The emergence of geometric order in proliferating metazoan epithelia

Periodic three-dimensional assemblies of polyhedral lipid vesicles

We theoretically study the structure of periodic bulk assemblies of identical lipid vesicles. In our model, each vesicle is represented as a convex polyhedron with flat faces, rounded edges, and rounded vertices. Each vesicle carries an elastic and an adhesion energy and in the limit of strong adhesion, the minimal-energy shape of cells minimizes the weighted total edge length. We calculate exactly the shape of the rounded edge and show that it can be well described by a cylindrical surface. By comparing several candidate space-filling polyhedra, we find that the oblate shapes are preferred over prolate shapes for all volume-to-surface ratios. We also study periodic assemblies of vesicles whose adhesion strength on lateral faces is different from that on basal or apical faces. The anisotropy needed to stabilize prolate shapes is determined and it is shown that, at any volume-to-surface ratio, the transition between oblate and prolate shapes is very sharp. The geometry of the model vesicle assemblies reproduces the shapes of cells in certain simple animal tissues.

Getting cells and tissues into shape

Cells of all shapes and sizes are able to calculate the location of their middles in order to divide into two during mitosis. Minc et al. (2011) and Gibson et al. (2011) now show that simple mechanical models accurately predict cleavage-plane positioning, and that geometrical interactions between neighboring cells are sufficient to generate ordered patterns of mitosis in growing epithelia.

Interkinetic nuclear migration is a broadly conserved feature of cell division in pseudostratified epithelia

Animal development requires tight integration between the processes of proliferative growth and epithelial morphogenesis, both of which play out at the level of individual cells. In this respect, not only must polarized epithelial cells assume complex morphologies, these distinct forms must be radically and repeatedly transformed to permit mitosis. A dramatic illustration of this integration between epithelial morphogenesis and cell proliferation is interkinetic nuclear migration (IKNM), wherein the nuclei of pseudostratified epithelial cells translocate to the apical epithelial surface to execute cell division. IKNM is widely considered a hallmark of pseudostratified vertebrate neuroepithelia, and prior investigations have proposed both actomyosin- and microtubule-dependent mechanisms for apical localization of the mitotic nucleus. Here, using comparative functional analysis in arthropod and cnidarian systems (Drosophila melanogaster and Nematostella vectensis), we show that actomyosin-dependent IKNM is likely to be a general feature of mitosis in pseudostratified epithelia throughout Eumetazoa. Furthermore, our studies suggest a mechanistic link between IKNM and the fundamental process of mitotic cell rounding.

Control of the mitotic cleavage plane by local epithelial topology

For nearly 150 years, it has been recognized that cell shape strongly influences the orientation of the mitotic cleavage plane (e.g., Hofmeister, 1863). However, we still understand little about the complex interplay between cell shape and cleavage-plane orientation in epithelia, where polygonal cell geometries emerge from multiple factors, including cell packing, cell growth, and cell division itself. Here, using mechanical simulations, we show that the polygonal shapes of individual cells can systematically bias the long-axis orientations of their adjacent mitotic neighbors. Strikingly, analyses of both animal epithelia and plant epidermis confirm a robust and nearly identical correlation between local cell topology and cleavage-plane orientation in vivo. Using simple mathematics, we show that this effect derives from fundamental packing constraints. Our results suggest that local epithelial topology is a key determinant of cleavage-plane orientation, and that cleavage-plane bias may be a widespread property of polygonal cell sheets in plants and animals.

Cortical forces in cell shape changes and tissue morphogenesis

Cortical forces drive a variety of cell shape changes and cell movements during tissue morphogenesis. While the molecular components underlying these forces have been largely identified, how they assemble and spatially and temporally organize at cell surfaces to promote cell shape changes in developing tissues are open questions. We present here different key aspects of cortical forces: their physical nature, some rules governing their emergence, and how their deployment at cell surfaces drives important morphogenetic movements in epithelia. We review a wide range of literature combining genetic/molecular, biophysical and modeling approaches, which explore essential features of cortical force generation and transmission in tissues.

Morphometry and structure of natural random tilings

A vast range of both living and inanimate planar cellular partitions obeys universal empirical laws describing their structure. To better understand this observation, we analyze the morphometric parameters of a sizeable set of experimental data that includes animal and plant tissues, patterns in desiccated starch slurry, suprafroth in type-I superconductors, soap froths, and geological formations. We characterize the tilings by the distributions of polygon reduced area, a scale-free measure of the roundedness of polygons. These distributions are fairly sharp and seem to belong to the same family. We show that the experimental tilings can be mapped onto the model tilings of equal-area, equal-perimeter polygons obtained by numerical simulations. This suggests that the random two-dimensional patterns can be parametrized by their median reduced area alone.

