Fig 1.
The abstraction of cell–cell interaction.
(a) (b) If only the same cells are present, there is only one interaction that needs to be considered. (a) When there are only intact cells, only interactions among intact cells are considered. (b) When there are only damaged cells, only interactions among damaged cells are considered. (c) When two different types of cells are mixed, in addition to interactions among the same cells, there are interactions between cells of different types. Therefore, four interactions must be considered. (d) The result of cell–cell interaction is summarized in a cost matrix. For example, when an intact cell interacts with a damaged cell, the intact cell suffers cost .
Fig 2.
The abstraction of the lattice-space model.
(a) Cells are arranged in a squared lattice in the lattice-space model. The numbers represent positions in the lattice. We assumed Moore neighborhood and periodic boundary condition. For example, a cell at location 1 interacts with cells at 2, 5, 6, 7, 10, 21, and 22. (b) The cost of each cell in the case of (a). The symbol is the cost of a cell in position
.
Fig 3.
Waiting time until damaged cells occupy the cell pool, , in the well-mixed model.
(a) The horizontal line represents the dose rate . The vertical axis represents
Circles indicate the average of 1,000 times simulations. Lines indicate the approximations shown in eq. (7a). The number of cells in the cell pool
is
. The parameters of the cost matrix are shown in the figure. Black dots and lines indicate the case in which the costs of all cells are equal, i.e., cell elimination and division occur randomly. We interpret that if
is larger than this, the accumulation of damaged cells is suppressed by stem cell competition, and conversely, if
is smaller, it is promoted. (b) The ratio of the simulation result to the approximation. Values close to 1 indicate good agreement.
Fig 4.
Dependence on the total number of cells.
The horizontal line represents the number of cells in the cell pool . The value of
is normalized as 1 for
. The vertical axis represents the
calculated under a very low dose rate condition in eq. (7a). (a)
, (b)
, (c),
, (d)
and (e)
.
Fig 5.
Summary of the shape of . Fixing
.
Gray, red, and green dots represent monotonic increase, monotonic decrease, and convex downward, respectively. Black dot represents the case that did not change depending on
. Vertical and horizontal lines in the diagram represent
and
, respectively. The dotted line represents the parameters
decreases when
changes from
to
. The dotted-dashed line represents the parameters
increases when
is very large, in which
hear.
Fig 6.
Comparison of the well-mixed model and the lattice space model.
White circles and asterisks are the average of 50 simulations of the well-mixed and the lattice space models, respectively. The black line is the approximated under the very low dose rate condition shown in eq. (7a). (a)
, (b)
, (c),
, (d)
and (e).
.