Evolution of phenotypic plasticity leads to tumor heterogeneity with implications for therapy
Fig 2
The lattice-gas cellular automaton (LGCA) model.
(A) Left: The LGCA model is implemented on a one-dimensional lattice, where each node comprises two velocity channels for movement to the nearest-neighbor nodes and one rest channel for no movement. Each channel can be occupied by any number of cells. Cells in velocity channels (marked red) have the migratory phenotype, and cells in rest channels have the proliferative phenotype (blue). White channels denote the absence of tumor cells. Right: Schematic illustration of model dynamics: Cells switch between phenotypes depending on their genotype κ and the local tumor cell density. Proliferative cells divide with a constant rate α. Migratory cells randomly choose a new direction of movement. All cells die with a constant rate δ. (B) Cell migration. Each migratory cell (red) moves in the direction of its respective velocity channel. (C and D) Phenotypic plasticity. The phenotypic switch probability rκ depends on the tumor cell density in the microenvironment and the cell’s genotype κ. The sign of κ determines the switch regulation. (C) κ > 0 results in attractive behavior (proliferating phenotype triggered by high cell density), and κ < 0 (D) leads to repulsive behavior (cells switch to migratory phenotype if the local cell density becomes too high). The parameter θ indicates the cell density threshold, where the probability for either phenotype is 1/2.