ECB-ART-46784
Elife
2018 Nov 27;7. doi: 10.7554/eLife.38407.
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Theoretical tool bridging cell polarities with development of robust morphologies.
Nissen SB
,
Rønhild S
,
Trusina A
,
Sneppen K
.
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Despite continual renewal and damages, a multicellular organism is able to maintain its complex morphology. How is this stability compatible with the complexity and diversity of living forms? Looking for answers at protein level may be limiting as diverging protein sequences can result in similar morphologies. Inspired by the progressive role of apical-basal and planar cell polarity in development, we propose that stability, complexity, and diversity are emergent properties in populations of proliferating polarized cells. We support our hypothesis by a theoretical approach, developed to effectively capture both types of polar cell adhesions. When applied to specific cases of development - gastrulation and the origins of folds and tubes - our theoretical tool suggests experimentally testable predictions pointing to the strength of polar adhesion, restricted directions of cell polarities, and the rate of cell proliferation to be major determinants of morphological diversity and stability.
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Genes referenced: LOC100887844 LOC100893907 LOC115919910 LOC583082
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Figure 1—figure supplement 1. Overview of the existing literature on models addressing specific developmental events discussed in our work.For more references on vertex models see Alt et al. (2017). | |
Figure 1. Two symmetry-breaking events, gain of apical-basal (AB) polarity and planar cell polarity (PCP), on cellular level coincide with the appearance of a rich set of morphologies.Starting from an aggregate of non-polarized cells (globular symmetry), individual cells can gain AB polarity and form one or multiple lumens (spherical symmetry). Additional, gain of PCP allows for tube formation (axial symmetry). Complex morphologies can be formed by combining cells with none, one, or two polarities. In Figure 1—figure supplement 1, we schematically illustrate how existing models capture different elements of development. | |
Figure 2—figure supplement 1. Dependence on the shape of the physical potential, the interaction partners, and noise.(A) Applying the neighborhood function shown in Figure 2, but changing the shape of the potential to the short-range potential written in Equation 2, the system unfolds and reaches a stable state (η = 10−4). (B) Full Voronoi interactions with a cut-off does also lead to a stable state, although a few cells might lose interaction with the majority of cells (cut-off at three shown). (C) However, a simple cut-off (and no Voronoi) does not result in stable morphologies but broken sheets on top of each other (cut-off at 2.5 shown). (D) The same happens, when all cells always interact with their six nearest neighbors. (E) With changed initial conditions compared to Figure 3, the system reaches a different stable state with low noise (η = 10−4). (F) However, this is comparable to the state obtained under high noise (η = 10−1). (G) Increasing the noise in (E) at time log(t) = 4 from η = 10−4 to η = 10−1, it results in fewer permutations than having high noise during the entire simulation which is shown in (F). The lower-case letters in (E–G) point at macroscopic features (a–h on one side in blue and r–u on the other side in red). The initial positions and polarities are identical for all seven simulations. | |
Figure 2—figure supplement 2. Changes in cell shapes may reorient apical-basal (AB) polarity.(A) In an epithelial sheet AB polarity (yellow arrows) points perpendicular to the sheet. (B) Regulated changes in planar cell polarity can reorient the AB polarities in neighboring cells by apical constriction (narrowing of the apical side) giving rise to a central bottle cell. (C) If the AB polarity is shortened, the neighboring cells will reorient in a similar way. These results are obtained under the assumption that the AB polarity tends to orient perpendicular to the distance vectors (black lines) connecting cells’ centers of masses (black dots) which are central to the model presented. | |