Mechanics and remodelling of cell packings in epithelia

Epithelia are sheets of cells that are dynamically remodelled by cell division and cell death during development. Here we describe the cell shapes and packings as networks of polygons: stable and stationary network configurations obey force balance and are represented as local minima of a potential function. We characterize the physical properties of this vertex model, including the set of ground states, and the energetics of topological rearrangements. We furthermore discuss a quasistatic description of cell division that allows us to study the mechanics and dynamics of tissue remodelling during growth. The biophysics of cells and their rearrangements can account for the morphology of cell packings observed in experiments.

Bioluminescent organs of two deep-sea arrow worms, Eukrohnia fowleri and Caecosagitta macrocephala, with further observations on Bioluminescence in chaetognaths

Bioluminescence in the deep-sea chaetognath Eukrohnia fowleri is reported for the first time, and behavioral, morphological, and chemical characteristics of bioluminescence in chaetognaths are examined. Until this study, the only known species of bioluminescent chaetognath was Caecosagitta macrocephala. The luminescent organ of that species is located on the ventral edge of each anterior lateral fin, whereas that of E. fowleri runs across the center of the tail fin on both dorsal and ventral sides. Scanning electron microscopy showed that the bioluminescent organs of both species consist of hexagonal chambers containing elongate ovoid particles-the organelles holding bioluminescent materials. No other luminous organism is known to use hexagonal packing to hold bioluminescent materials. Transmission electron microscopy of particles from C. macrocephala revealed a densely packed paracrystalline matrix punctuated by globular inclusions, which likely correspond to luciferin and luciferase, respectively. Both species use unique luciferases in conjunction with coelenterazine for light emission. Luciferase of C. macrocephala becomes inactive after 30 min, but luciferase of E. fowleri is highly stable. Although C. macrocephala has about 90 times fewer particles than E. fowleri, it has a similar bioluminescent capacity (total particle volume) due to its larger particle size. In situ observations of C. macrocephala from a remotely operated vehicle revealed that the luminous particles are released to form a cloud. The discovery of bioluminescence in a second chaetognath phylogenetically distant from the first highlights the importance of bioluminescence among deep-sea organisms.

Cellular dynamics in the early mouse embryo: from axis formation to gastrulation

Coordinated cell movements and reciprocal tissue interactions direct the formation of the definitive germ layers and the elaboration of the major axes of the mouse embryo. Genetic and embryological studies have defined the major molecular pathways that mediate these morphogenetic processes and provided 'snapshots' of the morphogenetic program. However, it is increasingly clear that this foundation needs to be validated, and can be significantly refined and extended using live imaging approaches. In situ visualization of these processes in living specimens is a major goal, as it provides unprecedented detail of the individual cellular behaviors, which translate into the large-scale tissue rearrangements that shape the embryo.

A modeling study on how cell division affects properties of epithelial tissues under isotropic growth

Cell proliferation affects both cellular geometry and topology in a growing tissue, and hence rules for cell division are key to understanding multicellular development. Epithelial cell layers have for long times been used to investigate how cell proliferation leads to tissue-scale properties, including organism-independent distributions of cell areas and number of neighbors. We use a cell-based two-dimensional tissue growth model including mechanics to investigate how different cell division rules result in different statistical properties of the cells at the tissue level. We focus on isotropic growth and division rules suggested for plant cells, and compare the models with data from the Arabidopsis shoot. We find that several division rules can lead to the correct distribution of number of neighbors, as seen in recent studies. In addition we find that when also geometrical properties are taken into account other constraints on the cell division rules result. We find that division rules acting in favor of equally sized and symmetrically shaped daughter cells can best describe the statistical tissue properties.

