Figure 1

Topological characteristics of cell-type domains in unsorted 3D aggregates. A 670-cell Voronoi tessellation of a sphere was briefly annealed with a cellular Potts model. Cells were then randomly assigned to one of two types. For each minority cell fraction, the topology was characterized for 100 sets of random cell-type assignments: Euler characteristic of minority cells (filled circles) and majority cells (open circles), and fraction of minority cells in the largest connected domain (solid line). The error bars and shaded region denote 1 standard deviation.Reuse & Permissions

Figure 2

Finite-element simulation of 3D cell sorting. The pseudorandom initial configuration of 454 cells has all 36 minority cells in one connected domain. (a) Cell configurations at the labeled times during sorting. For clarity, the majority cells are only indicated by thin gray outlines. Arrows $\mathbf{P}$ and $\mathbf{Q}$ indicate loops created by multiply connected chains of minority cells. (b) Close-up view as the loop indicated by $P$ seals off—breaking the bridge of majority cells that connected through its lumen. (c) Close-up view as the loop indicated by $Q$ opens by breaking a chain of minority cells. Reported times are dimensionless and defined as $\tau =\frac{3\overline{\gamma }}{\mu r}t$ where $\overline{\gamma }$ is the contact-area-weighted average tension, and $r$ is the average cell radius [19].Reuse & Permissions

Figure 3

Plateau-Rayleigh instabilities in thin rods of cells: (a) finite-element model and (b) cellular Potts model. Time advances down each column with breakage occurring at $\tau =78$ (a) or $t=2510$ MCS (b). In (b), the outer sheath of cells (light gray) is only shown in the early and late time insets. (c) Arrenhius plot showing how the rate of rod breakage depends on the Potts model temperature. Each point is the average of five simulations. The lines are the best linear fits.Reuse & Permissions

Figure 4

Dependence of sorting metrics on fluctuations and heterotypic interfacial tension. The target value for each metric after complete sorting is shown with thin gray lines (except $A_{D0}$ where the target value is zero). The finite-element simulations were stopped when sorting stopped. Each model’s results are plotted using its own time axis (MCS or dimensionless time).Reuse & Permissions