Active morphogenesis of patterned epithelial shells.

Shape transformations of epithelial tissues in three dimensions, which are crucial for embryonic development or in vitro organoid growth, can result from active forces generated within the cytoskeleton of the epithelial cells. How the interplay of local differential tensions with tissue geometry and with external forces results in tissue-scale morphogenesis remains an open question. Here, we describe epithelial sheets as active viscoelastic surfaces and study their deformation under patterned internal tensions and bending moments. In addition to isotropic effects, we take into account nematic alignment in the plane of the tissue, which gives rise to shape-dependent, anisotropic active tensions and bending moments. We present phase diagrams of the mechanical equilibrium shapes of pre-patterned closed shells and explore their dynamical deformations. Our results show that a combination of nematic alignment and gradients in internal tensions and bending moments is sufficient to reproduce basic building blocks of epithelial morphogenesis, including fold formation, budding, neck formation, flattening, and tubulation

Simulation results.

<p>Blue bars indicate the axis of cell polarization from PCP; longer bars correspond to stronger polarization. <b>A, B</b>) If all cells assume the cone fate simultaneously, whether under conditions of isotopic or anisotropic global stress, a disordered packing results. <b>C</b>) In the growing retina, cone photoreceptors are generated in a propagating, linear wave. Proliferative precursor cells are shown in white and cone photoreceptors in grey. To mimic growth and differentiation at the germinal zone in the simulations, successive columns of cells are induced to assume the cone fate. <b>D</b>) Induction of cones column-by-column with isotropic mechanical stress leads to a packing that is more ordered than in panel A, but still imperfect. <b>E</b>) Induction of cones column-by-column in the presence of anisotropic mechanical stress yields straight columns. <b>F</b>) When stress anisotropy is added during a simulation, ordering improves. Double-headed arrows indicate regions of the simulated packing where the initial induction of cone fate occurred under the indicated stresses.</p

Cone mosaics in the embryonic, larval, and adult zebrafish retina.

<p><b>A</b>) Schematic of photoreceptor packing in the apical plane of the adult retina, showing cones of red, green, blue, and UV (magenta) spectral sensitivities, and smaller rods (black). The 12-cell repeating motif of the cone mosaic pattern is outlined by the yellow rectangle. <b>B</b>) Regular pattern of cones visualized in a flat-mount retinal preparation from an adult, double transgenic zebrafish (<i>mi2009</i> line) in which UV and blue cones express different fluorescent reporters (pseudocolored magenta and blue) under the control of UV and blue opsin promoters, respectively. Apical boundaries of cells are delineated by ZO-1 immunostaining (yellow). Horizontal rows of alternating blue and UV cones alternate with horizontal rows of unlabeled cone profiles representing red-green double cone pairs. <b>C</b>) Rod photoreceptors are visualized in a flat-mount retinal preparation from an adult transgenic zebrafish (<i>kj2</i> line) in which the rod opsin promoter drives expression of a reporter gene (pseudocolored cyan). Apical boundaries of cells are delimited by ZO-1 immunostaining (yellow). Rods are largely excluded from the vertical columns of contiguous cones, and instead occupy the spaces between adjacent columns. <b>D</b>) Schematic of the hemispherical retinal epithelium. Retinal neurogenesis in the circumferential germinal zone at the peripheral margin adds annuli of new retinal neurons, such that the age of retinal cells is a direct function of their distance from the periphery. The ordered cone pattern illustrated in panels A–C is in the peripheral retina, whereas the central retina, surrounding the pole of the hemisphere, exhibits the disordered embryonic/larval pattern (panel E), with a transition zone in-between (panel G). The annular ligament (not shown) roughly encircles the germinal zone. <b>E</b>) Apical retinal surface of a double transgenic <i>mi2009</i> zebrafish at 4 days post-fertilization, showing the packing of cone cells that differentiated during embryonic development, before progressive addition of cones at the retinal margin begins: UV cones are magenta, blue cones are blue, ZO-1 immunostaining (yellow) outlines cell profiles at the level of the OLM. <b>F</b>) Average orientational order parameter (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002618#pcbi-1002618-g002" target="_blank">Fig. 2</a> and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002618#s4" target="_blank">Methods</a>) for embryonic and adult retina. (Three and six regions of ∼20 by 15 cone cells were used to calculate the values for embryonic and adult retina, respectively.) <b>G</b>) Transition from disordered cell packing in the larval remnant (left side) to ordered packing (right side) in a flat-mount retina of an adult double transgenic zebrafish, <i>mi2009</i> labeling blue and UV (magenta) cones, with cell boundaries visualized with ZO-1 immunostaining (yellow). The curved, dashed line segment traces a cone column. <b>H</b>) High magnification views of the angles at which three cone-cone interfaces meet (ZO-1 in yellow).</p