The effect of a DNA damaging agent on embryonic cell cycles of the cnidarian Hydractinia echinata

The onset of gastrulation at the Mid-Blastula Transition can accompany profound changes in embryonic cell cycles including the introduction of gap phases and the transition from maternal to zygotic control. Studies in Xenopus and Drosophila embryos have also found that cell cycles respond to DNA damage differently before and after MBT (or its equivalent, MZT, in Drosophila). DNA checkpoints are absent in Xenopus cleavage cycles but are acquired during MBT. Drosophila cleavage nuclei enter an abortive mitosis in the presence of DNA damage whereas post-MZT cells delay the entry into mitosis. Despite attributes that render them workhorses of embryonic cell cycle studies, Xenopus and Drosophila are hardly representative of diverse animal forms that exist. To investigate developmental changes in DNA damage responses in a distant phylum, I studied the effect of an alkylating agent, Methyl Methanesulfonate (MMS), on embryos of Hydractinia echinata. Hydractinia embryos are found to differ from Xenopus embryos in the ability to respond to a DNA damaging agent in early cleavage but are similar to Xenopus and Drosophila embryos in acquiring stronger DNA damage responses and greater resistance to killing by MMS after the onset of gastrulation. This represents the first study of DNA damage responses in the phylum Cnidaria.

Compartment boundaries: sorting cells with tension

The subdivision of proliferating tissues into groups of non-intermingling sets of cells, termed compartments, is a common process of animal development. Signaling between adjacent compartments induces the local expression of morphogens that pattern the surrounding tissue. Sharp and straight boundaries between compartments stabilize the source of such morphogens during tissue growth and, thus, are of crucial importance for pattern formation. Signaling pathways required to maintain compartment boundaries have been identified, yet the physical mechanisms that maintain compartment boundaries remained elusive. Recent data now show that a local increase in actomyosin-based mechanical tension on cell bonds is vital for maintaining compartment boundaries in Drosophila.

Intercellular mechanotransduction during multicellular morphodynamics

Multicellular structures are held together by cell adhesions. Forces that act upon these adhesions play an integral role in dynamically re-shaping multicellular structures during development and disease. Here, we describe different modes by which mechanical forces are transduced in a multicellular context: (i) indirect mechanosensing through compliant substratum, (ii) cytoskeletal 'tug-of-war' between cell-matrix and cell-cell adhesions, (iii) cortical contractility contributing to line tension, (iv) stresses associated with cell proliferation, and (v) forces mediating collective migration. These modes of mechanotransduction are recurring motifs as they play a key role in shaping multicellular structures in a wide range of biological contexts. Tissue morphodynamics may ultimately be understood as different spatio-temporal combinations of a select few multicellular transformations, which in turn are driven by these mechanotransduction motifs that operate at the bicellular to multicellular length scale.

Exploring the effects of mechanical feedback on epithelial topology

Apical cell surfaces in metazoan epithelia, such as the wing disc of Drosophila, resemble polygons with different numbers of neighboring cells. The distribution of these polygon numbers has been shown to be conserved. Revealing the mechanisms that lead to this topology might yield insights into how the structural integrity of epithelial tissues is maintained. It has previously been proposed that cell division alone, or cell division in combination with cell rearrangements, is sufficient to explain the observed epithelial topology. Here, we extend this work by including an analysis of the clustering and the polygon distribution of mitotic cells. In addition, we study possible effects of cellular growth regulation by mechanical forces, as such regulation has been proposed to be involved in wing disc size regulation. We formulated several theoretical scenarios that differ with respect to whether cell rearrangements are allowed and whether cellular growth rates are dependent on mechanical stress. We then compared these scenarios with experimental data on the polygon distribution of the entire cell population, that of mitotic cells, as well as with data on mitotic clustering. Surprisingly, we observed considerably less clustering in our experiments than has been reported previously. Only scenarios that include mechanical-stress-dependent growth rates are in agreement with the experimental data. Interestingly, simulations of these scenarios showed a large decrease in rearrangements and elimination of cells. Thus, a possible growth regulation by mechanical force could have a function in releasing the mechanical stress that evolves when all cells have similar growth rates.

Avian cone photoreceptors tile the retina as five independent, self-organizing mosaics

The avian retina possesses one of the most sophisticated cone photoreceptor systems among vertebrates. Birds have five types of cones including four single cones, which support tetrachromatic color vision and a double cone, which is thought to mediate achromatic motion perception. Despite this richness, very little is known about the spatial organization of avian cones and its adaptive significance. Here we show that the five cone types of the chicken independently tile the retina as highly ordered mosaics with a characteristic spacing between cones of the same type. Measures of topological order indicate that double cones are more highly ordered than single cones, possibly reflecting their posited role in motion detection. Although cones show spacing interactions that are cell type-specific, all cone types use the same density-dependent yardstick to measure intercone distance. We propose a simple developmental model that can account for these observations. We also show that a single parameter, the global regularity index, defines the regularity of all five cone mosaics. Lastly, we demonstrate similar cone distributions in three additional avian species, suggesting that these patterning principles are universal among birds. Since regular photoreceptor spacing is critical for uniform sampling of visual space, the cone mosaics of the avian retina represent an elegant example of the emergence of adaptive global patterning secondary to simple local interactions between individual photoreceptors. Our results indicate that the evolutionary pressures that gave rise to the avian retina's various adaptations for enhanced color discrimination also acted to fine-tune its spatial sampling of color and luminance.

