Two types of critical cell density for mechanical elimination of abnormal cell clusters from epithelial tissue
Fig 3
Mechanical homeostatic cell density and scaling of phase diagrams for elimination success/failure.
(A) The simulation settings in which cells continue proliferating within a restricted space with a fixed boundary (gray cells; left). The dependency of the number of cells in the domain (black) and mean cell area (red) on the domain size R (right). Each open circle indicates the temporal average of a single simulation run. The error bars indicate the standard deviation over time. (B) The distribution of the number of cell sides within an abnormal cell cluster in the growth suspension phase (black) and in a growing tissue composed of a single cell type under free boundary (white) and fixed boundary (gray) conditions. These histograms were obtained by the temporal average over a single simulation run. (C) The reciprocal values of mechanical homeostatic cell density ρ1 (red) and the upper limit of surrounding cell density below which a regular polygon with i edges can exist (ρMCE(i), i = 3, blue; i = 4, green; i = 5, black) for different sets of mechanical parameters (Λ,Γ). (D) Pairwise plots of 1/ρ1 and 1/ρMCE(i) (i = 3, left; i = 4, middle; i = 5, right) showing their positive correlations. (E) Comparison of the values of ρ1 and the multiple linear regression results for the nine different mechanical parameter sets (see also Eq (1)). The broken line represents
= ρ1. (F) A schematic diagram for the 2D Laplace’s law. At the interface, the energy is higher by ΛΔμ = Λ(μ−1) per unit edge length. PN and PA are the pressure within normal and abnormal cell populations, respectively, the difference in which is denoted by ΔP = PA − PN. Req is the radius of the abnormal cell cluster (denoted by R) at mechanical equilibrium. (G, H) The frequencies of elimination failure (red), growth suspension (black), and elimination success (green) against the rescaled contractility
for the tissues with lower fluidity (G) or higher fluidity (H). The thin curves show the results (fitted by the Hill functions) for Nθ = 100, 150, 200, and 250, and the thick curves show the approximations using the Hill functions for all of the simulation data with four different values of Nθ. In (A), (B), and (G), the parameter set (Λ,Γ = 0.12, 0.04) was used. In (C), (D), and (E), the nine parameter sets in Fig 1B were used. In (H), the parameter set (Λ,Γ = 0.01, 0.025) was used.