Figure 7. Classification of the expansion type in the ‘Go or Grow’ model.

Cells initially on the left-hand side or right-hand side of the peak get labeled differently (A and B). The labeling is neutral and does not change the dynamics of the cells. We let evolve the two colored population for some time and observe the mixing of the colors (C and D). (A and C) With $a_0=1\mu m\cdot {min}^{-1}$, the wave is pushed wave and after some time the front undergoes a spatially uniform mixing. (B and D) With ${\displaystyle a_0=0.1\mu m\cdot mi{n}^{-1}}$, the wave is pulled and only the fraction initially in the front is conserved in the front. $r_0=ln2/480{min}^{-1}$ and $C_0=0.7\%$ for all conditions.

Figure 7—figure supplement 1. Mixing in Potts models.

A simulation of the full model was stopped at an arbitrary time and cells were colored according to their position at this time. The simulation was then restarted from this time point and left to run for the equivalent of 10 hr, at which point complete mixing of both populations is clearly visible.

Figure 7—figure supplement 2. Heatmap of $\mathrm{\phi }=2\sqrt{{\mathrm{r}}_0\mathrm{D}}/\mathrm{\sigma }$ as a measure of the relative contribution of cell division to the overall wave speed $\mathrm{\sigma }$ in the space parameter ${1/\mathrm{r}}_0$ and ${\mathrm{a}}_0$ for the ‘Go or Grow’ model with a second threshold, under the specific condition that O₂ consumption term be $\mathrm{b}\left(\mathrm{C}\right)={\mathrm{b}}_0$ and that O₂ concentration may be negative (see Materials and methods).

The curve ${\mathrm{a}}_0=\sqrt{{\mathrm{r}}_0\mathrm{D}}$ is depicted in black.

Figure 7—figure supplement 3. Classification of the expansion type in the ‘Go or Grow’ model with a second-threshold.

Cells initially on the left-hand side or right-hand side of the peak get labeled differently (A and B). The labeling is neutral and does not change the dynamics of the cells. We let evolve the two colored population for some time and observe the mixing of the colors (C and D). (A and C) With ${\mathrm{a}}_0=1\mathrm{\mu }\mathrm{m}\cdot {\mathrm{m}\mathrm{i}\mathrm{n}}^{-1}$, the wave is pushed and after some time the front undergoes a spatially uniform mixing. (B and D) With ${\displaystyle {\mathrm{a}}_0=0.1\mu \mathrm{m}\cdot \mathrm{m}\mathrm{i}{\mathrm{n}}^{-1}}$, the wave is pulled and only the fraction initially in the front is conserved in the front.