A cell-based model of Nematostella vectensis gastrulation including bottle cell formation, invagination and zippering

SimuCell3D: three-dimensional simulation of tissue mechanics with cell polarization

The three-dimensional (3D) organization of cells determines tissue function and integrity, and changes markedly in development and disease. Cell-based simulations have long been used to define the underlying mechanical principles. However, high computational costs have so far limited simulations to either simplified cell geometries or small tissue patches. Here, we present SimuCell3D, an efficient open-source program to simulate large tissues in three dimensions with subcellular resolution, growth, proliferation, extracellular matrix, fluid cavities, nuclei and non-uniform mechanical properties, as found in polarized epithelia. Spheroids, vesicles, sheets, tubes and other tissue geometries can readily be imported from microscopy images and simulated to infer biomechanical parameters. Doing so, we show that 3D cell shapes in layered and pseudostratified epithelia are largely governed by a competition between surface tension and intercellular adhesion. SimuCell3D enables the large-scale in silico study of 3D tissue organization in development and disease at a great level of detail.

The mechanical influence of densification on epithelial architecture

Epithelial tissues are the most abundant tissue type in animals, lining body cavities and generating compartment barriers. The function of a monolayered epithelial tissue-whether protective, secretory, absorptive, or filtrative-relies on the side-by-side arrangement of its component cells. The mechanical parameters that determine the shape of epithelial cells in the apical-basal plane are not well-understood. Epithelial tissue architecture in culture is intimately connected to cell density, and cultured layers transition between architectures as they proliferate. This prompted us to ask to what extent epithelial architecture emerges from two mechanical considerations: A) the constraints of densification and B) cell-cell adhesion, a hallmark feature of epithelial cells. To address these questions, we developed a novel polyline cell-based computational model and used it to make theoretical predictions about epithelial architecture upon changes to density and cell-cell adhesion. We tested these predictions using cultured cell experiments. Our results show that the appearance of extended lateral cell-cell borders in culture arises as a consequence of crowding-independent of cell-cell adhesion. However, cadherin-mediated cell-cell adhesion is associated with a novel architectural transition. Our results suggest that this transition represents the initial appearance of a distinctive epithelial architecture. Together our work reveals the distinct mechanical roles of densification and adhesion to epithelial layer formation and provides a novel theoretical framework to understand the less well-studied apical-basal plane of epithelial tissues.

The Effect of Substrate Stiffness on Elastic Force Transmission in the Epithelial Monolayers over Short Timescales

Purpose

The importance of mechanical forces and microenvironment in guiding cellular behavior has been widely accepted. Together with the extracellular matrix (ECM), epithelial cells form a highly connected mechanical system subjected to various mechanical cues from their environment, such as ECM stiffness, and tensile and compressive forces. ECM stiffness has been linked to many pathologies, including tumor formation. However, our understanding of the effect of ECM stiffness and its heterogeneities on rapid force transduction in multicellular systems has not been fully addressed.

Methods

We used experimental and computational methods. Epithelial cells were cultured on elastic hydrogels with fluorescent nanoparticles. Single cells were moved by a micromanipulator, and epithelium and substrate deformation were recorded. We developed a computational model to replicate our experiments and quantify the force distribution in the epithelium. Our model further enabled simulations with local stiffness gradients.

Results

We found that substrate stiffness affects the force transduction and the cellular deformation following an external force. Also, our results indicate that the heterogeneities, e.g., gradients, in the stiffness can substantially influence the strain redistribution in the cell monolayers. Furthermore, we found that the cells' apico-basal elasticity provides a level of mechanical isolation between the apical cell-cell junctions and the basal focal adhesions.

Conclusions

Our simulation results show that increased ECM stiffness, e.g., due to a tumor, can mechanically isolate cells and modulate rapid mechanical signaling between cells over distances. Furthermore, the developed model has the potential to facilitate future studies on the interactions between epithelial monolayers and elastic substrates.