Geometric order in proliferating epithelia: impact of rearrangements and cleavage plane orientation

Regulation of proliferation is required for normal development of tissues and prevention of cancer formation. Continuous control of proliferation leads to regular shaped cells forming characteristic tissue patterns. Epithelial tissues serve as a model system for studying tissue morphogenesis. Several groups have studied epithelial morphogenesis using topological or geometric models, with various assumptions. In this study, we have developed a method to simulate the dynamic process of proliferating epithelia using an off-lattice cellular model. Our method realistically models the shape, size, geometry, lineage, cleavage plane orientation as well as topological properties of individual cells. We find that cellular rearrangements and cleavage plane orientation are critical in the formation of the observed cellular pattern of epithelia, including a high percentage of hexagons in proliferating epithelial cells. It is likely that the rearrangements and orientation of the cleavage plane reduces the overall stress on the cell. We show that a high percentage of hexagons in proliferating epithelia can be obtained using uniform growth rates, which was considered unlikely in previous studies. Our off-lattice cellular model provides an improvement over existing topological for studying the dynamics of proliferating epithelium.

Multi-scale mechanics from molecules to morphogenesis

Dynamic mechanical processes shape the embryo and organs during development. Little is understood about the basic physics of these processes, what forces are generated, or how tissues resist or guide those forces during morphogenesis. This review offers an outline of some of the basic principles of biomechanics, provides working examples of biomechanical analyses of developing embryos, and reviews the role of structural proteins in establishing and maintaining the mechanical properties of embryonic tissues. Drawing on examples we highlight the importance of investigating mechanics at multiple scales from milliseconds to hours and from individual molecules to whole embryos. Lastly, we pose a series of questions that will need to be addressed if we are to understand the larger integration of molecular and physical mechanical processes during morphogenesis and organogenesis.

Cell rearrangements, cell divisions and cell death in a migrating epithelial sheet in the abdomen of Drosophila

During morphogenesis, cell movements, cell divisions and cell death work together to form complex patterns and to shape organs. These events are the outcome of decisions made by many individual cells, but how these decisions are controlled and coordinated is elusive. The adult abdominal epidermis of Drosophila is formed during metamorphosis by divisions and extensive cell migrations of the diploid histoblasts, which replace the polyploid larval cells. Using in vivo 4D microscopy, we have studied the behaviour of the histoblasts and analysed in detail how they reach their final position and to what extent they rearrange during their spreading. Tracking individual cells, we show that the cells migrate in two phases that differ in speed, direction and amount of cellular rearrangement. Cells of the anterior (A) and posterior (P) compartments differ in their behaviour. Cells near the A/P border are more likely to change their neighbours during migration. The mitoses do not show any preferential orientation. After mitosis, the sisters become preferentially aligned with the direction of movement. Thus, in the abdomen, it is the extensive cell migrations that appear to contribute most to morphogenesis. This contrasts with other developing epithelia, such as the wing imaginal disc and the embryonic germband in Drosophila, where oriented mitoses and local cell rearrangements appear to direct morphogenesis. Furthermore, our results suggest that an active force created by the histoblasts contributes to the formation of the adult epidermis. Finally, we show that histoblasts occasionally undergo apoptosis.

Tropomodulin1 is required for membrane skeleton organization and hexagonal geometry of fiber cells in the mouse lens

Hexagonal packing geometry is a hallmark of close-packed epithelial cells in metazoans. Here, we used fiber cells of the vertebrate eye lens as a model system to determine how the membrane skeleton controls hexagonal packing of post-mitotic cells. The membrane skeleton consists of spectrin tetramers linked to actin filaments (F-actin), which are capped by tropomodulin1 (Tmod1) and stabilized by tropomyosin (TM). In mouse lenses lacking Tmod1, initial fiber cell morphogenesis is normal, but fiber cell hexagonal shapes and packing geometry are not maintained as fiber cells mature. Absence of Tmod1 leads to decreased gammaTM levels, loss of F-actin from membranes, and disrupted distribution of beta2-spectrin along fiber cell membranes. Regular interlocking membrane protrusions on fiber cells are replaced by irregularly spaced and misshapen protrusions. We conclude that Tmod1 and gammaTM regulation of F-actin stability on fiber cell membranes is critical for the long-range connectivity of the spectrin-actin network, which functions to maintain regular fiber cell hexagonal morphology and packing geometry.

