Vertex model of posterior compartment dynamics during the last division cycle in the <i>Drosophila</i> embryonic epidermis.

<p>(A) Snapshot of the initial tissue configuration for each simulation, with mechanical parameters in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004679#pcbi.1004679.e003" target="_blank">Eq (3)</a> annotated. (B) Schematic diagram of a junctional rearrangement (T1 swap), a cell removal (T2 transition), and cell division in the vertex model. Numbers indicate cell indices. (C) Snapshot of a <i>wt</i> simulation at the final time point, once all cell divisions have occurred, with annotation for the front and back halves of the P compartment. Parameter values are listed in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004679#pcbi.1004679.t001" target="_blank">Table 1</a>.</p

Cell area distributions in the <i>en>dap</i> and <i>en>CycE</i> perturbations are multimodal.

<p>Distributions of cell areas for each perturbation of cell division events (<i>wt</i>, <i>en>dap</i> and <i>en>CycE</i>) and each scenario of cellular asymmetry. Cell areas are recorded at the end of each simulation and error bars denote standard deviations across 100 simulations. Parameter values are given in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004679#pcbi.1004679.t001" target="_blank">Table 1</a> and in the main text.</p

Sensitivity of P compartment size and cell number to asymmetry.

<p>Variation of P compartment area (upper row) and cell number (middle row), and of the number of accumulated cell deaths over 100 simulations in the front and back halves of the P compartment (lower row), as the asymmetry parameters λ_<i>A</i>, λ_<i>l</i>, and λ_<i>p</i> are varied individually while holding all other parameters at their values listed in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004679#pcbi.1004679.t001" target="_blank">Table 1</a>. Shaded areas are added for comparison with Figs <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004679#pcbi.1004679.g003" target="_blank">3</a> and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004679#pcbi.1004679.g005" target="_blank">5</a>.</p

Compartment size control can emerge from passive mechanical forces.

<p>(A) Snapshots of <i>wt</i>, <i>en>dap</i> and <i>en>CycE</i> simulations, each following the final round of division. Parameter values are listed in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004679#pcbi.1004679.t001" target="_blank">Table 1</a>. (B) Comparison of simulated P compartment areas and cell numbers with observed values [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004679#pcbi.1004679.ref014" target="_blank">14</a>]. Mean values from 100 simulations are shown and error bars are standard deviations. (C) Variation of P compartment area (upper row) and cell number (middle row), and of the number of accumulated cell deaths in the <i>en>CycE</i> perturbation over 100 simulations in the front and back halves of the P compartment (lower row), as each mechanical parameter is varied individually, holding all other parameters at their values listed in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004679#pcbi.1004679.t001" target="_blank">Table 1</a>. Shaded areas in (B) and (C) mark the ranges of experimentally observed values and are added for reference (see main text for details).</p

Spatial regulation of mechanical cell properties can induce asymmetry of cell death occurrence inside posterior compartments.

<p>(A) Schematic of the distinct forms of mechanical asymmetries considered in this work. (B) Snapshot of final configuration of simulations for each considered perturbation. (C) Comparison of P compartment areas and cell numbers for each of the considered perturbations with experimental values. Mean values from 100 simulations are shown and error bars are standard deviations. Parameter values are given in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004679#pcbi.1004679.t001" target="_blank">Table 1</a> and in the main text. Shaded areas mark the ranges of experimentally observed values and are added for reference and comparison with <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004679#pcbi.1004679.g003" target="_blank">Fig 3</a>, <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004679#pcbi.1004679.s003" target="_blank">S1</a> and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004679#pcbi.1004679.s004" target="_blank">S2</a> Figs. (D) Comparison of accumulated number cell deaths over 100 simulations in the front and back halves of the P compartment for each of the considered perturbations.</p

The <i>Drosophila</i> embryo as a model system for size homeostasis.

