The emergence of geometric order in proliferating metazoan epithelia

Spatial Fluctuations at Vertices of Epithelial Layers: Quantification of Regulation by Rho Pathway

In living matter, shape fluctuations induced by acto-myosin are usually studied in vitro via reconstituted gels, whose properties are controlled by changing the concentrations of actin, myosin, and cross-linkers. Such an approach deliberately avoids consideration of the complexity of biochemical signaling inherent to living systems. Acto-myosin activity inside living cells is mainly regulated by the Rho signaling pathway, which is composed of multiple layers of coupled activators and inhibitors. Here, we investigate how such a pathway controls the dynamics of confluent epithelial tissues by tracking the displacements of the junction points between cells. Using a phenomenological model to analyze the vertex fluctuations, we rationalize the effects of different Rho signaling targets on the emergent tissue activity by quantifying the effective diffusion coefficient, and the persistence time and length of the fluctuations. Our results reveal an unanticipated correlation between layers of activation/inhibition and spatial fluctuations within tissues. Overall, this work connects regulation via biochemical signaling with mesoscopic spatial fluctuations, with potential application to the study of structural rearrangements in epithelial tissues.

Tissue tension and not interphase cell shape determines cell division orientation in the Drosophila follicular epithelium

We investigated the cell behaviors that drive morphogenesis of the Drosophila follicular epithelium during expansion and elongation of early-stage egg chambers. We found that cell division is not required for elongation of the early follicular epithelium, but drives the tissue toward optimal geometric packing. We examined the orientation of cell divisions with respect to the planar tissue axis and found a bias toward the primary direction of tissue expansion. However, interphase cell shapes demonstrate the opposite bias. Hertwig's rule, which holds that cell elongation determines division orientation, is therefore broken in this tissue. This observation cannot be explained by the anisotropic activity of the conserved Pins/Mud spindle-orienting machinery, which controls division orientation in the apical-basal axis and planar division orientation in other epithelial tissues. Rather, cortical tension at the apical surface translates into planar division orientation in a manner dependent on Canoe/Afadin, which links actomyosin to adherens junctions. These findings demonstrate that division orientation in different axes-apical-basal and planar-is controlled by distinct, independent mechanisms in a proliferating epithelium.

Early blastocyst expansion in euploid and aneuploid human embryos: evidence for a non-invasive and quantitative marker for embryo selection

RESEARCH QUESTION

How can the kinetics of human blastocyst expansion be used to evaluate an embryo's ploidy identified using preimplantation genetic testing for aneuploidy (PGT-A)?

DESIGN

This was a retrospective observational study of 188 autologous blastocysts from 34 sequential treatment cycles using PGT-A and blastocyst biopsy. Using time-lapse imaging, blastocyst expansion was evaluated using a quantitative standardized expansion assay (qSEA). Trophectoderm cell division was examined in selected, unbiopsied embryos (n = 7) to evaluate the contribution of mitosis to the expansion rate.

RESULTS

The averaged euploid blastocyst expansion rate was significantly (52.8%) faster than in aneuploid blastocysts (P = 0.0041). Scatterplots, representing 'expansion maps', revealed that both populations showed a similarly overlapping distribution of blastocyst formation times at 80-140 h from fertilization. Euploidy and aneuploidy were better distinguished in regions of higher and lower expansion, respectively, in expansion maps. Based upon the expansion slopes, rank-ordering of individual embryos within cohorts resulted in more than 90% euploid embryos in the first two ranks in patients less than 35 years of age. Additional detailed time-lapse image analysis provided evidence that rapid expansion was associated with robust, integrative cellular mitosis in trophectoderm cells.

CONCLUSIONS

The kinetics of human blastocyst expansion are related to an embryo's ploidy. These preliminary observations describe a new quantitative, non-invasive approach to embryo assessment that may be useful to identify single blastocysts for transfer, particularly in younger patient groups. However, this approach may also be useful for euploid embryo selection after PGT-A. The results support the hypothesis that aneuploidy universally impairs general cellular processes, including cell division, in differentiated cells.

Global Topological Order Emerges through Local Mechanical Control of Cell Divisions in the Arabidopsis Shoot Apical Meristem

The control of cell position and division act in concert to dictate multicellular organization in tissues and organs. How these processes shape global order and molecular movement across organs is an outstanding problem in biology. Using live 3D imaging and computational analyses, we extracted networks capturing cellular connectivity dynamics across the Arabidopsis shoot apical meristem (SAM) and topologically analyzed the local and global properties of cellular architecture. Locally generated cell division rules lead to the emergence of global tissue-scale organization of the SAM, facilitating robust global communication. Cells that lie upon more shorter paths have an increased propensity to divide, with division plane placement acting to limit the number of shortest paths their daughter cells lie upon. Cell shape heterogeneity and global cellular organization requires KATANIN, providing a multiscale link between cell geometry, mechanical cell-cell interactions, and global tissue order.

Actomyosin-Driven Tension at Compartmental Boundaries Orients Cell Division Independently of Cell Geometry In Vivo

Cell shape is known to influence the plane of cell division. In vitro, mechanical constraints can also orient mitoses; however, in vivo it is not clear whether tension can orient the mitotic spindle directly, because tissue-scale forces can change cell shape. During segmentation of the Drosophila embryo, actomyosin is enriched along compartment boundaries forming supracellular cables that keep cells segregated into distinct compartments. Here, we show that these actomyosin cables orient the planar division of boundary cells perpendicular to the boundaries. This bias overrides the influence of cell shape, when cells are mildly elongated. By decreasing actomyosin cable tension with laser ablation or, conversely, ectopically increasing tension with laser wounding, we demonstrate that local tension is necessary and sufficient to orient mitoses in vivo. This involves capture of the spindle pole by the actomyosin cortex. These findings highlight the importance of actomyosin-mediated tension in spindle orientation in vivo.

Ecology: Termite Patterning at Multiple Scales

A vast and ancient array of regularly spaced dirt mounds - the result of termite activities- has been discovered in Brazil. Might this inform our understanding of general mechanisms of spatial patterning at different scales?

Development of epithelial tissues: How are cleavage planes chosen?