Rap1 maintains adhesion between cells to affect Egfr signaling and planar cell polarity in Drosophila

The small GTPase Rap1 affects cell adhesion and cell motility in numerous developmental contexts. Loss of Rap1 in the Drosophila wing epithelium disrupts adherens junction localization, causing mutant cells to disperse, and dramatically alters epithelial cell shape. While the adhesive consequences of Rap1 inactivation have been well described in this system, the effects on cell signaling, cell fate specification, and tissue differentiation are not known. Here we demonstrate that Egfr-dependent cell types are lost from Rap1 mutant tissue as an indirect consequence of DE-cadherin mislocalization. Cells lacking Rap1 in the developing wing and eye are capable of responding to an Egfr signal, indicating that Rap1 is not required for Egfr/Ras/MAPK signal transduction. Instead, Rap1 regulates adhesive contacts necessary for maintenance of Egfr signaling between cells, and differentiation of wing veins and photoreceptors. Rap1 is also necessary for planar cell polarity in these tissues. Wing hair alignment and ommatidial rotation, functional readouts of planar cell polarity in the wing and eye respectively, are both affected in Rap1 mutant tissue. Finally, we show that Rap1 acts through the effector Canoe to regulate these developmental processes.

Live imaging of glial cell migration in the Drosophila eye imaginal disc

Glial cells of both vertebrate and invertebrate organisms must migrate to final target regions in order to ensheath and support associated neurons. While recent progress has been made to describe the live migration of glial cells in the developing pupal wing (1), studies of Drosophila glial cell migration have typically involved the examination of fixed tissue. Live microscopic analysis of motile cells offers the ability to examine cellular behavior throughout the migratory process, including determining the rate of and changes in direction of growth. Paired with use of genetic tools, live imaging can be used to determine more precise roles for specific genes in the process of development. Previous work by Silies et al. (2) has described the migration of glia originating from the optic stalk, a structure that connects the developing eye and brain, into the eye imaginal disc in fixed tissue. Here we outline a protocol for examining the live migration of glial cells into the Drosophila eye imaginal disc. We take advantage of a Drosophila line that expresses GFP in developing glia to follow glial cell progression in wild type and in mutant animals.

Functions of the intermediate filament cytoskeleton in the eye lens

Intermediate filaments (IFs) are a key component of the cytoskeleton in virtually all vertebrate cells, including those of the lens of the eye. IFs help integrate individual cells into their respective tissues. This Review focuses on the lens-specific IF proteins beaded filament structural proteins 1 and 2 (BFSP1 and BFSP2) and their role in lens physiology and disease. Evidence generated in studies in both mice and humans suggests a critical role for these proteins and their filamentous polymers in establishing the optical properties of the eye lens and in maintaining its transparency. For instance, mutations in both BFSP1 and BFSP2 cause cataract in humans. We also explore the potential role of BFSP1 and BFSP2 in aging processes in the lens.

Degenerate polygonal tilings in simple animal tissues

The salient feature of one-cell-thick epithelia is their en face view, which reveals the polygonal cross section of the close-packed prismatic cells. The physical mechanisms that shape these tissues were hitherto explored using theories based on cell proliferation, which were either entirely topological or included certain morphogenetic forces. But mitosis itself may not be instrumental in molding the tissue. We show that the structure of simple epithelia can be explained by an equilibrium model where energy-degenerate polygons in an entropy-maximizing tiling are described by a single geometric parameter encoding their inflation. The two types of tilings found numerically--ordered and disordered--closely reproduce the patterns observed in Drosophila, Hydra, and Xenopus and they generalize earlier theoretical results. Free of a specific cell self-energy, cell-cell interaction, and cell division kinetics, our model provides an insight into the universality of living and inanimate two-dimensional cellular structures.

