Emergence of collective propulsion through cell-cell adhesion

The mechanisms driving the collective movement of cells remain poorly understood. To contribute toward resolving this mystery, a model was formulated to theoretically explore the possible functions of polarized cell-cell adhesion in collective cell migration. The model consists of an amoeba cell with polarized cell-cell adhesion, which is controlled by positive feedback with cell motion. This model cell has no persistent propulsion and therefore exhibits a simple random walk when in isolation. However, at high density, these cells acquire collective propulsion and form ordered movement. This result suggests that cell-cell adhesion has a potential function, which induces collective propulsion with persistence.

Figure 1

(a) Schematic view of a model cell with polarized cell-cell adhesion. The shaded region represents a high-strength region of cell-cell adhesion. (b) The collision process of two cells. The arrows represent cell movement. $d\mathit{R}/dt$ represents the direction of cell motion. The saw-tooth shape of the bottom cell represents the protrusion that induces cell movement. The two cells collide and are then bound through cell-cell adhesion. As a result, the cells move in essentially the same direction. (c) Dynamics of polarized cell-cell adhesion. The arrow of $\mathit{p}$ represents the direction of single-side polarized cell-cell adhesion, and the curved arrow represents $d\mathit{p}/dt$ according to Eq. (1). The dotted line indicates the direction of $d\mathit{R}/dt$. (d) Schematic relation between $\mathit{p}$ and $d\mathit{R}/dt$.

Figure 2

(a) Order parameter of polarity $P$ as a function of the area fraction $\varphi$. (b) Snapshot of $\left\{m\right(\mathit{r}\left)\right\}$ and ${\mathit{p}}_m\mathrm{s}$ at $N=256(\varphi =42\%)$ and $\beta =0.5$. The colored region indicates cells. Different colors represent different cells. The black region represents empty space. White arrows represent the direction of polarized cell-cell adhesion.

Figure 3

(a) MSD as a function of the time step $t$. MSD is scaled by MSD at the time step $t=1$ for data sorting. The symbol $+$ represents the MSD for isolated cells, which is averaged over 64 cells. The symbol $\times$ represents the MSD for $J_p=2.0$. The symbol $\times +$ represents the MSD for $J_p=0.0$. (b) $v$ and $P$ as a function of $J_p$.

Figure 4

Schematic diagram of collective propulsion in the cases of (a) high cell density and (b) an isolated cell. The arrows of $\mathit{p}$ represent the direction of polarized cell-cell adhesion, and the shaded region represents the high-strength region of cell-cell adhesion.