Supplementary Information

The online version of this article (10.1007/s12195-023-00772-0) contains supplementary material, which is available to authorized users.

The Mechanical Influence of Densification on Initial Epithelial Architecture

Epithelial tissues are the most abundant tissue type in animals, lining body cavities and generating compartment barriers. The function of a monolayer epithelium - whether protective, secretory, absorptive, or filtrative -relies on regular tissue architecture with respect to the apical-basal axis. Using an unbiased 3D analysis pipeline developed in our lab, we previously showed that epithelial tissue architectures in culture can be divided into distinct developmental categories, and that these are intimately connected to cell density: at sparse densities, cultured epithelial cell layers have a squamous morphology (Immature); at intermediate densities, these layers develop lateral cell-cell borders and rounded cell apices (Intermediate); cells at the highest densities reach their full height and demonstrate flattened apices (Mature). These observations prompted us to ask whether epithelial architecture emerges from the mechanical constraints of densification, and to what extent a hallmark feature of epithelial cells, namely cell-cell adhesion, contributes. In other words, to what extent is the shape of cells in an epithelial layer a simple matter of sticky, deformable objects squeezing together? We addressed this problem using a combination of computational modeling and experimental manipulations. Our results show that the first morphological transition, from Immature to Intermediate, can be explained simply by cell crowding. Additionally, we identify a new division (and thus transition) within the Intermediate category, and find that this second morphology relies on cell-cell adhesion.

Embryonic development of the moon jellyfish Aurelia aurita (Cnidaria, Scyphozoa): another variant on the theme of invagination

Background

Aurelia aurita (Scyphozoa, Cnidaria) is an emblematic species of the jellyfish. Currently, it is an emerging model of Evo-Devo for studying evolution and molecular regulation of metazoans' complex life cycle, early development, and cell differentiation. For Aurelia, the genome was sequenced, the molecular cascades involved in the life cycle transitions were characterized, and embryogenesis was studied on the level of gross morphology. As a reliable representative of the class Scyphozoa, Aurelia can be used for comparative analysis of embryonic development within Cnidaria and between Cnidaria and Bilateria. One of the intriguing questions that can be posed is whether the invagination occurring during gastrulation of different cnidarians relies on the same cellular mechanisms. To answer this question, a detailed study of the cellular mechanisms underlying the early development of Aurelia is required.

Methods

We studied the embryogenesis of A. aurita using the modern methods of light microscopy, immunocytochemistry, confocal laser microscopy, scanning and transmission electron microscopy.

Results

In this article, we report a comprehensive study of the early development of A. aurita from the White Sea population. We described in detail the embryonic development of A. aurita from early cleavage up to the planula larva. We focused mainly on the cell morphogenetic movements underlying gastrulation. The dynamics of cell shape changes and cell behavior during invagination of the archenteron (future endoderm) were characterized. That allowed comparing the gastrulation by invagination in two cnidarian species-scyphozoan A. aurita and anthozoan Nematostella vectensis. We described the successive stages of blastopore closure and found that segregation of the germ layers in A. aurita is linked to the 'healing' of the blastopore lip. We followed the developmental origin of the planula body parts and characterized the planula cells' ultrastructure. We also found that the planula endoderm consists of three morphologically distinct compartments along the oral-aboral axis.

Conclusions

Epithelial invagination is a fundamental morphogenetic movement that is believed as highly conserved across metazoans. Our data on the cell shaping and behaviours driving invagination in A. aurita contribute to understanding of morphologically similar morphogenesis in different animals. By comparative analysis, we clearly show that invagination may differ at the cellular level between cnidarian species belonging to different classes (Anthozoa and Scyphozoa). The number of cells involved in invagination, the dynamics of the shape of the archenteron cells, the stage of epithelial-mesenchymal transition that these cells can reach, and the fate of blastopore lip cells may vary greatly between species. These results help to gain insight into the evolution of morphogenesis within the Cnidaria and within Metazoa in general.