The cross-section of a cell in a monolayer epithelial tissue can be modeled mathematically as a k-sided polygon. Empirically studied distributions of the proportions of k-sided cells in epithelia show remarkable similarities in a wide range of evolutionarily distant organisms. A variety of mathematical models have been proposed for explaining this phenomenon. The highly parsimonious simulation model of (Patel et al., PLoS Comput. Biol., 2009) that takes into account only the number of sides of a given cell and cell division already achieves a remarkably good fit with empirical distributions from Drosophila, Hydra, Xenopus, Cucumber, and Anagallis. Within the same modeling framework as in that paper, we introduce additional options for the choice of the endpoints of the cleavage plane that appear to be biologically more realistic. By taking the same data sets as our benchmarks, we found that combinations of some of our new options consistently gave better fits with each of these data sets than previously studied ones. Both our algorithm and simulation data are made available as research tools for future investigations.

Relating cell shape and mechanical stress in a spatially disordered epithelium using a vertex-based model

Using a popular vertex-based model to describe a spatially disordered planar epithelial monolayer, we examine the relationship between cell shape and mechanical stress at the cell and tissue level. Deriving expressions for stress tensors starting from an energetic formulation of the model, we show that the principal axes of stress for an individual cell align with the principal axes of shape, and we determine the bulk effective tissue pressure when the monolayer is isotropic at the tissue level. Using simulations for a monolayer that is not under peripheral stress, we fit parameters of the model to experimental data for Xenopus embryonic tissue. The model predicts that mechanical interactions can generate mesoscopic patterns within the monolayer that exhibit long-range correlations in cell shape. The model also suggests that the orientation of mechanical and geometric cues for processes such as cell division are likely to be strongly correlated in real epithelia. Some limitations of the model in capturing geometric features of Xenopus epithelial cells are highlighted.

Mechanics of epithelial tissue formation

A key process in the life of any multicellular organism is its development from a single egg into a full grown adult. The first step in this process often consists of forming a tissue layer out of randomly placed cells on the surface of the egg. We present a model for generating such a tissue, based on mechanical interactions between the cells, and find that the resulting cellular pattern corresponds to the Voronoi tessellation of the nuclei of the cells. Experimentally, we obtain the same result in both fruit flies and flour beetles, with a distribution of cell shapes that matches that of the model, without any adjustable parameters. Finally, we show that this pattern is broken when the cells grow at different rates.

The force-sensitive protein Ajuba regulates cell adhesion during epithelial morphogenesis

The reorganization of cells in response to mechanical forces converts simple epithelial sheets into complex tissues of various shapes and dimensions. Epithelial integrity is maintained throughout tissue remodeling, but the mechanisms that regulate dynamic changes in cell adhesion under tension are not well understood. In Drosophila melanogaster, planar polarized actomyosin forces direct spatially organized cell rearrangements that elongate the body axis. We show that the LIM-domain protein Ajuba is recruited to adherens junctions in a tension-dependent fashion during axis elongation. Ajuba localizes to sites of myosin accumulation at adherens junctions within seconds, and the force-sensitive localization of Ajuba requires its N-terminal domain and two of its three LIM domains. We demonstrate that Ajuba stabilizes adherens junctions in regions of high tension during axis elongation, and that Ajuba activity is required to maintain cell adhesion during cell rearrangement and epithelial closure. These results demonstrate that Ajuba plays an essential role in regulating cell adhesion in response to mechanical forces generated by epithelial morphogenesis.

Epithelial cell shape change of Drosophila as a biomonitoring model for the dose assessment of environmental radiation

Inevitable exposure to ionizing radiation from natural and human-made sources has been increasing over time. After nuclear disasters, such as the Fukushima accident, the public concerns on health risk of radiation exposure because of radioactive contamination of the environment have increased. However, it is very difficult to assess the biological effects of exposure caused by environmental radiation. A reliable and rapid bioassay to monitor the physiological effects of radiation exposure is therefore needed. Here, we quantitatively analyzed the changes in cell shape in Drosophila epidermis after irradiation as a model for biomonitoring of radiation. Interestingly, the number of irregularly shaped epithelial cells was increased by irradiation in a dose-dependent manner. A dose-response curve constructed with the obtained data suggests that the measurement of the number of irregular shaped cell in the epidermis is useful for the assessment of radiation dose. In addition, a comparison of the variation in the different samples and the data scored by different observers showed that our evaluation for cellular morphology was highly reliable and accurate and would, therefore, have immense practical application. Overall, our study suggests that detection of morphological changes in the epithelial cells is one of the efficient ways to quantify the levels of exposure to radioactive radiation from the environment.

Scutoids are a geometrical solution to three-dimensional packing of epithelia

As animals develop, tissue bending contributes to shape the organs into complex three-dimensional structures. However, the architecture and packing of curved epithelia remains largely unknown. Here we show by means of mathematical modelling that cells in bent epithelia can undergo intercalations along the apico-basal axis. This phenomenon forces cells to have different neighbours in their basal and apical surfaces. As a consequence, epithelial cells adopt a novel shape that we term "scutoid". The detailed analysis of diverse tissues confirms that generation of apico-basal intercalations between cells is a common feature during morphogenesis. Using biophysical arguments, we propose that scutoids make possible the minimization of the tissue energy and stabilize three-dimensional packing. Hence, we conclude that scutoids are one of nature's solutions to achieve epithelial bending. Our findings pave the way to understand the three-dimensional organization of epithelial organs.

A Markovian Approach towards Bacterial Size Control and Homeostasis in Anomalous Growth Processes

Regardless of the progress achieved during recent years, the mechanisms coupling growth and division to attain cell size homeostasis in bacterial populations are still not well understood. In particular, there is a gap of knowledge about the mechanisms controlling anomalous growth events that are ubiquitous even in wild-type phenotypes. Thus, when cells exceed the doubling size the divisome dynamics sets a characteristic length scale that suggests a sizer property. Yet, it has been recently shown that the size at birth and the size increment still satisfy an adder-like correlation. Herein we propose a Markov chain model, that we complement with computational and experimental approaches, to clarify this issue. In this context, we show that classifying cells as a function of the characteristic size set by the divisome dynamics provides a compelling framework to understand size convergence, growth, and division at the large length scale, including the adaptation to, and rescue from, filamentation processes. Our results reveal the independence of size homeostasis on the division pattern of long cells and help to reconcile sizer concepts at the single cell level with an adder-like behavior at a population level.