Figure 2—figure supplement 3. Examples of simple systems consisting of only two or six cells (see also Figure 2—video 1).(A) Two cells initially aligned do not result in any movement. (B) If both cells’ polarities are 45 degrees to the plane, the axis of position becomes tilted by 30 degrees. (C) If one cell points away from another in a two-cell system, it tilts the axis of position. (D) Similar to (C), if one cell points towards another, it tilts in the other direction. (E) Similar to (B), but with six cells instead of two. In this case, the final axis of position is only tilted by five degrees compared to the initial axis. (F) Similar to (C) and (E), with three cells pointing up and three cells pointing to the right. This also gives a final axis of position that is tilted by five degrees compared to the initial axis. | |
Figure 2. Cells are modeled as interacting particles with a polarity-dependent potential.(A) Potential between two interacting cells with apical-basal polarity (see Equation 6). Cells repulse when polarities are antiparallel (top/green part) and attract when they are parallel (orange/bottom part). (B–C) Two cells interact only if no other cells block the line of sight between them. (B) Cell i and j do not interact if ij’s midpoint (black dot) is inside of the Voronoi diagram for cell k (shaded in grey). (C) Cell i and j interact because cell k is further away than the distance ij/2 and ij’s midpoint therefore lie outside of cell k’s Voronoi diagram. In the related Figure 2—figure supplement 1A–D, we test the sensitivity of our model to the details of the potential and neighborhood assignments. In Figure 2—figure supplement 2, we relate changes in cell shapes to the model components, and in Figure 2—figure supplement 3 (Figure 2—video 1), we illustrate how altering polarity affects the dynamics of the systems with two and six cells. | |
Figure 3—figure supplement 2. The complex morphology in Figure 3 self-seals and is robust to overall system growth.(A–C) Self-sealing properties of polarized cell surfaces when close to a final stable state in Figure 3. While the internal morphology remains the same from time log(t) = 3.6 (Figure 3C–D and Figure 3—video 1), some of the outer surfaces subsequently reorganize to form a less disrupted torus-like structure with multiple handles. (D–F) The final structure in (C) (and Figure 3D–E together with the end of Figure 3—video 1) is robust to cell divisions. For every 10th time step, we select a cell by random, and let it divide in an arbitrary direction. We see that the overall shape of the structure is maintained, and that it expands equally in all directions. | |
Figure 3. Development of 8000 cells from a compact aggregate starting at time 0.(A) Cells are assigned random apical-basal polarity directions and attract each other through polar interactions (see Equation 6). (A–D) Cross-section of the system at different time points with red and blue marking two opposite sides of the polar cells. Cells closest to the viewer are marked red/blue, whereas cells furthest away are yellow/white. (E) Full system at the time point shown in (D). (F) Development of the number of neighbors per cell (red) and the energy per cell (blue), as defined by the potential between neighbor cells in Figure 2. Dark colors show the mean over all cells while light-shaded regions show the cell–cell variations. The yellow dot marks the energy for a hollow sphere with the same number of cells. See Figure 3—video 1 for full time series. In Figure 2—figure supplement 1E–G and Figure 3—figure supplement 1, we study how the final morphology depends on noise. In Figure 3—figure supplement 2, we show how the outer surface self-seals, and that the shape is maintained when cells divide. | |
Figure 4. Different morphologies can be obtained by varying boundary conditions (Figure 4—video 1).(A) A hollow sphere emerges if polarities are fixed and initially point radially out from the center of mass. (B) A hollow tube is obtained if polarities point radially out from a central axis. (C) Two flat planes pointing in opposite directions are obtained if polarities point away from a central plane. (D) For all three initial conditions (A–C), if the polarities are allowed to change dynamically and the noise is high (η = 100 compared to η = 10−1 in A–C), the resulting shape consists of three nested ‘Russian doll’-like hollow spheres that will never merge due to opposing polarities. In contrast to the random initial condition in Figure 3, the initial conditions in (D) are symmetric. | |