Modeling and inferring cleavage patterns in proliferating epithelia

The regulation of cleavage plane orientation is one of the key mechanisms driving epithelial morphogenesis. Still, many aspects of the relationship between local cleavage patterns and tissue-level properties remain poorly understood. Here we develop a topological model that simulates the dynamics of a 2D proliferating epithelium from generation to generation, enabling the exploration of a wide variety of biologically plausible cleavage patterns. We investigate a spectrum of models that incorporate the spatial impact of neighboring cells and the temporal influence of parent cells on the choice of cleavage plane. Our findings show that cleavage patterns generate "signature" equilibrium distributions of polygonal cell shapes. These signatures enable the inference of local cleavage parameters such as neighbor impact, maternal influence, and division symmetry from global observations of the distribution of cell shape. Applying these insights to the proliferating epithelia of five diverse organisms, we find that strong division symmetry and moderate neighbor/maternal influence are required to reproduce the predominance of hexagonal cells and low variability in cell shape seen empirically. Furthermore, we present two distinct cleavage pattern models, one stochastic and one deterministic, that can reproduce the empirical distribution of cell shapes. Although the proliferating epithelia of the five diverse organisms show a highly conserved cell shape distribution, there are multiple plausible cleavage patterns that can generate this distribution, and experimental evidence suggests that indeed plants and fruitflies use distinct division mechanisms.

Programming with models: modularity and abstraction provide powerful capabilities for systems biology

Mathematical models are increasingly used to understand how phenotypes emerge from systems of molecular interactions. However, their current construction as monolithic sets of equations presents a fundamental barrier to progress. Overcoming this requires modularity, enabling sub-systems to be specified independently and combined incrementally, and abstraction, enabling generic properties of biological processes to be specified independently of specific instances. These, in turn, require models to be represented as programs rather than as datatypes. Programmable modularity and abstraction enables libraries of modules to be created, which can be instantiated and reused repeatedly in different contexts with different components. We have developed a computational infrastructure that accomplishes this. We show here why such capabilities are needed, what is required to implement them and what can be accomplished with them that could not be done previously.

The actin cytoskeleton in spindle assembly and positioning

The most dramatic changes in eukaryotic cytoskeletal organization and dynamics occur during passage through mitosis. Although both spindle self-organization and actin-dependent cytokinesis have long been the subject of intense investigation, it has only recently become apparent that the actin cortex also has a key role during early mitosis. This is most striking in animal cells, in which changes in the actin cytoskeleton drive mitotic cell rounding and cortical stiffening. This mitotic cortex then functions as a foundation for spindle assembly and to guide spindle orientation with respect to extracellular chemical and mechanical cues. Here, we discuss this recent work and the possible role of crosstalk between the mitotic actin cortex and the plus ends of astral microtubules in this process.

Topological control of life and death in non-proliferative epithelia

Programmed cell death is one of the most fascinating demonstrations of the plasticity of biological systems. It is classically described to act upstream of and govern major developmental patterning processes (e.g. inter-digitations in vertebrates, ommatidia in Drosophila). We show here the first evidence that massive apoptosis can also be controlled and coordinated by a pre-established pattern of a specific ‘master cell’ population. This new concept is supported by the development and validation of an original model of cell patterning. Ciona intestinalis eggs are surrounded by a three-layered follicular organization composed of 60 elongated floating extensions made of as many outer and inner cells, and indirectly spread through an extracellular matrix over 1200 test cells. Experimental and selective ablation of outer and inner cells results in the abrogation of apoptosis in respective remaining neighbouring test cells. In addition incubation of outer/inner follicular cell-depleted eggs with a soluble extract of apoptotic outer/inner cells partially restores apoptosis to apoptotic-defective test cells. The 60 inner follicular cells were thus identified as ‘apoptotic master’ cells which collectively are induction sites for programmed cell death of the underlying test cells. The position of apoptotic master cells is controlled by topological constraints exhibiting a tetrahedral symmetry, and each cell spreads over and can control the destiny of 20 smaller test cells, which leads to optimized apoptosis signalling.