Cellular aspect ratio and cell division mechanics underlie the patterning of cell progeny in diverse mammalian epithelia

Cell division is essential to expand, shape, and replenish epithelia. In the adult small intestine, cells from a common progenitor intermix with other lineages, whereas cell progeny in many other epithelia form contiguous patches. The mechanisms that generate these distinct patterns of progeny are poorly understood. Using light sheet and confocal imaging of intestinal organoids, we show that lineages intersperse during cytokinesis, when elongated interphase cells insert between apically displaced daughters. Reducing the cellular aspect ratio to minimize the height difference between interphase and mitotic cells disrupts interspersion, producing contiguous patches. Cellular aspect ratio is similarly a key parameter for division-coupled interspersion in the early mouse embryo, suggesting that this physical mechanism for patterning progeny may pertain to many mammalian epithelia. Our results reveal that the process of cytokinesis in elongated mammalian epithelia allows lineages to intermix and that cellular aspect ratio is a critical modulator of the progeny pattern.

Geometric constraints during epithelial jamming

As an injury heals, an embryo develops, or a carcinoma spreads, epithelial cells systematically change their shape. In each of these processes cell shape is studied extensively whereas variability of shape from cell-to-cell is regarded most often as biological noise. But where do cell shape and its variability come from? Here we report that cell shape and shape variability are mutually constrained through a relationship that is purely geometrical. That relationship is shown to govern processes as diverse as maturation of the pseudostratified bronchial epithelial layer cultured from non-asthmatic or asthmatic donors, and formation of the ventral furrow in the Drosophila embryo. Across these and other epithelial systems, shape variability collapses to a family of distributions that is common to all. That distribution, in turn, is accounted for by a mechanistic theory of cell-cell interaction showing that cell shape becomes progressively less elongated and less variable as the layer becomes progressively more jammed. These findings suggest a connection between jamming and geometry that spans living organisms and inert jammed systems, and thus transcends system details. Although molecular events are needed for any complete theory of cell shape and cell packing, observations point to the hypothesis that jamming behavior at larger scales of organization sets overriding geometrical constraints.

Coccolith arrangement follows Eulerian mathematics in the coccolithophore Emiliania huxleyi

Background

The globally abundant coccolithophore, Emiliania huxleyi, plays an important ecological role in oceanic carbon biogeochemistry by forming a cellular covering of plate-like CaCO₃ crystals (coccoliths) and fixing CO₂. It is unknown how the cells arrange different-sized coccoliths to maintain full coverage, as the cell surface area of the cell changes during daily cycle.

Methods

We used Euler’s polyhedron formula and CaGe simulation software, validated with the geometries of coccoliths, to analyze and simulate the coccolith topology of the coccosphere and to explore the arrangement mechanisms.

Results

There were only small variations in the geometries of coccoliths, even when the cells were cultured under variable light conditions. Because of geometric limits, small coccoliths tended to interlock with fewer and larger coccoliths, and vice versa. Consequently, to sustain a full coverage on the surface of cell, each coccolith was arranged to interlock with four to six others, which in turn led to each coccosphere contains at least six coccoliths.

Conclusion

The number of coccoliths per coccosphere must keep pace with changes on the cell surface area as a result of photosynthesis, respiration and cell division. This study is an example of natural selection following Euler’s polyhedral formula, in response to the challenge of maintaining a CaCO₃ covering on coccolithophore cells as cell size changes.

Riding the cell jamming boundary: Geometry, topology, and phase of human corneal endothelium

It is important to assess the viability of eye-banked corneas prior to transplantation due to inherent senescence and known loss of endothelial cells during surgical manipulation. Corneal endothelial cells have a complex basal and paracellular shape making them challenging to accurately measure, particularly in oedematous ex vivo tissue. This study used calibrated centroidal Voronoi Diagrams to segment cells in images of these human corneas, in order to characterize endothelial geometry, topology, and phase. Hexagonal cells dominated the endothelia, with most comprised of five different pleomorphs exhibiting self-similar topological coarsening through most of the endothelial cell density range. There was a linear relationship between cell size and shape, though cells with greater than six sides were present in larger proportions than cells with less. Hexagonal cell regularity was stable and largely independent of density. Cell and tissue phase was also examined, using the cell shape index relative to the recently discovered 'cell jamming' phase transition boundary. Images showed fluid endothelia with a range of shape indices spanning the boundary, independent of density but dependent on hexagonal regularity. The cells showed a bimodal distribution centred at the boundary, with the largest proportion of cells on the fluid side. A shoulder at the boundary suggested phase switching via shape transformation across the energy barrier, with cells either side having distinctly different size and shape characteristics. Regular hexagonal cells were closest to the boundary. This study showed the corneal endothelium acts as a glassy viscous foam characterized by well-established physical laws. Endothelial cell death transiently and locally increases cell fluidity, which is subsequently arrested by jamming of the pleomorphically diverse cell collective, via rearrangement and shape change of a small proportion of cells, which become locked in place by their neighbours thereby maintaining structural equilibrium with little energy expenditure.

'The Forms of Tissues, or Cell-aggregates': D'Arcy Thompson's influence and its limits

In two chapters of his book On Growth and Form, D'Arcy Thompson used numerous biological and physical observations to show how principles from mathematics and physics - such as pressure differences, surface tension and viscosity - could explain cell shapes and packing within tissues. In this Review, we depict influences that enabled the genesis of his ideas, report examples of his visionary observations and trace his impact over the past 100 years. Recently, his ideas have been revisited as a new field of research emerged, linking cell-level physics with epithelial tissue structure and development. We critically discuss the potential and the limitations of both Thompson's and the modern approaches.