Figure 5. The number of complex folds in a growing organoid depends on the generation time and the pressure from the surrounding medium (Figure 5—video 1).(A) Number of local minima as a function of 1/(generation time), tG−1. In silico organoids grow from 200 cells up to 8000, 12,000, or 16,000 cells with different generation times and no outer pressure. (B) Number of local minima as a function of pressure, P. In silico organoids grow to the same size with the same 1/(generation time), tG−1 = 1.4⋅10−4 but different outer pressure. The images illustrate the 16,000 cells stage. Blue dots mark the average, while light shaded regions show the SEM based on triplicates. See also Figure 5—figure supplement 1 for additional measurements on the differences between rapid growth and pressure. | |
Figure 6—figure supplement 1. Removing the influence of planar cell polarity (PCP) on apical-basal (AB) polarity.This figure is identical to Figure 6 with the only difference that now λ2 = 0 when updating AB polarity (λ2 = 0.5 when updating position and PCP as in Figure 6). The strength of PCP (λ3) is defined as shown along the x-axis. λ1 = 1 - λ2 - λ3 for updating position and PCP, and for updating AB polarity λ1 = 0.5 - λ3. This way λ1 and λ3 are the same for position, AB polarity, and PCP, and the only change is the value of λ2. The final tubes are slightly wider and shorter compared to Figure 6 since the tips become more rounded when PCP does not affect AB polarity. Throughout, all the simulations in this figure, dt = 0.2 and the noise parameter η = 5⋅10−5. | |
Figure 6—figure supplement 2. A lumen forms inside a developing tube in areas that lack planar cell polarity (PCP).(A) Similar to Figure 6, a hollow sphere of cells is initialized. However, in this example only cells inside zone (i) have PCP while cells inside zone (ii) do not have PCP. (B) At the final stage, an elongated tube with a central lumen has formed. Images to the left show the entire system while images to the right show a cross-section. Cells inside zone (i) develop with λ1 = 0.41, λ2 = 0.5, and λ3 = 0.09 while cells inside zone (ii) develop with λ1 = 1, and λ2 = λ3 = 0. The central third of the 1000 cells in the system belong to zone (ii). Throughout, the simulation dt = 0.1 and η = 10−4. | |
Figure 6—figure supplement 3. T1 exchanges occur during sphere–tube transition.Two consecutive time frames of the most extreme scenario in Figure 6 (λ1 = 0.41, λ2 = 0.5, and λ3 = 0.09, see also Figure 6—video 1). (A) Snapshot of the entire system at time t = 1259.0. (B) Snapshot slightly later at time t = 1288.3. In both panels, the cell centers (light grey vertices) are triangulated (light grey edges). Triangle centers (red vertices) are calculated in order to get an approximate location of the cell borders (red edges). Inside the black box, two T1 exchanges (bold red lines) are highlighted. | |
Figure 6. The length and width of tubes are set by the strength of planar cell polarity (PCP, λ3).For each value of λ3, we initialize 1000 cells on a hollow sphere with PCP whirling around an internal axis (PCP orientation marked by cyan arrows in the top-left inset). Semi-major axis (dark blue) and semi-minor axis (light blue) are measured at the final stage (Materials and methods). Images show the final state. Throughout the figure, λ2 = 0.5 and λ1 = 1 - λ2 - λ3. The animated evolution from sphere to tube is shown in Figure 6—video 1. See also Figure 6—figure supplement 1 where we show that tubes also form when we disable the direct influence of PCP on apical-basal polarity, and Figure 6—figure supplement 2 where we vary the degree of PCP along the axis of the tube. In Figure 6—figure supplement 3, we show that cell intercalations result in experimentally reported T1 neighbor exchanges during convergent extension. | |
Figure 7—figure supplement 1. Directed changes in the direction of planar cell polarity (PCP) may drive invagination in gastrulation and neurulation.(A–D) Gastrulation in sea urchin modeled without the apical constriction in Figure 7. (A) The lower third of the cells in the blastula acquire PCP (cyan–green) pointing opposite to the apical-basal (AB) polarity (red–yellow). (B) Flattening of the blastula and invagination occur if direction of PCP is maintained for some time. During this initial phase λ2 = 0.1, and there is no convergent extension (λ3 = 0). (C) In the final phase, we increase λ2 to 0.4 and turn on λ3 = 0.1. With this, we let PCP relax so it curls around the bottom, and allow it to change dynamically in time. (D) As a result, tube narrows and elongates, until it finally connects and merges with the top. (E–H) Initial conditions on PCP enable neural plate bending and neural