Fig. 5: A physical model of Drosophila ventral furrow formation.
From: Highly dynamic mechanical transitions in embryonic cell populations during Drosophila gastrulation
a 2D model of the ventral half of the Drosophila embryo with 19 mesodermal cells (yellow arrow range) and 28 neuroectodermal cells. a’ Furrow depth metric, measured as the normalised distance between the apical-most coordinate of the central mesodermal cell and the lowest point of the mesoderm from the initial condition in units of initial apical-basal cell height. Snapshot taken from a simulation corresponding to highlighted values in panel (f). b Each cell contains 4 compartments: apical, basal and two core compartments, where core2 increases over time in order to reproduce the observed cell heightening during VFF. Hookean links between compartments’ centre of mass are used to model apical constriction, and sub-apical and sub-basal longitudinal stiffness. Those constraints are part of an effective energy equation (H) that guides the model evolution and also includes adhesion, surface and volume terms. c Smoothed profiles of experimentally measured6 time varying myosin concentrations used to impose apical constriction on mesodermal cells. d Furrow depth as a function of sub-apical and sub-basal longitudinal stiffness of mesodermal cells. Furrow depth correlates with higher sub-apical stiffness, but not with sub-basal stiffness. e Furrow depth as a function of sub-apical longitudinal stiffness of central and peripheral cells. When either cell population is too soft, furrows fail to form. Higher values of central cell stiffness promote furrow formation, with optimal results when peripheral cell stiffness is lower (but not zero). Sub-basal stiffness was the same for both cell populations. e’ Representative simulation snapshots of 4 cases from panel (e) (indicated by corresponding outline colour). f Furrow depth as a function of increasing sub-apical central cell longitudinal stiffness, and decreasing sub-apical peripheral cell stiffness. Grid coordinate indicates final values of central and peripheral cell stiffness. Colour bar cropped at the furrow depth value of simulations where stiffness of both cell populations remains constant at 30. Sub-basal stiffness was kept constant and the same for both cell populations. Highlighted value at (peripheral: 18, central: 170) indicates simulation sets with deepest furrow. A snapshot of a simulation with these values is shown in panel (a’). d–f Each grid point value shows the average of 30 simulations. Source data is provided as a Source Data file.