Geometric constraints alter cell arrangements within curved epithelial tissues

Organ and tissue formation are complex three-dimensional processes involving cell division, growth, migration, and rearrangement, all of which occur within physically constrained regions. However, analyzing such processes in three dimensions in vivo is challenging. Here, we focus on the process of cellularization in the anterior pole of the early Drosophila embryo to explore how cells compete for space under geometric constraints. Using microfluidics combined with fluorescence microscopy, we extract quantitative information on the three-dimensional epithelial cell morphology. We observed a cellular membrane rearrangement in which cells exchange neighbors along the apical-basal axis. Such apical-to-basal neighbor exchanges were observed more frequently in the anterior pole than in the embryo trunk. Furthermore, cells within the anterior pole skewed toward the trunk along their long axis relative to the embryo surface, with maximum skew on the ventral side. We constructed a vertex model for cells in a curved environment. We could reproduce the observed cellular skew in both wild-type embryos and embryos with distorted morphology. Further, such modeling showed that cell rearrangements were more likely in ellipsoidal, compared with cylindrical, geometry. Overall, we demonstrate that geometric constraints can influence three-dimensional cell morphology and packing within epithelial tissues.

Myosin II Controls Junction Fluctuations to Guide Epithelial Tissue Ordering

Under conditions of homeostasis, dynamic changes in the length of individual adherens junctions (AJs) provide epithelia with the fluidity required to maintain tissue integrity in the face of intrinsic and extrinsic forces. While the contribution of AJ remodeling to developmental morphogenesis has been intensively studied, less is known about AJ dynamics in other circumstances. Here, we study AJ dynamics in an epithelium that undergoes a gradual increase in packing order, without concomitant large-scale changes in tissue size or shape. We find that neighbor exchange events are driven by stochastic fluctuations in junction length, regulated in part by junctional actomyosin. In this context, the developmental increase of isotropic junctional actomyosin reduces the rate of neighbor exchange, contributing to tissue order. We propose a model in which the local variance in tension between junctions determines whether actomyosin-based forces will inhibit or drive the topological transitions that either refine or deform a tissue.

Tricellular junctions: how to build junctions at the TRICkiest points of epithelial cells

Tricellular contacts are the places where three cells meet. In vertebrate epithelial cells, specialized structures called tricellular tight junctions (tTJs) and tricellular adherens junctions (tAJs) have been identified. tTJs are important for the maintenance of barrier function, and disruption of tTJ proteins contributes to familial deafness. tAJs have recently been attracting the attention of mechanobiologists because these sites are hot spots of epithelial tension. Although the molecular components, regulation, and function of tTJs and tAJs, as well as of invertebrate tricellular junctions, are beginning to be characterized, many questions remain. Here we broadly cover what is known about tricellular junctions, propose a new model for tension transmission at tAJs, and discuss key open questions.

Anisotropic Müller glial scaffolding supports a multiplex lattice mosaic of photoreceptors in zebrafish retina

Background

The multiplex, lattice mosaic of cone photoreceptors in the adult fish retina is a compelling example of a highly ordered epithelial cell pattern, with single cell width rows and columns of cones and precisely defined neighbor relationships among different cone types. Cellular mechanisms patterning this multiplex mosaic are not understood. Physical models can provide new insights into fundamental mechanisms of biological patterning. In earlier work, we developed a mathematical model of photoreceptor cell packing in the zebrafish retina, which predicted that anisotropic mechanical tension in the retinal epithelium orients planar polarized adhesive interfaces to align the columns as cone photoreceptors are generated at the retinal margin during post-embryonic growth.

Methods

With cell-specific fluorescent reporters and in vivo imaging of the growing retinal margin in transparent juvenile zebrafish we provide the first view of how cell packing, spatial arrangement, and cell identity are coordinated to build the lattice mosaic. With targeted laser ablation we probed the tissue mechanics of the retinal epithelium.

Results

Within the lattice mosaic, planar polarized Crumbs adhesion proteins pack cones into a single cell width column; between columns, N-cadherin-mediated adherens junctions stabilize Müller glial apical processes. The concentration of activated pMyosin II at these punctate adherens junctions suggests that these glial bands are under tension, forming a physical barrier between cone columns and contributing to mechanical stress anisotropies in the epithelial sheet. Unexpectedly, we discovered that the appearance of such parallel bands of Müller glial apical processes precedes the packing of cones into single cell width columns, hinting at a possible role for glia in the initial organization of the lattice mosaic. Targeted laser ablation of Müller glia directly demonstrates that these glial processes support anisotropic mechanical tension in the planar dimension of the retinal epithelium.

Conclusions

These findings uncovered a novel structural feature of Müller glia associated with alignment of photoreceptors into a lattice mosaic in the zebrafish retina. This is the first demonstration, to our knowledge, of planar, anisotropic mechanical forces mediated by glial cells.

Electronic supplementary material

The online version of this article (10.1186/s13064-017-0096-z) contains supplementary material, which is available to authorized users.

A hybrid computational model to explore the topological characteristics of epithelial tissues

Epithelial tissues show a particular topology where cells resemble a polygon-like shape, but some biological processes can alter this tissue topology. During cell proliferation, mitotic cell dilation deforms the tissue and modifies the tissue topology. Additionally, cells are reorganized in the epithelial layer and these rearrangements also alter the polygon distribution. We present here a computer-based hybrid framework focused on the simulation of epithelial layer dynamics that combines discrete and continuum numerical models. In this framework, we consider topological and mechanical aspects of the epithelial tissue. Individual cells in the tissue are simulated by an off-lattice agent-based model, which keeps the information of each cell. In addition, we model the cell-cell interaction forces and the cell cycle. Otherwise, we simulate the passive mechanical behaviour of the cell monolayer using a material that approximates the mechanical properties of the cell. This continuum approach is solved by the finite element method, which uses a dynamic mesh generated by the triangulation of cell polygons. Forces generated by cell-cell interaction in the agent-based model are also applied on the finite element mesh. Cell movement in the agent-based model is driven by the displacements obtained from the deformed finite element mesh of the continuum mechanical approach. We successfully compare the results of our simulations with some experiments about the topology of proliferating epithelial tissues in Drosophila. Our framework is able to model the emergent behaviour of the cell monolayer that is due to local cell-cell interactions, which have a direct influence on the dynamics of the epithelial tissue.