tube closure. (E) Starting with 1000 cells on a plane with AB polarity, we induce PCP along the plane together with two rows where the PCP points parallel and antiparallel to AB polarity (shown with cyan arrows). Here, we simulate the neural plate (cells in the middle, between the two rows with constrained PCP) surrounded by the epidermis (the rest of the cells). The two rows of cells with PCP pointing out of epithelial plane correspond to the cells at the dorsolateral hinge points next to the neural plate (epidermis boundaries). In chick, spinal neural tube can close with only these two hinge points (Nikolopoulou et al., 2017). The bending is driven by apical constriction and PCP is essential for bending, convergent extension and closure. (F) This enables neural plate bending and formation of the neural groove. (G) Continuing the simulation leads to contact of the two sides of the neural plate and hereby neural tube closure. (H) Finally, the system stabilizes with the neural plate on top of the neural tube. Comparing the initial stage to the final stage, the overall direction of PCP in the plate is conserved while in the tube PCP goes around an internal axis. For this simulation, we set λ2 = 0.5 and λ3 = 0. Turning on convergent extension (λ3) at the final stage will allow for elongating the system along the axis going through the tube and narrowing it in another direction. The concept is similar to gastrulation in Drosophila. In both simulations, sea urchin and neurulation, dt = 0.3. In sea urchin (A–D), the noise parameter η = 3.3⋅10−5, and in neurulation (E–H), η = 3.3⋅10−2. | |
Figure 7. External constraints on apical-basal (AB) polarity and planar cell polarity (PCP) can initiate invagination and drive gastrulation in sea urchin.(A) The lower third of the cells in a blastula with AB polarity (apical is blue–white, basal is red–orange) pointing radially out acquire PCP (cyan–green) in apical plane pointing around the anterior-posterior (top-bottom) axis (as in the inset to Figure 6). (B) Flattening of the blastula and (C) invagination occur due to external force reorienting AB polarity (Materials and methods). (D–E) Tube elongation is due to PCP-driven convergent extension and (F) merging with the top of the blastula happens when the tube approaches the top. Throughout the simulation, λ1 = 0.5, λ2 = 0.4, and λ3 = 0.1 for the lower cells while the top cells have λ1 = 1 and λ2 = λ3 = 0. For full time dynamics see Figure 7—video 1. In Figure 7—figure supplement 1, we consider alternative scenarios of sea urchin gastrulation and and neurulation. | |
Author response image 1. Changing the polarized direction of a plane of cells does not rotate the plane as a whole but breaks it into smaller planes.Time t = 0 shows a plane consisting of 500 cells with AB polarity pointing to the right. At time t = 0.1, the direction of the polarity is shifted by 45 degrees. Since the polarity is fixed in time, the planes break into smaller pieces, and at time 104 they have merged into two planes that are separated by several cell diameters. | |
Author response image 2. At cell division, the daughter cell equilibrates by half a cell radius in one time unit, which is of order 1/1000 the generation time.Here, we show how a new cell (in blue) reaches equilibrium (in red). Cell division happens at time 0. At time 5, the next consecutive division happens in the system (not shown). The systems consists of 200 cells placed on a hollow sphere which is the initial condition in our organoid simulations (Figure 5). A new cell is introduced half a cell radius in a random direction away from the mother cell. The red line is the mean distance from the mother cell to all it’s neighbor cells at t = 1000. The generation time is intermediate (Figure 5A). |
References [+] :
Aigouy,
Cell flow reorients the axis of planar polarity in the wing epithelium of Drosophila.
2010, Pubmed
Aigouy, Cell flow reorients the axis of planar polarity in the wing epithelium of Drosophila. 2010, Pubmed
Aigouy, The PCP pathway regulates Baz planar distribution in epithelial cells. 2016, Pubmed
Aliee, Physical mechanisms shaping the Drosophila dorsoventral compartment boundary. 2012, Pubmed
Alt, Vertex models: from cell mechanics to tissue morphogenesis. 2017, Pubmed
Amonlirdviman, Mathematical modeling of planar cell polarity to understand domineering nonautonomy. 2005, Pubmed
Andrew, Morphogenesis of epithelial tubes: Insights into tube formation, elongation, and elaboration. 2010, Pubmed