<p>(A) Specification of embryonic stages over time; the red boxed region represents the time period of simulations [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004679#pcbi.1004679.ref018" target="_blank">18</a>]. (B) Summary of genetic perturbations simulated in this study. The wt genotype is <i>engrailed>GAL4</i>, <i>UAS>GFP</i>. The perturbations are crosses between the <i>wt</i> and <i>UAS>CyclinE</i> and <i>UAS>dacapo</i> lines, respectively. (C) Stage 11 embryo expressing GFP in the posterior compartment, stained for DE-cadherin to show cell boundaries. (D) High magnification image of simulation domain. (E, F) Data extracted from [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004679#pcbi.1004679.ref014" target="_blank">14</a>] demonstrating that compartment dimensions are robust to manipulations that change the number of cells. (G) Cell death, indicated by cleaved <i>Drosophila</i> death caspase-1 (DCP-1) antibody staining [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004679#pcbi.1004679.ref019" target="_blank">19</a>], is statistically more likely to occur in the front half of the posterior compartment in <i>en>CycE</i> embryos [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004679#pcbi.1004679.ref014" target="_blank">14</a>].</p

Simulated laser ablation experiments allow discrimination between asymmetry scenarios.

<p>Average initial vertex recoil velocities and total recoil distances across simulations of <i>wt</i> and perturbations. Error bars denote standard deviations across 100 simulations. Parameter values are given in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004679#pcbi.1004679.t001" target="_blank">Table 1</a> and in the main text.</p

Diagram of the underlying physical basis of model simulations.

<p>(A) Intracellular and intercellular interactions between different elements of the model. Symbols and notations are indicated in the legend. (B) Implementation of the simulation of cell cycle in the model.</p

Epithelial mechanics and workflow outline.

<p>(A) Apical surface of epithelial cells within the <i>Drosophila</i> wing imaginal disc that are marked by E-cadherin tagged with fluorescent GFP (DE-cadherin::GFP). Multiple cells within the displayed region are undergoing mitotic rounding with a noticeable decrease in fluorescent intensities of E-Cadherin. (B) Experimental image of cross-section of wing disc marking levels of actomyosin (Myosin II::GFP). (C) Cartoon abstraction of epithelial cells, which are polarized with apical and basal sides. Actomyosin and mechanical forces during mitotic rounding are primarily localized near the apical surface. (D) At the molecular scale, the boundary between cells consists of a lipid bilayer membrane for each cell, E-cadherin molecules that bind to each other through homophilic interactions, and adaptor proteins that connect the adhesion complexes to an underlying actomyosin cortex that provides tensile forces along the rim of apical areas of cells. (E) The graphical workflow of the computational modeling setup, calibration, verification and predictions. Arrows indicate mitotic cells. Scale bars are 10 micrometers.</p

Quantitation of relative sensitivity of mitotic area expansion and roundness to adhesion, stiffness and pressure changes within the physiological property space.

<p>Sensitivity estimation of (A) (<i>A</i>_<i>mit</i>/<i>A</i>_<i>inter</i>) and (B) <i>R</i>_<i>norm</i> to small perturbation in the three mitotic parameter set points, , , and Δ<i>P</i>. Sensitivity was estimated from the reduced RSM model described in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005533#pcbi.1005533.g007" target="_blank">Fig 7C–7F</a> after stepwise model regression (p-value cutoff of 0.01). (C) Proposed mechanical regulatory network defined for “physiological ranges” within the parameter ranges defined by the CCD (Run 2, <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005533#pcbi.1005533.g007" target="_blank">Fig 7A</a>) that summarizes the local sensitivity analysis. Cell adhesivity, an increase in , slightly inhibits area expansion and strongly inhibits roundness. Membrane stiffness, inhibits area expansion and promotes roundness. Mitotic area expansion is most sensitive to variation in the mitotic pressure change (Δ<i>P</i>), but pressure has little effect on roundness over the calibrated physiological ranges.</p