Pavement cells and the topology puzzle

D'Arcy Thompson emphasised the importance of surface tension as a potential driving force in establishing cell shape and topology within tissues. Leaf epidermal pavement cells grow into jigsaw-piece shapes, highly deviating from such classical forms. We investigate the topology of developing Arabidopsis leaves composed solely of pavement cells. Image analysis of around 50,000 cells reveals a clear and unique topological signature, deviating from previously studied epidermal tissues. This topological distribution is established early during leaf development, already before the typical pavement cell shapes emerge, with topological homeostasis maintained throughout growth and unaltered between division and maturation zones. Simulating graph models, we identify a heuristic cellular division rule that reproduces the observed topology. Our parsimonious model predicts how and when cells effectively place their division plane with respect to their neighbours. We verify the predicted dynamics through in vivo tracking of 800 mitotic events, and conclude that the distinct topology is not a direct consequence of the jigsaw piece-like shape of the cells, but rather owes itself to a strongly life history-driven process, with limited impact from cell-surface mechanics.

Cell dynamics underlying oriented growth of the Drosophila wing imaginal disc

Quantitative analysis of the dynamic cellular mechanisms shaping the Drosophila wing during its larval growth phase has been limited, impeding our ability to understand how morphogen patterns regulate tissue shape. Such analysis requires explants to be imaged under conditions that maintain both growth and patterning, as well as methods to quantify how much cellular behaviors change tissue shape. Here, we demonstrate a key requirement for the steroid hormone 20-hydroxyecdysone (20E) in the maintenance of numerous patterning systems in vivo and in explant culture. We find that low concentrations of 20E support prolonged proliferation in explanted wing discs in the absence of insulin, incidentally providing novel insight into the hormonal regulation of imaginal growth. We use 20E-containing media to observe growth directly and to apply recently developed methods for quantitatively decomposing tissue shape changes into cellular contributions. We discover that whereas cell divisions drive tissue expansion along one axis, their contribution to expansion along the orthogonal axis is cancelled by cell rearrangements and cell shape changes. This finding raises the possibility that anisotropic mechanical constraints contribute to growth orientation in the wing disc.

SERCA directs cell migration and branching across species and germ layers

Branching morphogenesis underlies organogenesis in vertebrates and invertebrates, yet is incompletely understood. Here, we show that the sarco-endoplasmic reticulum Ca2+ reuptake pump (SERCA) directs budding across germ layers and species. Clonal knockdown demonstrated a cell-autonomous role for SERCA in Drosophila air sac budding. Live imaging of Drosophila tracheogenesis revealed elevated Ca2+ levels in migratory tip cells as they form branches. SERCA blockade abolished this Ca2+ differential, aborting both cell migration and new branching. Activating protein kinase C (PKC) rescued Ca2+ in tip cells and restored cell migration and branching. Likewise, inhibiting SERCA abolished mammalian epithelial budding, PKC activation rescued budding, while morphogens did not. Mesoderm (zebrafish angiogenesis) and ectoderm (Drosophila nervous system) behaved similarly, suggesting a conserved requirement for cell-autonomous Ca2+ signaling, established by SERCA, in iterative budding.

Network-based approaches to quantify multicellular development

Multicellularity and cellular cooperation confer novel functions on organs following a structure-function relationship. How regulated cell migration, division and differentiation events generate cellular arrangements has been investigated, providing insight into the regulation of genetically encoded patterning processes. Much less is known about the higher-order properties of cellular organization within organs, and how their functional coordination through global spatial relations shape and constrain organ function. Key questions to be addressed include: why are cells organized in the way they are? What is the significance of the patterns of cellular organization selected for by evolution? What other configurations are possible? These may be addressed through a combination of global cellular interaction mapping and network science to uncover the relationship between organ structure and function. Using this approach, global cellular organization can be discretized and analysed, providing a quantitative framework to explore developmental processes. Each of the local and global properties of integrated multicellular systems can be analysed and compared across different tissues and models in discrete terms. Advances in high-resolution microscopy and image analysis continue to make cellular interaction mapping possible in an increasing variety of biological systems and tissues, broadening the further potential application of this approach. Understanding the higher-order properties of complex cellular assemblies provides the opportunity to explore the evolution and constraints of cell organization, establishing structure-function relationships that can guide future organ design.

Basement Membrane Manipulation in Drosophila Wing Discs Affects Dpp Retention but Not Growth Mechanoregulation

Basement membranes (BMs) are extracellular matrix polymers basally underlying epithelia, where they regulate cell signaling and tissue mechanics. Constriction by the BM shapes Drosophila wing discs, a well-characterized model of tissue growth. Recently, the hypothesis that mechanical factors govern wing growth has received much attention, but it has not been definitively tested. In this study, we manipulated BM composition to cause dramatic changes in tissue tension. We found that increased tissue compression when perlecan was knocked down did not affect adult wing size. BM elimination, decreasing compression, reduced wing size but did not visibly affect Hippo signaling, widely postulated to mediate growth mechanoregulation. BM elimination, in contrast, attenuated signaling by bone morphogenetic protein/transforming growth factor β ligand Dpp, which was not efficiently retained within the tissue and escaped to the body cavity. Our results challenge mechanoregulation of wing growth, while uncovering a function of BMs in preserving a growth-promoting tissue environment.

The E-cadherin/AmotL2 complex organizes actin filaments required for epithelial hexagonal packing and blastocyst hatching

Epithelial cells connect via cell-cell junctions to form sheets of cells with separate cellular compartments. These cellular connections are essential for the generation of cellular forms and shapes consistent with organ function. Tissue modulation is dependent on the fine-tuning of mechanical forces that are transmitted in part through the actin connection to E-cadherin as well as other components in the adherens junctions. In this report we show that p100 amotL2 forms a complex with E-cadherin that associates with radial actin filaments connecting cells over multiple layers. Genetic inactivation or depletion of amotL2 in epithelial cells in vitro or zebrafish and mouse in vivo, resulted in the loss of contractile actin filaments and perturbed epithelial packing geometry. We further showed that AMOTL2 mRNA and protein was expressed in the trophectoderm of human and mouse blastocysts. Genetic inactivation of amotL2 did not affect cellular differentiation but blocked hatching of the blastocysts from the zona pellucida. These results were mimicked by treatment with the myosin II inhibitor blebbistatin. We propose that the tension generated by the E-cadherin/AmotL2/actin filaments plays a crucial role in developmental processes such as epithelial geometrical packing as well as generation of forces required for blastocyst hatching.