Baer, Cellular and molecular mechanisms underlying the formation of biological tubes. 2009, Pubmed
Beati, The adherens junction-associated LIM domain protein Smallish regulates epithelial morphogenesis. 2018, Pubmed
Belmonte, Filopodial-Tension Model of Convergent-Extension of Tissues. 2016, Pubmed
Burak, Order and stochastic dynamics in Drosophila planar cell polarity. 2009, Pubmed
Buske, On the biomechanics of stem cell niche formation in the gut--modelling growing organoids. 2012, Pubmed
Carroll, The kidney and planar cell polarity. 2012, Pubmed
Cerruti, Polarity, cell division, and out-of-equilibrium dynamics control the growth of epithelial structures. 2013, Pubmed
Cherry, Comparisons of frogs, humans, and chimpanzees. 1979, Pubmed
Choi, The involvement of lethal giant larvae and Wnt signaling in bottle cell formation in Xenopus embryos. 2009, Pubmed
Chu, Wnt proteins can direct planar cell polarity in vertebrate ectoderm. 2016, Pubmed
Chung, Uncoupling apical constriction from tissue invagination. 2017, Pubmed
Collinet, Local and tissue-scale forces drive oriented junction growth during tissue extension. 2015, Pubmed
Croce, Frizzled5/8 is required in secondary mesenchyme cells to initiate archenteron invagination during sea urchin development. 2006, Pubmed , Echinobase
Dallon, How cellular movement determines the collective force generated by the Dictyostelium discoideum slug. 2004, Pubmed
Dollar, Regulation of Lethal giant larvae by Dishevelled. 2005, Pubmed
Eguchi, Regenerative capacity in newts is not altered by repeated regeneration and ageing. 2011, Pubmed
Engelberg, In silico simulation of epithelial cell tubulogenesis. 2008, Pubmed
Etournay, Interplay of cell dynamics and epithelial tension during morphogenesis of the Drosophila pupal wing. 2015, Pubmed
Gjorevski, Designer matrices for intestinal stem cell and organoid culture. 2016, Pubmed
Gong, Planar cell polarity signalling controls cell division orientation during zebrafish gastrulation. 2004, Pubmed
Gould, Punctuated equilibrium comes of age. 1993, Pubmed
Greggio, Artificial three-dimensional niches deconstruct pancreas development in vitro. 2013, Pubmed
Habib, A localized Wnt signal orients asymmetric stem cell division in vitro. 2013, Pubmed
Hannezo, A Unifying Theory of Branching Morphogenesis. 2017, Pubmed
Hannezo, Theory of epithelial sheet morphology in three dimensions. 2014, Pubmed
Hočevar Brezavšček, A model of epithelial invagination driven by collective mechanics of identical cells. 2012, Pubmed
Hufnagel, On the mechanism of wing size determination in fly development. 2007, Pubmed
Humphries, From instruction to output: Wnt/PCP signaling in development and cancer. 2018, Pubmed
Kaplan, Spatially defined Dsh-Lgl interaction contributes to directional tissue morphogenesis. 2010, Pubmed
Karner, Wnt9b signaling regulates planar cell polarity and kidney tubule morphogenesis. 2009, Pubmed
Kimberly, Bottle cells are required for the initiation of primary invagination in the sea urchin embryo. 1998, Pubmed , Echinobase
Kinoshita, Apical accumulation of Rho in the neural plate is important for neural plate cell shape change and neural tube formation. 2008, Pubmed
Krupinski, Simulating the mammalian blastocyst--molecular and mechanical interactions pattern the embryo. 2011, Pubmed
Kunimoto, Disruption of Core Planar Cell Polarity Signaling Regulates Renal Tubule Morphogenesis but Is Not Cystogenic. 2017, Pubmed
Lane, A role for regulated secretion of apical extracellular matrix during epithelial invagination in the sea urchin. 1993, Pubmed , Echinobase
Laprise, Epithelial polarity proteins regulate Drosophila tracheal tube size in parallel to the luminal matrix pathway. 2010, Pubmed
Le Garrec, Establishment and maintenance of planar epithelial cell polarity by asymmetric cadherin bridges: a computer model. 2006, Pubmed
Lee, Wnt/Frizzled signaling controls C. elegans gastrulation by activating actomyosin contractility. 2006, Pubmed
Levayer, Oscillation and polarity of E-cadherin asymmetries control actomyosin flow patterns during morphogenesis. 2013, Pubmed
Li, Induction of Expansion and Folding in Human Cerebral Organoids. 2017, Pubmed
Li, Symmetry breaking in biology. 2010, Pubmed
Libby, Exclusion rules, bottlenecks and the evolution of stochastic phenotype switching. 2011, Pubmed
Little, Organoids: a Special Issue. 2017, Pubmed
Loh, Generating Cellular Diversity and Spatial Form: Wnt Signaling and the Evolution of Multicellular Animals. 2016, Pubmed
