A modeling study on how cell division affects properties of epithelial tissues under isotropic growth

Abstract

Cell proliferation affects both cellular geometry and topology in a growing tissue, and hence rules for cell division are key to understanding multicellular development. Epithelial cell layers have for long times been used to investigate how cell proliferation leads to tissue-scale properties, including organism-independent distributions of cell areas and number of neighbors. We use a cell-based two-dimensional tissue growth model including mechanics to investigate how different cell division rules result in different statistical properties of the cells at the tissue level. We focus on isotropic growth and division rules suggested for plant cells, and compare the models with data from the Arabidopsis shoot. We find that several division rules can lead to the correct distribution of number of neighbors, as seen in recent studies. In addition we find that when also geometrical properties are taken into account other constraints on the cell division rules result. We find that division rules acting in favor of equally sized and symmetrically shaped daughter cells can best describe the statistical tissue properties.

Figure 1. Distributions of number of neighbors and internal vertex angles from simulations with different division rules.

Error bars represent standard deviation. A) Distributions of number of neighbors. Experimental data from Arabidopsis thaliana is also presented for comparison. B) Distributions of internal vertex angles before and after suppression of cell division. For comparison, the ideal distribution of internal vertex angles if all cells were regular polygons is plotted.

Figure 2. Topological and geometrical properties of simulated tissues.

A) The deviation of each division rule. The deviation quantitatively measures how well resulting tissues of simulations with a given division rule reproduces the distribution of number of neighbors compared with experimental data of Arabidopsis thaliana. B) Results from the quantitatively measurement of cell shape (Methods). The numerical values for the shape measurement range from zero (“flat” cells without area) and (circular cells). The vertical line marks the value 0.072, which is the approximate value corresponding to a regular hexagon.

Figure 3. Example images of tissues from simulations with different division rules.

The stars in the tissues from the oryzalin experiment identify cells before and after cell division has been suspended. The width and height of all images are ten length units.

Figure 4. Cell area plotted as a function of number of neighbors for different division rules.

Cell areas are normalized such that the average cell area – including all cells of the tissue – is equal to unity. Presented data is average values together with standard deviations. The diagonal line is the relationship: , where is number of neighbors, defining Lewis' law .