Convergent extension requires adhesion-dependent biomechanical integration of cell crawling and junction contraction

Convergent extension (CE) is an evolutionarily conserved collective cell movement that elongates several organ systems during development. Studies have revealed two distinct cellular mechanisms, one based on cell crawling and the other on junction contraction. Whether these two behaviors collaborate is unclear. Here, using live-cell imaging, we show that crawling and contraction act both independently and jointly but that CE is more effective when they are integrated via mechano-reciprocity. We thus developed a computational model considering both crawling and contraction. This model recapitulates the biomechanical efficacy of integrating the two modes and further clarifies how the two modes and their integration are influenced by cell adhesion. Finally, we use these insights to understand the function of an understudied catenin, Arvcf, during CE. These data are significant for providing interesting biomechanical and cell biological insights into a fundamental morphogenetic process that is implicated in human neural tube defects and skeletal dysplasias.

Adhesion-regulated junction slippage controls cell intercalation dynamics in an Apposed-Cortex Adhesion Model

Cell intercalation is a key cell behaviour of morphogenesis and wound healing, where local cell neighbour exchanges can cause dramatic tissue deformations such as body axis extension. Substantial experimental work has identified the key molecular players facilitating intercalation, but there remains a lack of consensus and understanding of their physical roles. Existing biophysical models that represent cell-cell contacts with single edges cannot study cell neighbour exchange as a continuous process, where neighbouring cell cortices must uncouple. Here, we develop an Apposed-Cortex Adhesion Model (ACAM) to understand active cell intercalation behaviours in the context of a 2D epithelial tissue. The junctional actomyosin cortex of every cell is modelled as a continuous viscoelastic rope-loop, explicitly representing cortices facing each other at bicellular junctions and the adhesion molecules that couple them. The model parameters relate directly to the properties of the key subcellular players that drive dynamics, providing a multi-scale understanding of cell behaviours. We show that active cell neighbour exchanges can be driven by purely junctional mechanisms. Active contractility and cortical turnover in a single bicellular junction are sufficient to shrink and remove a junction. Next, a new, orthogonal junction extends passively. The ACAM reveals how the turnover of adhesion molecules regulates tension transmission and junction deformation rates by controlling slippage between apposed cell cortices. The model additionally predicts that rosettes, which form when a vertex becomes common to many cells, are more likely to occur in actively intercalating tissues with strong friction from adhesion molecules.

Distinct Frizzled receptors independently mediate endomesoderm specification and primary archenteron invagination during gastrulation in Nematostella

Endomesodermal cell fate specification and archenteron formation during gastrulation are tightly linked developmental processes in most metazoans. However, studies have shown that in the anthozoan cnidarian Nematostella vectensis, Wnt/β-catenin (cWnt) signalling-mediated endomesodermal cell fate specification can be experimentally uncoupled from Wnt/Planar Cell Polarity (PCP) signalling-mediated primary archenteron invagination. The upstream signalling mechanisms regulating cWnt signalling-dependent endomesoderm cell fate specification and Wnt/PCP signalling-mediated primary archenteron invagination in Nematostella embryos are not well understood. By screening for potential upstream mediators of cWnt and Wnt/PCP signalling, we identified two Nematostella Frizzled homologs that are expressed early in development. NvFzd1 is expressed maternally and in a broad pattern during early development while NvFzd10 is zygotically expressed at the animal pole in blastula stage embryos and is restricted to the invaginating cells of the presumptive endomesoderm. Molecular and morphological characterization of NvFzd1 and NvFzd10 knock-down phenotypes provide evidence for distinct regulatory roles for the two receptors in endomesoderm cell fate specification and primary archenteron invagination. These results provide further experimental evidence for the independent regulation of endomesodermal cell fate specification and primary archenteron invagination during gastrulation in Nematostella. Moreover, these results provide additional support for the previously proposed two-step model for the independent evolution of cWnt-mediated cell fate specification and Wnt/PCP-mediated primary archenteron invagination.