Long, Jun N-terminal kinase activity is required for invagination but not differentiation of the sea urchin archenteron. 2015, Pubmed , Echinobase
Lye, Tension and epithelial morphogenesis in Drosophila early embryos. 2011, Pubmed
Lyons, Morphogenesis in sea urchin embryos: linking cellular events to gene regulatory network states. 2012, Pubmed , Echinobase
Martik, New insights from a high-resolution look at gastrulation in the sea urchin, Lytechinus variegatus. 2017, Pubmed , Echinobase
Martin-Belmonte, Epithelial cell polarity, stem cells and cancer. 2011, Pubmed
Minegishi, A Wnt5 Activity Asymmetry and Intercellular Signaling via PCP Proteins Polarize Node Cells for Left-Right Symmetry Breaking. 2017, Pubmed
Misra, Shape Transformations of Epithelial Shells. 2016, Pubmed
Monier, Apico-basal forces exerted by apoptotic cells drive epithelium folding. 2015, Pubmed
Muguruma, Self-organization of polarized cerebellar tissue in 3D culture of human pluripotent stem cells. 2015, Pubmed
Murisic, From discrete to continuum models of three-dimensional deformations in epithelial sheets. 2015, Pubmed
Müller, Molecular networks controlling epithelial cell polarity in development. 2003, Pubmed
Nagai, Computer simulation of wound closure in epithelial tissues: cell-basal-lamina adhesion. 2009, Pubmed
Newman, Grid-free models of multicellular systems, with an application to large-scale vortices accompanying primitive streak formation. 2008, Pubmed
Nikolopoulou, Neural tube closure: cellular, molecular and biomechanical mechanisms. 2017, Pubmed
Nishimura, Planar cell polarity links axes of spatial dynamics in neural-tube closure. 2012, Pubmed
Nissen, Four simple rules that are sufficient to generate the mammalian blastocyst. 2017, Pubmed
Ochoa-Espinosa, Tubulogenesis: Src42A goes to great lengths in tube elongation. 2012, Pubmed
Odell, The mechanical basis of morphogenesis. I. Epithelial folding and invagination. 1981, Pubmed
Ossipova, Role of Rab11 in planar cell polarity and apical constriction during vertebrate neural tube closure. 2014, Pubmed
Osterfield, Three-dimensional epithelial morphogenesis in the developing Drosophila egg. 2013, Pubmed
Overeem, Mechanisms of apical-basal axis orientation and epithelial lumen positioning. 2015, Pubmed
Panousopoulou, Invagination of Ectodermal Placodes Is Driven by Cell Intercalation-Mediated Contraction of the Suprabasal Tissue Canopy. 2016, Pubmed
Polyakov, Passive mechanical forces control cell-shape change during Drosophila ventral furrow formation. 2014, Pubmed
Rauzi, Embryo-scale tissue mechanics during Drosophila gastrulation movements. 2015, Pubmed
Rauzi, Physical models of mesoderm invagination in Drosophila embryo. 2013, Pubmed
Rembold, Individual cell migration serves as the driving force for optic vesicle evagination. 2006, Pubmed
Roignot, Polarity in mammalian epithelial morphogenesis. 2013, Pubmed
Saburi, Loss of Fat4 disrupts PCP signaling and oriented cell division and leads to cystic kidney disease. 2008, Pubmed
Sanchez-Corrales, Radially patterned cell behaviours during tube budding from an epithelium. 2018, Pubmed
Schierenberg, The role of eggshell and underlying vitelline membrane for normal pattern formation in the early C. elegans embryo. 1992, Pubmed
Seybold, Sequential development of apical-basal and planar polarities in aggregating epitheliomuscular cells of Hydra. 2016, Pubmed
Simões, Rho-kinase directs Bazooka/Par-3 planar polarity during Drosophila axis elongation. 2010, Pubmed
Song, Planar cell polarity breaks bilateral symmetry by controlling ciliary positioning. 2010, Pubmed
Tamada, Abl Regulates Planar Polarized Junctional Dynamics through β-Catenin Tyrosine Phosphorylation. 2017, Pubmed
Tamulonis, A cell-based model of Nematostella vectensis gastrulation including bottle cell formation, invagination and zippering. 2011, Pubmed
Tanimizu, Liver progenitor cells fold up a cell monolayer into a double-layered structure during tubular morphogenesis. 2009, Pubmed
Wang, Order from disorder: Self-organization in mammalian hair patterning. 2006, Pubmed
Warrington, The Frizzled-dependent planar polarity pathway locally promotes E-cadherin turnover via recruitment of RhoGEF2. 2013, Pubmed
Wu, Wg and Wnt4 provide long-range directional input to planar cell polarity orientation in Drosophila. 2013, Pubmed
Wu, Drosophila vitelline membrane assembly: a critical role for an evolutionarily conserved cysteine in the "VM domain" of sV23. 2010, Pubmed
Zegers, 3D in vitro cell culture models of tube formation. 2014, Pubmed
Zorn, Vertebrate endoderm development and organ formation. 2009, Pubmed