Four-dimensional realistic modeling of pancreatic organogenesis

Organogenesis, the process by which organs develop from individual precursor stem cells, requires that the precursor cells proliferate, differentiate, and aggregate to form a functioning structure. This process progresses through changes in 4 dimensions: time and 3 dimensions of space-4D. Experimental analysis of organogenesis, by its nature, cuts the 4D developmental process into static, 2D histological images or into molecular or cellular markers and interactions with little or no spatial dimensionality and minimal dynamics. Understanding organogenesis requires integration of the piecemeal experimental data into a running, realistic and interactive 4D simulation that allows experimentation and hypothesis testing in silico. Here, we describe a fully executable, interactive, visual model for 4D simulation of organogenic development using the mouse pancreas as a representative case. Execution of the model provided a dynamic description of pancreas development, culminating in a structure that remarkably recapitulated morphologic features seen in the embryonic pancreas. In silico mutations in key signaling molecules resulted in altered patterning of the developing pancreas that were in general agreement with in vivo data. The modeling approach described here thus typifies a useful platform for studying organogenesis as a phenomenon in 4 dimensions.

Multicellular dynamics during epithelial elongation

The reorganization of multicellular populations to produce an elongated tissue structure is a conserved mechanism for shaping the body axis and several organ systems. In the Drosophila germband epithelium, this process is accompanied by the formation of a planar polarized network of junctional and cytoskeletal proteins in response to striped patterns of gene expression. Actomyosin cables and adherens junctions are dynamically remodeled during intercalation, providing the basis for polarized cell behavior. Quantitative analysis of cell behavior in living embryos reveals unexpected cell population dynamics that include the formation of multicellular rosette structures as well as local neighbor exchange.

Developmental regulation of central spindle assembly and cytokinesis during vertebrate embryogenesis

Mitosis and cytokinesis not only ensure the proper segregation of genetic information but also contribute importantly to morphogenesis in embryos. Cytokinesis is controlled by the central spindle, a microtubule-based structure containing numerous microtubule motors and microtubule-binding proteins, including PRC1. We show here that central spindle assembly and function differ dramatically between two related populations of epithelial cells in developing vertebrate embryos examined in vivo. Compared to epidermal cells, early neural epithelial cells undergo exaggerated anaphase chromosome separation, rapid furrowing, and a marked reduction of microtubule density in the spindle midzone. Cytokinesis in normal early neural epithelial cells thus resembles that in cultured vertebrate cells experimentally depleted of PRC1. We find that PRC1 mRNA and protein expression is surprisingly dynamic in early vertebrate embryos and that neural-plate cells contain less PRC1 than do epidermal cells. Expression of excess PRC1 ameliorates both the exaggerated anaphase and reduced midzone microtubule density observed in early neural epithelial cells. These PRC1-mediated modifications to the cytokinetic mechanism may be related to the specialization of the midbody in neural cells. These data suggest that PRC1 is a dose-dependent regulator of the central spindle in vertebrate embryos and demonstrate unexpected plasticity to fundamental mechanisms of cell division.

Epithelial topology

It is universally accepted that genetic control over basic aspects of cell and molecular biology is the primary organizing principle in development and homeostasis of living systems. However, instances do exist where important aspects of biological order arise without explicit genetic instruction, emerging instead from simple physical principles, stochastic processes, or the complex self-organizing interaction between random and seemingly unrelated parts. Being mostly resistant to direct genetic dissection, the analysis of such emergent processes falls into a grey area between mathematics, physics and molecular cell biology and therefore remains very poorly understood. We recently proposed a mathematical model predicting the emergence of a specific non-Gaussian distribution of polygonal cell shapes from the stochastic cell division process in epithelial cell sheets; this cell shape distribution appears to be conserved across a diverse set of animals and plants.1 The use of such topological models to study the process of cellular morphogenesis has a long history, starting almost a century ago, and many insights from those original works influence current experimental studies. Here we review current and past literature on this topic while exploring some new ideas on the origins and implications of topological order in proliferating epithelia.

Expression of avian prickle genes during early development and organogenesis

Chicken homologues of prickle-1 (pk-1) and prickle-2 (pk-2) were isolated to gain insight into the extent of planar cell polarity signaling during avian embryogenesis. Bioinformatics analyses demonstrated homology and showed that pk-1 and pk-2 exhibited conserved synteny with ADAMTS20 and ADAMTS9, GON-related zinc metalloproteases. Expression of pk-1 and pk-2 was established during embryogenesis and early organogenesis, using in situ hybridization and sections of chicken embryos. At early stages, pk-1 was expressed in Hensen's node, primitive streak, ventral neural tube, and foregut. In older embryos, pk-1 transcripts were detected in dorsolateral epithelial somites, dorsomedial lip of dermomyotomes, and differentiating myotomes. Furthermore, pk-1 expression was seen in lateral body folds, limb buds, and ventral metencephalon. pk-2 was expressed in Hensen's node and neural ectoderm at early stages. In older embryos, pk-2 expression was restricted to ventromedial epithelial somites, except in the most recently formed somite pair, and limb bud mesenchyme.