Self-organized optimal packing of kinesin-5-driven microtubule asters scales with cell size

Radial microtubule (MT) arrays or asters determine cell geometry in animal cells. Multiple asters interacting with motors, such as those in syncytia, form intracellular patterns, but the mechanical principles behind this are not clear. Here, we report that oocytes of the marine ascidian Phallusia mammillata treated with the drug BI-D1870 spontaneously form cytoplasmic MT asters, or cytasters. These asters form steady state segregation patterns in a shell just under the membrane. Cytaster centers tessellate the oocyte cytoplasm, that is divide it into polygonal structures, dominated by hexagons, in a kinesin-5-dependent manner, while inter-aster MTs form 'mini-spindles'. A computational model of multiple asters interacting with kinesin-5 can reproduce both tessellation patterns and mini-spindles in a manner specific to the number of MTs per aster, MT lengths and kinesin-5 density. Simulations predict that the hexagonal tessellation patterns scale with increasing cell size, when the packing fraction of asters in cells is ∼1.6. This self-organized in vivo tessellation by cytasters is comparable to the 'circle packing problem', suggesting that there is an intrinsic mechanical pattern-forming module that is potentially relevant to understanding the role of collective mechanics of cytoskeletal elements in embryogenesis. This article has an associated First Person interview with the first author of the paper.

Impact of Force Function Formulations on the Numerical Simulation of Centre-Based Models

Centre-based or cell-centre models are a framework for the computational study of multicellular systems with widespread use in cancer modelling and computational developmental biology. At the core of these models are the numerical method used to update cell positions and the force functions that encode the pairwise mechanical interactions of cells. For the latter, there are multiple choices that could potentially affect both the biological behaviour captured, and the robustness and efficiency of simulation. For example, available open-source software implementations of centre-based models rely on different force functions for their default behaviour and it is not straightforward for a modeller to know if these are interchangeable. Our study addresses this problem and contributes to the understanding of the potential and limitations of three popular force functions from a numerical perspective. We show empirically that choosing the force parameters such that the relaxation time for two cells after cell division is consistent between different force functions results in good agreement of the population radius of a two-dimensional monolayer relaxing mechanically after intense cell proliferation. Furthermore, we report that numerical stability is not sufficient to prevent unphysical cell trajectories following cell division, and consequently, that too large time steps can cause geometrical differences at the population level.

Gastrulation and germ layer formation in the sea anemone Nematostella vectensis and other cnidarians

Among the basally branching metazoans, cnidarians display well-defined gastrulation processes leading to a diploblastic body plan, consisting of an endodermal and an ectodermal cell layer. As the outgroup to all Bilateria, cnidarians are an interesting group to investigate ancestral developmental mechanisms. Interestingly, all known gastrulation mechanisms known in Bilateria are already found in different species of Cnidaria. Here I review the morphogenetic processes found in different Cnidaria and focus on the investigation of the cellular and molecular mechanisms in the sea anemone Nematostella vectensis, which has been a major model organism among cnidarians for evolutionary developmental biology. Many of the genes involved in germ layer specification and morphogenetic processes in Bilateria are also found active during gastrulation of Nematostella and other cnidarians, suggesting an ancestral role of this process. The molecular analyses indicate a tight link between gastrulation and axis patterning processes by Wnt and FGF signaling. Interestingly, the endodermal layer displays many features of the mesodermal layer in Bilateria, while the pharyngeal ectoderm has an endodermal expression profile. Comparative analyses as well as experimental studies using embryonic aggregates suggest that minor differences in the gene regulatory networks allow the embryo to transition relatively easily from one mode of gastrulation to another.

