0$ (a), $t={10}^5$ (b), $t={10}^7$ (c), and $t={10}^8$ (d). In all cases $N=8000$, $\delta =4,$ and $\alpha =0$.

Figure 4

Speed ratio $\delta$ vs parameter of coordinated movement $\alpha$ in models a, b, and c. The curves separate regions of different center-of-mass behavior. Each point in this parameter space is generated using $N=2000$ particles. See text for details.

Figure 5

Evolution of the segregation parameter $\gamma$ in models a, b, and c. Values for parameters $\delta$ and $\alpha$ are indicated in the figure. The system contains $N=8000$ particles. Dotted lines represent logarithmic (up) and power-law (down) fits.