Self-Propelled Particle Model for Cell-Sorting Phenomena

A self-propelled particle model is introduced to study cell sorting occurring in some living organisms. This allows us to evaluate the influence of intrinsic cell motility separately from differential adhesion with fluctuations, a mechanism previously shown to be sufficient to explain a variety of cell rearrangement processes. We find that the tendency of cells to actively follow their neighbors greatly reduces segregation time scales. A finite-size analysis of the sorting process reveals clear algebraic growth laws as in physical phase-ordering processes, albeit with unusual scaling exponents.

Figure 1

Sorting of 800 cells. Black and gray circles represent, respectively, endodermic and ectodermic cells. (a) Initial configuration; (b) $t=3\times {10}^3$; (c) $t=3\times {10}^5$; (d) $t=2\times {10}^7$.

Figure 2

Cell sorting in two dimensions from a random, roughly circular initial aggregate of $N=6400$ cells in a proportion of $1:3$ endodermic to ectodermic cells. Evolution of ${\gamma }_1$ for different $\alpha$ values. The dashed line has slope $-\lambda =-0.18$. Inset: Same in three dimensions but with $\alpha =0.01$ and ${\beta }_{11}=8.3$. The dashed line has slope $-0.16$.

Figure 3

(a) Rescaling of the segregation evolution for different total numbers of cells. The raw data are shown in the inset with the same symbol convention. Parameters: ${\beta }_{11}=3.83$, ${\beta }_{12}=2.53$, ${\beta }_{22}=2.5$, and $\alpha =0.01$. (b) Asymptotic order parameter ${\gamma }_1^{*}$ vs $N$; the straight line has slope $-\mu =-0.32$. (c) Saturation time $t^{*}$ vs $N$. The straight line has slope $\nu =1.77$.