A cell-based boundary model of gastrulation by unipolar ingression in the hydrozoan cnidarian Clytia hemisphaerica

In Cnidaria, modes of gastrulation to produce the two body layers vary greatly between species. In the hydrozoan species Clytia hemisphaerica gastrulation involves unipolar ingression of presumptive endoderm cells from an oral domain of the blastula, followed by migration of these cells to fill the blastocoel with concomitant narrowing of the gastrula and elongation along the oral-aboral axis. We developed a 2D computational boundary model capable of simulating the morphogenetic changes during embryonic development from early blastula stage to the end of gastrulation. Cells are modeled as polygons with elastic membranes and cytoplasm, colliding and adhering to other cells, and capable of forming filopodia. With this model we could simulate compaction of the embryo preceding gastrulation, bottle cell formation, ingression, and intercalation between cells of the ingressing presumptive endoderm. We show that embryo elongation is dependent on the number of endodermal cells, low endodermal cell-cell adhesion, and planar cell polarity (PCP). When the strength of PCP is reduced in our model, resultant embryo morphologies closely resemble those reported previously following morpholino-mediated knockdown of the core PCP proteins Strabismus and Frizzled. Based on our results, we postulate that cellular processes of apical constriction, compaction, ingression, and then reduced cell-cell adhesion and mediolateral intercalation in the presumptive endoderm, are required and when combined, sufficient for Clytia gastrulation.

Simulations of sea urchin early development delineate the role of oriented cell division in the morula-to-blastula transition

The sea urchin morula to blastula transition has long been thought to require oriented cell divisions and blastomere adherence to the enveloping hyaline layer. In a computer simulation model, cell divisions constrained by a surface plane division rule are adequate to effect morphological transition. The hyaline membrane acts as an enhancer but is not essential. The model is consistent with the orientation of micromere divisions and the open blastulae of direct developing species. The surface plane division rule precedes overt epithelization of surface cells and acts to organize the developing epithelium. It is a universal feature of early metazoan development and simulations of non-echinoid cleavage patterns support its role throughout Metazoa. The surface plane division rule requires only local cues and cells need not reference global positional information or embryonic axes.

Viscoelastic voyages - Biophysical perspectives on cell intercalation during Drosophila gastrulation

Developmental processes are driven by a combination of cytoplasmic, cortical, and surface-associated forces. However, teasing apart the contributions of these forces and how a viscoelastic cell responds has long been a key question in developmental biology. Recent advances in applying biophysical approaches to these questions is leading to a fundamentally new understanding of morphogenesis. In this review, we discuss how computational analysis of experimental findings and in silico modeling of Drosophila gastrulation processes has led to a deeper comprehension of the physical principles at work in the early embryo. We also summarize many of the emerging methodologies that permit biophysical analysis as well as those that provide direct and indirect measurements of force directions and magnitudes. Finally, we examine the multiple frameworks that have been used to model tissue and cellular behaviors.

Adapting a Plant Tissue Model to Animal Development: Introducing Cell Sliding into VirtualLeaf

Cell-based, mathematical modeling of collective cell behavior has become a prominent tool in developmental biology. Cell-based models represent individual cells as single particles or as sets of interconnected particles and predict the collective cell behavior that follows from a set of interaction rules. In particular, vertex-based models are a popular tool for studying the mechanics of confluent, epithelial cell layers. They represent the junctions between three (or sometimes more) cells in confluent tissues as point particles, connected using structural elements that represent the cell boundaries. A disadvantage of these models is that cell-cell interfaces are represented as straight lines. This is a suitable simplification for epithelial tissues, where the interfaces are typically under tension, but this simplification may not be appropriate for mesenchymal tissues or tissues that are under compression, such that the cell-cell boundaries can buckle. In this paper, we introduce a variant of VMs in which this and two other limitations of VMs have been resolved. The new model can also be seen as on off-the-lattice generalization of the Cellular Potts Model. It is an extension of the open-source package VirtualLeaf, which was initially developed to simulate plant tissue morphogenesis where cells do not move relative to one another. The present extension of VirtualLeaf introduces a new rule for cell-cell shear or sliding, from which cell rearrangement (T1) and cell extrusion (T2) transitions emerge naturally, allowing the application of VirtualLeaf to problems of animal development. We show that the updated VirtualLeaf yields different results than the traditional vertex-based models for differential adhesion-driven cell sorting and for the neighborhood topology of soft cellular networks.