Cell and Tissue Scale Forces Coregulate Fgfr2-Dependent Tetrads and Rosettes in the Mouse Embryo

What motivates animal cells to intercalate is a longstanding question that is fundamental to morphogenesis. A basic mode of cell rearrangement involves dynamic multicellular structures called tetrads and rosettes. The contribution of cell-intrinsic and tissue-scale forces to the formation and resolution of these structures remains unclear, especially in vertebrates. Here, we show that Fgfr2 regulates both the formation and resolution of tetrads and rosettes in the mouse embryo, possibly in part by spatially restricting atypical protein kinase C, a negative regulator of non-muscle myosin IIB. We employ micropipette aspiration to show that anisotropic tension is sufficient to rescue the resolution, but not the formation, of tetrads and rosettes in Fgfr2 mutant limb-bud ectoderm. The findings underscore the importance of cell contractility and tissue stress to multicellular vertex formation and resolution, respectively.

Inference of Cell Mechanics in Heterogeneous Epithelial Tissue Based on Multivariate Clone Shape Quantification

Cell populations in multicellular organisms show genetic and non-genetic heterogeneity, even in undifferentiated tissues of multipotent cells during development and tumorigenesis. The heterogeneity causes difference of mechanical properties, such as, cell bond tension or adhesion, at the cell–cell interface, which determine the shape of clonal population boundaries via cell sorting or mixing. The boundary shape could alter the degree of cell–cell contacts and thus influence the physiological consequences of sorting or mixing at the boundary (e.g., tumor suppression or progression), suggesting that the cell mechanics could help clarify the physiology of heterogeneous tissues. While precise inference of mechanical tension loaded at each cell–cell contacts has been extensively developed, there has been little progress on how to distinguish the population-boundary geometry and identify the cause of geometry in heterogeneous tissues. We developed a pipeline by combining multivariate analysis of clone shape with tissue mechanical simulations. We examined clones with four different genotypes within Drosophila wing imaginal discs: wild-type, tartan (trn) overexpression, hibris (hbs) overexpression, and Eph RNAi. Although the clones were previously known to exhibit smoothed or convoluted morphologies, their mechanical properties were unknown. By applying a multivariate analysis to multiple criteria used to quantify the clone shapes based on individual cell shapes, we found the optimal criteria to distinguish not only among the four genotypes, but also non-genetic heterogeneity from genetic one. The efficient segregation of clone shape enabled us to quantitatively compare experimental data with tissue mechanical simulations. As a result, we identified the mechanical basis contributed to clone shape of distinct genotypes. The present pipeline will promote the understanding of the functions of mechanical interactions in heterogeneous tissue in a non-invasive manner.

The role of apical contractility in determining cell morphology in multilayered epithelial sheets and tubes

A multilayered epithelium is made up of individual cells that are stratified in an orderly fashion, layer by layer. In such tissues, individual cells can adopt a wide range of shapes ranging from columnar to squamous. From histological images, we observe that, in flat epithelia such as the skin, the cells in the top layer are squamous while those in the middle and bottom layers are columnar, whereas in tubular epithelia, the cells in all layers are columnar. We develop a computational model to understand how individual cell shape is governed by the mechanical forces within multilayered flat and curved epithelia. We derive the energy function for an epithelial sheet of cells considering intercellular adhesive and intracellular contractile forces. We determine computationally the cell morphologies that minimize the energy function for a wide range of cellular parameters. Depending on the dominant adhesive and contractile forces, we find four dominant cell morphologies for the multilayered-layered flat sheet and three dominant cell morphologies for the two-layered curved sheet. We study the transitions between the dominant cell morphologies for the two-layered flat sheet and find both continuous and discontinuous transitions and also the presence of multistable states. Matching our computational results with histological images, we conclude that apical contractile forces from the actomyosin belt in the epithelial cells is the dominant force determining cell shape in multilayered epithelia. Our computational model can guide tissue engineers in designing artificial multilayered epithelia, in terms of figuring out the cellular parameters needed to achieve realistic epithelial morphologies.

Topological analysis of multicellular complexity in the plant hypocotyl

Multicellularity arose as a result of adaptive advantages conferred to complex cellular assemblies. The arrangement of cells within organs endows higher-order functionality through a structure-function relationship, though the organizational properties of these multicellular configurations remain poorly understood. We investigated the topological properties of complex organ architecture by digitally capturing global cellular interactions in the plant embryonic stem (hypocotyl), and analyzing these using quantitative network analysis. This revealed the presence of coherent conduits of reduced path length across epidermal atrichoblast cell files. The preferential movement of small molecules along this cell type was demonstrated using fluorescence transport assays. Both robustness and plasticity in this higher order property of atrichoblast patterning was observed across diverse genetic backgrounds, and the analysis of genetic patterning mutants identified the contribution of gene activity towards their construction. This topological analysis of multicellular structural organization reveals higher order functions for patterning and principles of complex organ construction.

Structural Characterization and Statistical-Mechanical Model of Epidermal Patterns

In proliferating epithelia of mammalian skin, cells of irregular polygon-like shapes pack into complex, nearly flat two-dimensional structures that are pliable to deformations. In this work, we employ various sensitive correlation functions to quantitatively characterize structural features of evolving packings of epithelial cells across length scales in mouse skin. We find that the pair statistics in direct space (correlation function) and Fourier space (structure factor) of the cell centroids in the early stages of embryonic development show structural directional dependence (statistical anisotropy), which is a reflection of the fact that cells are stretched, which promotes uniaxial growth along the epithelial plane. In the late stages, the patterns tend toward statistically isotropic states, as cells attain global polarization and epidermal growth shifts to produce the skin's outer stratified layers. We construct a minimalist four-component statistical-mechanical model involving effective isotropic pair interactions consisting of hard-core repulsion and extra short-range soft-core repulsion beyond the hard core, whose length scale is roughly the same as the hard core. The model parameters are optimized to match the sample pair statistics in both direct and Fourier spaces. By doing this, the parameters are biologically constrained. In contrast with many vertex-based models, our statistical-mechanical model does not explicitly incorporate information about the cell shapes and interfacial energy between cells; nonetheless, our model predicts essentially the same polygonal shape distribution and size disparity of cells found in experiments, as measured by Voronoi statistics. Moreover, our simulated equilibrium liquid-like configurations are able to match other nontrivial unconstrained statistics, which is a testament to the power and novelty of the model. The array of structural descriptors that we deploy enable us to distinguish between normal, mechanically deformed, and pathological skin tissues. Our statistical-mechanical model enables one to generate tissue microstructure at will for further analysis. We also discuss ways in which our model might be extended to better understand morphogenesis (in particular the emergence of planar cell polarity), wound healing, and disease-progression processes in skin, and how it could be applied to the design of synthetic tissues.