The influence of cell mechanics, cell-cell interactions, and proliferation on epithelial packing

BACKGROUND

Epithelial junctional networks assume packing geometries characterized by different cell shapes, neighbor number distributions and areas. The development of specific packing geometries is tightly controlled; in the Drosophila wing epithelium, cells convert from an irregular to a hexagonal array shortly before hair formation. Packing geometry is determined by developmental mechanisms that likely control the biophysical properties of cells and their interactions.

RESULTS

To understand how physical cellular properties and proliferation determine cell-packing geometries, we use a vertex model for the epithelial junctional network in which cell packing geometries correspond to stable and stationary network configurations. The model takes into account cell elasticity and junctional forces arising from cortical contractility and adhesion. By numerically simulating proliferation, we generate different network morphologies that depend on physical parameters. These networks differ in polygon class distribution, cell area variation, and the rate of T1 and T2 transitions during growth. Comparing theoretical results to observed cell morphologies reveals regions of parameter space where calculated network morphologies match observed ones. We independently estimate parameter values by quantifying network deformations caused by laser ablating individual cell boundaries.

CONCLUSIONS

The vertex model accounts qualitatively and quantitatively for the observed packing geometry in the wing disc and its response to perturbation by laser ablation. Epithelial packing geometry is a consequence of both physical cellular properties and the disordering influence of proliferation. The occurrence of T2 transitions during network growth suggests that elimination of cells from the proliferating disc epithelium may be the result of junctional force balances.

"Developmental mechanics": cellular patterns controlled by adhesion, cortical tension and cell division

How embryos are shaped during development has inspired the work of many, embryologists, geneticists, but also mathematicians such as Turing, and physicists. Despite the inherent complexity of the problems it tackles, developmental biology has produced one of the most spectacular conceptual achievements, demonstrating that embryos are built with conserved molecules that orchestrate pattern and morphogenesis. As the logic of development now emerges, new challenges arise, such as how tissue mechanics is controlled. Quantitative approaches and computational models are essential to predict tissue organization and cell shapes. I review briefly how physical concepts have fueled this research in the past decades.

Orchestrating size and shape during morphogenesis

Living organisms exhibit tremendous diversity, evident in the large repertoire of forms and considerable size range. Scientists have discovered that conserved mechanisms control the development of all organisms. Drosophila has proved to be a particularly powerful model system with which to identify the signalling pathways that organize tissue patterns. More recently, much has been learned about the control of tissue growth, tissue shape and their coordination at the cellular and tissue levels. New models integrate how specific signals and mechanical forces shape tissues and may also control their size.

Freeze-crack technique to study epidermal development in zebrafish using differential interference contrast microscopy and fluorescent markers

The zebrafish is a model organism used to study organogenesis during vertebrate development; however epidermis development has been the focus of only a few studies. Thus, new methodologies to highlight and study epidermal cells could be valuable to deepen our understanding of skin development. Large-scale mutagenic screenings have already identified many zebrafish mutants, which are models for human developmental diseases, however only four epidermis mutants have been isolated. Novel screening techniques are needed to improve this collection. We designed and tested a novel freeze-crack technique to obtain, fix, and stain epidermal cells from 5 days postfertilization zebrafish larvae. Using commercially available fluorescent markers and differential interference contrast (DIC) microscopy, we were able to label and highlight subcellular structures such as microridges, cell boundaries, nuclei, and the Golgi complex from epidermis cells. Acquiring and processing epidermis samples from 15 to 75 larvae takes about 2-4 h, respectively. Therefore this method could be used as part of large-scale screenings. In addition, we present a more extensive protocol for antibody staining, which could be employed for more specific studies.

Cell surface mechanics and the control of cell shape, tissue patterns and morphogenesis

Embryonic morphogenesis requires the execution of complex mechanisms that regulate the local behaviour of groups of cells. The orchestration of such mechanisms has been mainly deciphered through the identification of conserved families of signalling pathways that spatially and temporally control cell behaviour. However, how this information is processed to control cell shape and cell dynamics is an open area of investigation. The framework that emerges from diverse disciplines such as cell biology, physics and developmental biology points to adhesion and cortical actin networks as regulators of cell surface mechanics. In this context, a range of developmental phenomena can be explained by the regulation of cell surface tension.