Balance of mechanical forces drives endothelial gap formation and may facilitate cancer and immune-cell extravasation

The formation of gaps in the endothelium is a crucial process underlying both cancer and immune cell extravasation, contributing to the functioning of the immune system during infection, the unfavorable development of chronic inflammation and tumor metastasis. Here, we present a stochastic-mechanical multiscale model of an endothelial cell monolayer and show that the dynamic nature of the endothelium leads to spontaneous gap formation, even without intervention from the transmigrating cells. These gaps preferentially appear at the vertices between three endothelial cells, as opposed to the border between two cells. We quantify the frequency and lifetime of these gaps, and validate our predictions experimentally. Interestingly, we find experimentally that cancer cells also preferentially extravasate at vertices, even when they first arrest on borders. This suggests that extravasating cells, rather than initially signaling to the endothelium, might exploit the autonomously forming gaps in the endothelium to initiate transmigration.

Theoretical tool bridging cell polarities with development of robust morphologies

Despite continual renewal and damages, a multicellular organism is able to maintain its complex morphology. How is this stability compatible with the complexity and diversity of living forms? Looking for answers at protein level may be limiting as diverging protein sequences can result in similar morphologies. Inspired by the progressive role of apical-basal and planar cell polarity in development, we propose that stability, complexity, and diversity are emergent properties in populations of proliferating polarized cells. We support our hypothesis by a theoretical approach, developed to effectively capture both types of polar cell adhesions. When applied to specific cases of development – gastrulation and the origins of folds and tubes – our theoretical tool suggests experimentally testable predictions pointing to the strength of polar adhesion, restricted directions of cell polarities, and the rate of cell proliferation to be major determinants of morphological diversity and stability.

Cells have the power to organise themselves to form complex and stable structures, whether it is to create a fully shaped baby from a single egg, or to allow adult salamanders to grow a new limb after losing a leg. This ability has been scrutinised at many different levels. For example, researchers have looked at the chemical messages exchanged by cells, or they have recorded the different shapes an embryo goes through during development. However, it is still difficult to reconcile the information from these approaches into a description that makes sense at multiple scales.

When an embryo develops, sheets of cells fold and unfold to create complex 3D shapes, like the tubes that make our lungs. Moulding sheets into tubes relies on interactions between cells that are not the same in all directions. In fact, two types of asymmetry (or polarity) guide these interactions. Apical-basal polarity runs across a sheet of cells, which means that the top surface of the sheet differs from the bottom. Planar cell polarity runs along the sheet and distinguishes one end from the other. For instance, apical-basal polarity marks the inner and outer surfaces of our skin, while planar cell polarity controls the direction in which our hair grows.

Nissen et al. set out to investigate how these polarities help cells in an embryo organise themselves to form complicated folds and tubes. To do this, simple mathematical representations of both apical-basal and planar cell polarities were designed. The representations were then combined to create computer simulations of groups of cells as these divide and interact with each other.

Simulations of ‘cells’ with only apical-basal polarity were able to generate different shapes in the ‘tissues’ produced, including many found in living organisms. External conditions, such as how cells were arranged to start with, determined the resulting shape. With both apical-basal and planar cell polarities, the simulations reproduced an important change that occurs during early development. They also replicated how the tubes that transport nutrients and oxygen form.

These results show that simple properties of individual cells, such as polarities, can produce different shapes in developing tissues and organs, without the need for a complicated overarching program. Abnormal changes in cell polarity are also associated with diseases such as cancer. The mathematical model developed by Nissen et al. could therefore be a useful tool to study these events.