Expanding signaling-molecule wavefront model of cell polarization in the Drosophila wing primordium

In developing tissues, cell polarization and proliferation are regulated by morphogens and signaling pathways. Cells throughout the Drosophila wing primordium typically show subcellular localization of the unconventional myosin Dachs on the distal side of cells (nearest the center of the disc). Dachs localization depends on the spatial distribution of bonds between the protocadherins Fat (Ft) and Dachsous (Ds), which form heterodimers between adjacent cells; and the Golgi kinase Four-jointed (Fj), which affects the binding affinities of Ft and Ds. The Fj concentration forms a linear gradient while the Ds concentration is roughly uniform throughout most of the wing pouch with a steep transition region that propagates from the center to the edge of the pouch during the third larval instar. Although the Fj gradient is an important cue for polarization, it is unclear how the polarization is affected by cell division and the expanding Ds transition region, both of which can alter the distribution of Ft-Ds heterodimers around the cell periphery. We have developed a computational model to address these questions. In our model, the binding affinity of Ft and Ds depends on phosphorylation by Fj. We assume that the asymmetry of the Ft-Ds bond distribution around the cell periphery defines the polarization, with greater asymmetry promoting cell proliferation. Our model predicts that this asymmetry is greatest in the radially-expanding transition region that leaves polarized cells in its wake. These cells naturally retain their bond distribution asymmetry after division by rapidly replenishing Ft-Ds bonds at new cell-cell interfaces. Thus we predict that the distal localization of Dachs in cells throughout the pouch requires the movement of the Ds transition region and the simple presence, rather than any specific spatial pattern, of Fj.

In the tissues of a developing organism, specialized proteins can control cell growth and give cells a sense of direction, e.g., which way is the head or the tail, by having their concentration vary throughout the tissue. In cells of the developing fruit fly wing, a protein called Dachs localizes on the side of the cell closest to the center of the tissue, indicating a directionality. The localization of Dachs is determined by the spatial distribution, around the periphery of a cell, of intercellular bonds of the proteins Fat and Dachsous between adjacent cells. Here we asked how this cell directionality is affected when cells divide and when the concentration of Dachsous changes over time. We use a computational model to show that as the circular step-up region of the Dachsous concentration profile sweeps radially outward, like rings radiating outward from where a pebble was dropped in a pond, it leaves polarized cells in its wake. Our model also shows how cells can naturally recover their directionality after cell division.

Hexagonal Patterning of the Insect Compound Eye: Facet Area Variation, Defects, and Disorder

The regular hexagonal array morphology of facets (ommatidia) in the Drosophila compound eye is accomplished by regulation of cell differentiation and planar cell polarity during development. Mutations in certain genes disrupt regulation, causing a breakdown of this perfect symmetry, so that the ommatidial pattern shows onset of disorder in the form of packing defects. We analyze a variety of such mutants and compare them to normal (wild-type), finding that mutants show increased local variation in ommatidial area, which is sufficient to induce a significant number of defects. A model formalism based on Voronoi construction is developed to predict the observed correlation between ommatidium size variation and the number of defects, and to study the onset of disorder in this system with statistical tools. The model uncovers a previously unknown large-scale systematic size variation of the ommatidia across the eye of both wild-type and mutant animals. Such systematic variation of area, as well as its statistical fluctuations, are found to have distinct effects on eye disorder that can both be quantitatively modeled. Furthermore, the topological order is also influenced by the internal structure of the ommatidia, with cells of greater relative mechanical stiffness providing constraints to ommatidial deformation and thus to defect generation. Without free parameters, the simulation predicts the size-topology correlation for both wild-type and mutant eyes. This work develops formalisms of size-topology correlation that are very general and can be potentially applied to other cellular structures near the onset of disorder.

Active Vertex Model for cell-resolution description of epithelial tissue mechanics

We introduce an Active Vertex Model (AVM) for cell-resolution studies of the mechanics of confluent epithelial tissues consisting of tens of thousands of cells, with a level of detail inaccessible to similar methods. The AVM combines the Vertex Model for confluent epithelial tissues with active matter dynamics. This introduces a natural description of the cell motion and accounts for motion patterns observed on multiple scales. Furthermore, cell contacts are generated dynamically from positions of cell centres. This not only enables efficient numerical implementation, but provides a natural description of the T1 transition events responsible for local tissue rearrangements. The AVM also includes cell alignment, cell-specific mechanical properties, cell growth, division and apoptosis. In addition, the AVM introduces a flexible, dynamically changing boundary of the epithelial sheet allowing for studies of phenomena such as the fingering instability or wound healing. We illustrate these capabilities with a number of case studies.

Oxygenation and adenosine deaminase support growth and proliferation of ex vivo cultured Drosophila wing imaginal discs

The Drosophila wing imaginal disc has been an important model system over past decades for discovering novel biology related to development, signaling and epithelial morphogenesis. Novel experimental approaches have been enabled using a culture setup that allows ex vivo cultures of wing discs. Current setups, however, are not able to sustain both growth and cell-cycle progression of wing discs ex vivo We discover here a setup that requires both oxygenation of the tissue and adenosine deaminase activity in the medium, and supports both growth and proliferation of wing discs for 9 h. Nonetheless, further work will be required to extend the duration of the culturing and to enable live imaging of the cultured discs in the future.

Cells tile a flat plane by controlling geometries during morphogenesis of Pyropia thalli

Background

Pyropia haitanensis thalli, which are made of a single layer of polygonal cells, are a perfect model for studying the morphogenesis of multi-celled organisms because their cell proliferation process is an excellent example of the manner in which cells control their geometry to create a two-dimensional plane.

