Fig. 4: Fate choice imbalance Δ increases as a function tension ratio R, in tandem with cell-shape changes.

a Schematic shows the probability distribution of homeostatic and tumor fate choices, where Basal and supra-basal cells are depicted in magenta and blue respectively. In balanced mode, the distribution between all three fates (basal-basal, basal-suprabasal, suprabasal) is symmetric, with r denoting the basal cell doubling. In tumors, the symmetric fates get imbalanced by Δ. b, c Representative examples of lineage trees are shown for tension ratios--R = 1.0(above) and R = 1.1 (below). Being a basal cell, magenta cells have the power to divide, whereas blue cells typically lose it upon extrusion. All the trees are to scale with time, shown in units of t/τ_D on the right. Magenta cells at the end of a tree have an unknown fate as they survive in the basal layer till the simulation ends. The division time corresponds to the appearance of daughter cells, and not the mother cell. d Proportion of all three fates-- basal-basal in pink, basal-suprabasal in gray, suprabasal in blue, of all cell divisions that took place within the first turnover i.e., time ≤ 1, is plotted with respect R. The distribution is initially symmetric with values-- 25%, 50%, 25%. Δ becomes the difference between magenta and blue curves, that increases with increasing R because the proportion of suprabasal cells plummet to zero, and is balanced by the ever-increasing ratio of basal-basal fate. The asymmetric fate shows a moderate decline. e Schematic to show the qualitative change in cell shape from prism-like to more pyramidal frustums. Basal area A_T is represented in red. f A_T is plotted with respect to R. Insets show the representative polyhedral cells that corroborate the increasing trend of A_T with their increasingly wider base. Error bars mean ± SEM (at least 60 simulations per value of R). g Connection between fate imbalance and cell-shape changes. Fate choice imbalance Δ is plotted with respect to basal area A_T (normalized by the cell volume for the given value of R) in a black dashed curve, and shows a linear relationship between both.