Epithelial folding in the morphogenesis of the colonial marine hydrozoan, Dynamena pumila

Epithelial folding (EF) is a fundamental morphogenetic process that can be observed in the development of many organisms ranging from metazoans to green algae. Being early branching metazoans, cnidarians represent the best models to study evolutionarily conserved morphogenetic processes, including EF. Hydrozoa is the most evolutionary advanced group of the phylum Cnidaria. All colonial hydrozoans grow continuously, changing the shape of their colonies and spreading over the substrate with the help of elongating stolons. Owing to high diversity of colony architecture, they are ideal objects for comparative and evolutionary morphology. In the hydrozoan Dynamena pumila, the growth of the colony proceeds via a variety of morphogenetic processes. Our work is focused on the formation of the anchoring disc of the stolon, which is accompanied by inward-folding morphogenesis of the ectodermal layer. Successive stages of anchoring disc development were described with light, confocal transmission electron microscopy. We have shown that EF in Dynamena is associated with accumulation of F-actin in the constricting apical domains of forming bottle cells located at the bottom of the emerging fold. In addition, the nuclei of these cells are displaced to the basal domains. Taken together, these features may indicate that EF in Dynamena proceeds as an active invagination, although this process has never been described in the development of hydrozoans. Apparently, development of the anchoring disc can be viewed as a reliable and versatile model system for studying the cell-shape-change-driven epithelial sheet morphogenesis, which can be easily observed and analysed.

Germ layer-specific regulation of cell polarity and adhesion gives insight into the evolution of mesoderm

In triploblastic animals, Par-proteins regulate cell-polarity and adherens junctions of both ectodermal and endodermal epithelia. But, in embryos of the diploblastic cnidarian Nematostella vectensis, Par-proteins are degraded in all cells in the bifunctional gastrodermal epithelium. Using immunohistochemistry, CRISPR/Cas9 mutagenesis, and mRNA overexpression, we describe the functional association between Par-proteins, ß-catenin, and snail transcription factor genes in N. vectensis embryos. We demonstrate that the aPKC/Par complex regulates the localization of ß-catenin in the ectoderm by stabilizing its role in cell-adhesion, and that endomesodermal epithelial cells are organized by a different cell-adhesion system than overlying ectoderm. We also show that ectopic expression of snail genes, which are expressed in mesodermal derivatives in bilaterians, is sufficient to downregulate Par-proteins and translocate ß-catenin from the junctions to the cytoplasm in ectodermal cells. These data provide molecular insight into the evolution of epithelial structure and distinct cell behaviors in metazoan embryos.

Complex structures from patterned cell sheets

The formation of three-dimensional structures from patterned epithelial sheets plays a key role in tissue morphogenesis. An important class of morphogenetic mechanisms relies on the spatio-temporal control of apical cell contractility, which can result in the localized bending of cell sheets and in-plane cell rearrangements. We have recently proposed a modified vertex model that can be used to systematically explore the connection between the two-dimensional patterns of cell properties and the emerging three-dimensional structures. Here we review the proposed modelling framework and illustrate it through the computational analysis of the vertex model that captures the salient features of the formation of the dorsal appendages during Drosophila oogenesis.This article is part of the themed issue 'Systems morphodynamics: understanding the development of tissue hardware'.

Mechanocellular models of epithelial morphogenesis

Embryonic epithelia achieve complex morphogenetic movements, including in-plane reshaping, bending and folding, through the coordinated action and rearrangement of individual cells. Technical advances in molecular and live-imaging studies of epithelial dynamics provide a very real opportunity to understand how cell-level processes facilitate these large-scale tissue rearrangements. However, the large datasets that we are now able to generate require careful interpretation. In combination with experimental approaches, computational modelling allows us to challenge and refine our current understanding of epithelial morphogenesis and to explore experimentally intractable questions. To this end, a variety of cell-based modelling approaches have been developed to describe cell-cell mechanical interactions, ranging from vertex and 'finite-element' models that approximate each cell geometrically by a polygon representing the cell's membrane, to immersed boundary and subcellular element models that allow for more arbitrary cell shapes. Here, we review how these models have been used to provide insights into epithelial morphogenesis and describe how such models could help future efforts to decipher the forces and mechanical and biochemical feedbacks that guide cell and tissue-level behaviour. In addition, we discuss current challenges associated with using computational models of morphogenetic processes in a quantitative and predictive way.This article is part of the themed issue 'Systems morphodynamics: understanding the development of tissue hardware'.