Methods

Cellular geometries of thalli at different stages of growth revealed by light microscope analysis.

Results

This study showed the cell division transect the middle of the selected paired-sides to divide the cell into two equal portions, thus resulting in cell sides ≥4 and keeping the average number of cell sides at approximately six even as the thallus continued to grow, such that more than 90% of the cells in thalli longer than 0.08 cm had 5–7 sides. However, cell division could not fully explain the distributions of intracellular angles. Results showed that cell-division-associated fast reorientation of cell sides and cell divisions together caused 60% of the inner angles of cells from longer thalli to range from 100–140°. These results indicate that cells prefer to form regular polygons.

Conclusions

This study suggests that appropriate cell-packing geometries maintained by cell division and reorientation of cell walls can keep the cells bordering each other closely, without gaps.

A Method to Categorize 2-Dimensional Patterns Using Statistics of Spatial Organization

We developed a measurement framework of spatial organization to categorize 2-dimensional patterns from 2 multiscalar biological architectures. We propose that underlying shapes of biological entities can be approached using the statistical concept of degrees of freedom, defining it through expansion of area variability in a pattern. To help scope this suggestion, we developed a mathematical argument recognizing the deep foundations of area variability in a polygonal pattern (spatial heterogeneity). This measure uses a parameter called eutacticity. Our measuring platform of spatial heterogeneity can assign particular ranges of distribution of spatial areas for 2 biological architectures: ecological patterns of Namibia fairy circles and epithelial sheets. The spatial organizations of our 2 analyzed biological architectures are demarcated by being in a particular position among spatial order and disorder. We suggest that this theoretical platform can give us some insights about the nature of shapes in biological systems to understand organizational constraints.

Cell division and death inhibit glassy behaviour of confluent tissues

We investigate the effects of cell division and apoptosis on collective dynamics in two-dimensional epithelial tissues. Our model includes three key ingredients observed across many epithelia, namely cell-cell adhesion, cell death and a cell division process that depends on the surrounding environment. We show a rich non-equilibrium phase diagram depending on the ratio of cell death to cell division and on the adhesion strength. For large apoptosis rates, cells die out and the tissue disintegrates. As the death rate decreases, however, we show, consecutively, the existence of a gas-like phase, a gel-like phase, and a dense confluent (tissue) phase. Most striking is the observation that the tissue is self-melting through its own internal activity, ruling out the existence of any glassy phase.

Multi-scale computational study of the mechanical regulation of cell mitotic rounding in epithelia

Mitotic rounding during cell division is critical for preventing daughter cells from inheriting an abnormal number of chromosomes, a condition that occurs frequently in cancer cells. Cells must significantly expand their apical area and transition from a polygonal to circular apical shape to achieve robust mitotic rounding in epithelial tissues, which is where most cancers initiate. However, how cells mechanically regulate robust mitotic rounding within packed tissues is unknown. Here, we analyze mitotic rounding using a newly developed multi-scale subcellular element computational model that is calibrated using experimental data. Novel biologically relevant features of the model include separate representations of the sub-cellular components including the apical membrane and cytoplasm of the cell at the tissue scale level as well as detailed description of cell properties during mitotic rounding. Regression analysis of predictive model simulation results reveals the relative contributions of osmotic pressure, cell-cell adhesion and cortical stiffness to mitotic rounding. Mitotic area expansion is largely driven by regulation of cytoplasmic pressure. Surprisingly, mitotic shape roundness within physiological ranges is most sensitive to variation in cell-cell adhesivity and stiffness. An understanding of how perturbed mechanical properties impact mitotic rounding has important potential implications on, amongst others, how tumors progressively become more genetically unstable due to increased chromosomal aneuploidy and more aggressive.

Emerging Mechanisms and Roles for Asymmetric Cytokinesis

Cytokinesis completes cell division by physically separating the contents of the mother cell between the two daughter cells. This event requires the highly coordinated reorganization of the cytoskeleton within a precise window of time to ensure faithful genomic segregation. In addition, recent progress in the field highlighted the importance of cytokinesis in providing particularly important cues in the context of multicellular tissues. The organization of the cytokinetic machinery and the asymmetric localization or inheritance of the midbody remnants is critical to define the spatial distribution of mechanical and biochemical signals. After a brief overview of the conserved steps of animal cytokinesis, we review the mechanisms controlling polarized cytokinesis focusing on the challenges of epithelial cytokinesis. Finally, we discuss the significance of these asymmetries in defining embryonic body axes, determining cell fate, and ensuring the correct propagation of epithelial organization during proliferation.

Rules of tissue packing involving different cell types: human muscle organization

Natural packed tissues are assembled as tessellations of polygonal cells. These include skeletal muscles and epithelial sheets. Skeletal muscles appear as a mosaic composed of two different types of cells: the "slow" and "fast" fibres. Their relative distribution is important for the muscle function but little is known about how the fibre arrangement is established and maintained. In this work we capture the organizational pattern in two different healthy muscles: biceps brachii and quadriceps. Here we show that the biceps brachii muscle presents a particular arrangement, based on the different sizes of slow and fast fibres. By contrast, in the quadriceps muscle an unbiased distribution exists. Our results indicate that the relative size of each cellular type imposes an intrinsic organization into natural tessellations. These findings establish a new framework for the analysis of any packed tissue where two or more cell types exist.

Direct reprogramming and biomaterials for controlling cell fate

Direct reprogramming which changes the fate of matured cell is a very useful technique with a great interest recently. This approach can eliminate the drawbacks of direct usage of stem cells and allow the patient specific treatment in regenerative medicine. Overexpression of diverse factors such as general reprogramming factors or lineage specific transcription factors can change the fate of already differentiated cells. On the other hand, biomaterials can provide physical and topographical cues or biochemical cues on cells, which can dictate or significantly affect the differentiation of stem cells. The role of biomaterials on direct reprogramming has not been elucidated much, but will be potentially significant to improve the efficiency or specificity of direct reprogramming. In this review, the strategies for general direct reprogramming and biomaterials-guided stem cell differentiation are summarized with the addition of the up-to-date progress on biomaterials for direct reprogramming.