Relationship between epithelial organization and morphogen interpretation

SimuCell3D: three-dimensional simulation of tissue mechanics with cell polarization

The three-dimensional (3D) organization of cells determines tissue function and integrity, and changes markedly in development and disease. Cell-based simulations have long been used to define the underlying mechanical principles. However, high computational costs have so far limited simulations to either simplified cell geometries or small tissue patches. Here, we present SimuCell3D, an efficient open-source program to simulate large tissues in three dimensions with subcellular resolution, growth, proliferation, extracellular matrix, fluid cavities, nuclei and non-uniform mechanical properties, as found in polarized epithelia. Spheroids, vesicles, sheets, tubes and other tissue geometries can readily be imported from microscopy images and simulated to infer biomechanical parameters. Doing so, we show that 3D cell shapes in layered and pseudostratified epithelia are largely governed by a competition between surface tension and intercellular adhesion. SimuCell3D enables the large-scale in silico study of 3D tissue organization in development and disease at a great level of detail.

2D effects enhance precision of gradient-based tissue patterning

Robust embryonic development requires pattern formation with high spatial accuracy. In epithelial tissues that are patterned by morphogen gradients, the emerging patterns achieve levels of precision that have recently been explained by a simple one-dimensional reaction-diffusion model with kinetic noise. Here, we show that patterning precision is even greater if transverse diffusion effects are at play in such tissues. The positional error, a measure for spatial patterning accuracy, decreases in wider tissues but then saturates beyond a width of about ten cells. This demonstrates that the precision of gradient-based patterning in two- or higher-dimensional systems can be even greater than predicted by 1D models, and further attests to the potential of noisy morphogen gradients for high-precision tissue patterning.

Hedgehog morphogen gradient is robust towards variations in tissue morphology in Drosophila

During tissue development, gradients of secreted signaling molecules known as morphogens provide cells with positional information. The mechanisms underlying morphogen spreading have been widely studied, however, it remains largely unexplored whether the shape of morphogen gradients is influenced by tissue morphology. Here, we developed an analysis pipeline to quantify the distribution of proteins within a curved tissue. We applied it to the Hedgehog morphogen gradient in the Drosophila wing and eye-antennal imaginal discs, which are flat and curved tissues, respectively. Despite a different expression profile, the slope of the Hedgehog gradient was comparable between the two tissues. Moreover, inducing ectopic folds in wing imaginal discs did not affect the slope of the Hedgehog gradient. Suppressing curvature in the eye-antennal imaginal disc also did not alter the Hedgehog gradient slope but led to ectopic Hedgehog expression. In conclusion, through the development of an analysis pipeline that allows quantifying protein distribution in curved tissues, we show that the Hedgehog gradient is robust towards variations in tissue morphology.

Patterning precision under non-linear morphogen decay and molecular noise

Morphogen gradients can instruct cells about their position in a patterned tissue. Non-linear morphogen decay has been suggested to increase gradient precision by reducing the sensitivity to variability in the morphogen source. Here, we use cell-based simulations to quantitatively compare the positional error of gradients for linear and non-linear morphogen decay. While we confirm that non-linear decay reduces the positional error close to the source, the reduction is very small for physiological noise levels. Far from the source, the positional error is much larger for non-linear decay in tissues that pose a flux barrier to the morphogen at the boundary. In light of this new data, a physiological role of morphogen decay dynamics in patterning precision appears unlikely.