Coupling Mechanical Deformations and Planar Cell Polarity to Create Regular Patterns in the Zebrafish Retina

<div><p>The orderly packing and precise arrangement of epithelial cells is essential to the functioning of many tissues, and refinement of this packing during development is a central theme in animal morphogenesis. The mechanisms that determine epithelial cell shape and position, however, remain incompletely understood. Here, we investigate these mechanisms in a striking example of planar order in a vertebrate epithelium: The periodic, almost crystalline distribution of cone photoreceptors in the adult teleost fish retina. Based on observations of the emergence of photoreceptor packing near the retinal margin, we propose a mathematical model in which ordered columns of cells form as a result of coupling between planar cell polarity (PCP) and anisotropic tissue-scale mechanical stresses. This model recapitulates many observed features of cone photoreceptor organization during retinal growth and regeneration. Consistent with the model's predictions, we report a planar-polarized distribution of Crumbs2a protein in cone photoreceptors in both unperturbed and regenerated tissue. We further show that the pattern perturbations predicted by the model to occur if the imposed stresses become isotropic closely resemble defects in the cone pattern in zebrafish <em>lrp2</em> mutants, in which intraocular pressure is increased, resulting in altered mechanical stress and ocular enlargement. Evidence of interactions linking PCP, cell shape, and mechanical stresses has recently emerged in a number of systems, several of which show signs of columnar cell packing akin to that described here. Our results may hence have broader relevance for the organization of cells in epithelia. Whereas earlier models have allowed only for unidirectional influences between PCP and cell mechanics, the simple, phenomenological framework that we introduce here can encompass a broad range of bidirectional feedback interactions among planar polarity, shape, and stresses; our model thus represents a conceptual framework that can address many questions of importance to morphogenesis.</p> </div

Model rationale and main ingredients.

<p><b>A</b>) Cell boundaries at the level of the zonula adherens of the larval retina are revealed by ZO-1 immunostaining; note the fragments of straight, aligned rows of cones (top left, red dashed lines). We propose that this organization reflects an underlying planar cell polarity (schematic, bottom left): polarity proteins (dark blue lines) accumulate on certain interfaces, lowering their tension and leading to cell polarization (arrows). Without a global ordering signal, domains of aligned cell polarity (red dashed lines) appear. In the presence of a global ordering signal, all cones polarize in the same direction (bottom right) leading to the observed rectangular lattice and columns of cones in the adult retina (top right). <b>B</b>) Model ingredients: Cell shape is determined by interfacial tensions and pressures ; tensions must balance at vertices in mechanical equilibrium (green arrows, top left). Proteins A and B define planar cell polarity (top right) and prefer to collect on shorter interfaces (bottom right). Interfacial tensions depend on polarity protein concentrations <i>c</i> (bottom left).</p

Planar cell polarity in intact and regenerated retina.

<p><b>A</b>) Crb2a protein localized by immunocytochemistry in a flat-mount preparation at the margin of the adult retina (germinal zone to the right). The focal plane is at the level of the zonula adherens/OLM (left panel, projection of 12 confocal z slices, cyan); at the level of the inner segments/SAR of cone photoreceptors (middle panel, single confocal z slice, red); an overlay of both panels (right). See also <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002618#pcbi.1002618.s004" target="_blank">Fig. S4J–L</a>. <b>B</b>) Schematic illustrating Crb2a distribution along cone-cone interfaces within a column at the level of the SAR. Note that Crb2a does not localize to the orthogonal interfaces between adjacent cones across columns, as would be expected if Crb2a mediated unpolarized, but spectral-subtype-dependent, interactions between cones. <b>C</b>) At the level of the OLM, cone photoreceptors (large profiles) in regenerated retina are not organized in a rectangular lattice, but aggregate into short chains one cell wide, indicating polarized interactions (left panel). The planar polarized interfaces are verified by Crb2a localization in the SAR of these cones (middle panel). By tracing the Crb2a signal through successive focal planes in the Z-stack some planar polarized SAR interfaces between cone inner segments were associated with the corresponding cone-cone interfaces at the OLM, as indicated by white line segments (right panel). <b>D</b>) At the level of the OLM, cone profiles in the adult <i>bugeye</i> mutant are organized similarly to the regenerated retina, here visualized with a cocktail of antibodies against ZO-1 and Crb2a (left panel). Again similar to the regenerated retina, Crb2a localizes to planar polarized SAR interfaces between cone inner segments (middle panel), and some of these were traced to the cone-cone interfaces at the OLM (right panel).</p

Generation of cone photoreceptors in larval and adult fish.

