Figure 1.
Three different growth mechanisms of tissues on hexagonal lattices.
A). Cell division: A random cell in the tissue is doubled in each time step. The daughter cell is born in the same state as the mother cell and existing cells are pushed outwards (in a random direction) by the newly born cell. After each cell cycle the entire tissue is equilibrated by the dynamical equations (eq. 2). B). Cell migration: Cells are in each time step migrated onto the entire boundary of the tissue. All newly arriving cells are in the silenced state. The tissue is equilibrated between each growth step. C). Lateral growth: the tissue is grown only along one side through cell divisions, where each daughter cell is born in the same state as the mother. Between each addition of a new layer, the entire tissue is equilibrated. The parameter values were: ,
,
,
,
.
Figure 2.
Tissue growth under cell division where in each cell cycle, a random cell is chosen and multiplied such that the daughter cell is born in the same state as the mother cell.
The new cell pushes existing states in a random direction. The cells are graded from black (active cell) down to light gray (silenced cell). Note that the center of the tissue becomes completely ordered, i.e. each active cell is surrounded by six silenced cells.
Figure 3.
Total effect of mutations of single cells in the tissue.
Starting from three different equilibrated tissues formed by cell division and migration (A), lateral growth (B) and random initial conditions (C), respectively, each cell of the tissue is mutated by the following rule: silenced active or active
silenced. The mutated cell is kept in the state it is set to after mutation. Panel (D–F): the color scheme indicates the sum of the activity changes over the entire tissue due to the mutation of one single cell. The lower panels (G–I) display the number of nodes affected by the mutation of the given cell. We note that the effects of mutations in the ordered tissue (A,D,G) are small. The tissues with disordered patches are very sensitive to mutations on the default lines separating these two phases. This is also apparent in the preformed tissue starting with cells being in random initial conditions where a larger effect occurs all along the default boundaries.
Figure 4.
The mutation of a single cell in a tissue grown through cell division.
On the default boundary between the ordered and disordered tissue (left panel), a silenced state is mutated into an active state (middle panel). The rightmost panel shows the effect of the mutation, where red symbolizes the largest effect and blue the smallest. The total number of cells that are affected more than 5% by the mutation is 10 (all colored).
Table 1.
Average number of cells which are affected by more than 5 due to a single cell mutation of either a silenced to active cell, or an active to silenced cell, mean (standard deviation) in lattices with dimensions of 90×90 cells.
Figure 5.
Disordered patches appear when cells are mutated during tissue growth and when grown with accelerated speed.
(1A–C) Mutations during growth. In 5% of the cell divisions, the mother cell is mutated (and kept) in either a silenced (yellow) or active state (green) state. This creates a tissue with strongly disordered patches. (2A–C) Effect of growth speed on the activity pattern. The equilibration time between each cell cycle is now of the size of the degradation time
and is thus much shorter than the equilibration time used in Figure 2. Both disordered and ordered patches now appear side by side in the tissue.