<p><b>A</b>) Top: developmental time is indicated from right to left. Neuroepithelial progenitor cells in the retinal germinal zone proliferate, exit the cell cycle, and differentiate into cone photoreceptors, Müller glia (shaded grey), and retinal neurons (not shown). Rod photoreceptors are later added to the differentiated retina (left). The apical epithelial surface of the retina (cyan line) is the outer limiting membrane (OLM), as defined by the zonula adherens (ZA). The junctional protein Zonula Occludens (ZO-1) localizes to the OLM. The subapical region (SAR) of the plasma membrane shown in red is in the inner segment of the photoreceptors and is the site of localization of the Crumbs complex. The outer segments of photoreceptors contain the rod and cone opsins and are colored to represent the wavelength absorption maxima of their respective visual pigments. Bottom: the dotted rectangle indicates the retinal margin region illustrated in panels B and D, which straddles the proliferative germinal zone and the adjacent zone of differentiating cones. <b>B</b>) Larval retinal margin with cell boundaries at the level of the zonula adherens indicated by ZO-1 immunostaining, showing the packing of cone cells added through growth at the margin during the larval stage. The germinal zone is at the right. <b>C</b>) The Q₄ orientational order parameter from the image in panel B is plotted as a function of distance from the proliferating germinal zone (at ∼15 µm). <b>D</b>) Adult retinal margin; note that straight vertical columns of cones appear abruptly at the edge of the germinal zone and represent a cohort of cells generated approximately synchronously from the germinal zone at the right. The polygonal profiles marked by white stars represent profiles of Müller glia (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002618#pcbi.1002618.s001" target="_blank">Fig. S1J, L</a>). <b>E</b>) The orientational order parameter from the image in panel C; note that the value of increases sharply at the edge of the germinal zone (at ∼15 µm) in the adult retina.</p

Defining the orientational order parameter <i>Q</i>₄.

<p>Top two panels of A and B represent disordered cell packing; the bottom two panels of A and B represent ordered cell packing. <b>A</b>) A cross (blue) is placed at the geometric center of each cell profile, and the local fourfold orientation is chosen by minimizing the mean square distance between neighboring cells and the arms of the cross (red lines). One neighboring cell is chosen in each quadrant (dashed lines). <b>B</b>) The orientation of the crosses varies less in an ordered packing. <b>C</b>) The magnitude of the fourth order parameter ranges from 0 to 1 and increases as variability in the orientation of the crosses decreases. (See also <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002618#s4" target="_blank">Methods</a>.)</p

Additional file 1: of Steering cell migration by alternating blebs and actin-rich protrusions

Supplementary Methods. Supplementary methods file with detailed description of: 1. Data analysis: (A) Automatic Protrusion Analyzer (APA) software. (B) Polar Order Parameter (POP) used to characterize the distribution of orientations of protrusions of the model. (C) Automatic detection of run and tumbles. 2. Model of cell migration: (A) Cell migration model description [41–44]. (B) Parameterization of the computational model using experimental measurements [45]. (C) Model Predictions – Distance to target and position variance [31]. (PDF 203 kb

Additional file 7: Figure S3. of Steering cell migration by alternating blebs and actin-rich protrusions

Frequency of actin-rich protrusions, orientation of cell protrusions, and summary of POP values. (A) Frequency of actin-rich protrusions in control and ezrin-MO-injected mesendoderm cells. Arbitrary units (AU) are used as actin-rich protrusions are weighted with the intensity of the Lifeact signal in the protrusion. (B) Orientation of blebs with respect to the local migration axis. POP: Mean ± SEM of the magnitude of the polar order parameter. Number of analyzed cells = 17 for wt, 6 for ezrin-MO, and 6 for CAEzrin. Number of blebs n = 349 for wt, 163 for ezrin-MO, and 6 for CAEzrin. Statistical significance was determined comparing the mean ± SEM of the magnitude of the POP of the angular distributions. (C) Orientation of bleb and actin-rich protrusion formation with respect to the Yolk-ectoderm axis. For all experimental conditions, protrusions are almost exclusively oriented perpendicular to the Yolk-ectoderm axis, indicating that protrusions are formed into the extracellular space between the Yolk cell and the overlaying ectoderm layer. (D) Mean values ± SEM of the magnitude of the POP of the angular distributions of the analyzed protrusions. Green shaded area covers the wt mean ± SEM. Number of analyzed cells = 17 for wt, 6 for ezrin-MO, and 6 for CAEzrin. Number of actin-rich protrusions = 10853 for wt, 1501 for ezrin-MO, 1160 and 2549 for CAEzrin. Number of blebs n = 349 for wt and 163 for ezrin-MO. For CAEzrin only 6 blebs were observed so the POP was not calculated. (PDF 600 kb