Cas9-mediated excision of Nematostella brachyury disrupts endoderm development, pharynx formation and oral-aboral patterning

The mesoderm is a key novelty in animal evolution, although we understand little of how the mesoderm arose. brachyury, the founding member of the T-box gene family, is a key gene in chordate mesoderm development. However, the brachyury gene was present in the common ancestor of fungi and animals long before mesoderm appeared. To explore ancestral roles of brachyury prior to the evolution of definitive mesoderm, we excised the gene using CRISPR/Cas9 in the diploblastic cnidarian Nematostella vectensis Nvbrachyury is normally expressed in precursors of the pharynx, which separates endoderm from ectoderm. In knockout embryos, the pharynx does not form, embryos fail to elongate, and endoderm organization, ectodermal cell polarity and patterning along the oral-aboral axis are disrupted. Expression of many genes both inside and outside the Nvbrachyury expression domain is affected, including downregulation of Wnt genes at the oral pole. Our results point to an ancient role for brachyury in morphogenesis, cell polarity and the patterning of both ectodermal and endodermal derivatives along the primary body axis.

A novel technique to combine and analyse spatial and temporal expression datasets: A case study with the sea anemone Nematostella vectensis to identify potential gene interactions

Understanding genetic interactions during early development of a given organism, is the first step toward unveiling gene regulatory networks (GRNs) that govern a biological process of interest. Predicting such interactions from large expression datasets by performing targeted knock-down/knock-out approaches is a challenging task. We use the currently available expression datasets (in situ hybridization images & qPCR time series) for a basal anthozoan the sea anemone N. vectensis to construct continuous spatiotemporal gene expression patterns during its early development. Moreover, by combining cluster results from each dataset we develop a method that provides testable hypotheses about potential genetic interactions. We show that the analysis of spatial gene expression patterns reveals functional regions of the embryo during the gastrulation. The clustering results from qPCR time series unveils significant temporal events and highlights genes potentially involved in N. vectensis gastrulation. Furthermore, we introduce a method for merging the clustering results from spatial and temporal datasets by which we can group genes that are expressed in the same region and at the time. We demonstrate that the merged clusters can be used to identify GRN interactions involved in various processes and to predict possible activators or repressors of any gene in the dataset. Finally, we validate our methods and results by predicting the repressor effect of NvErg on NvBra in the central domain during the gastrulation that has recently been confirmed by functional analysis.

Shape Transformations of Epithelial Shells

Regulated deformations of epithelial sheets are frequently foreshadowed by patterning of their mechanical properties. The connection between patterns of cell properties and the emerging tissue deformations is studied in multiple experimental systems, but the general principles remain poorly understood. For instance, it is in general unclear what determines the direction in which the patterned sheet is going to bend and whether the resulting shape transformation will be discontinuous or smooth. Here these questions are explored computationally, using vertex models of epithelial shells assembled from prismlike cells. In response to rings and patches of apical cell contractility, model epithelia smoothly deform into invaginated or evaginated shapes similar to those observed in embryos and tissue organoids. Most of the observed effects can be captured by a simpler model with polygonal cells, modified to include the effects of the apicobasal polarity and natural curvature of epithelia. Our models can be readily extended to include the effects of multiple constraints and used to describe a wide range of morphogenetic processes.

The mechanical properties of a cell-based numerical model of epithelium

In this work we use a computational cell-based model to study the influence of the mechanical properties of cells on the mechanics of epithelial tissues. We analyze the effect of the model parameters on the elasticity and the mechanical response of tissues subjected to stress loading application. We compare our numerical results with experimental measurements of epithelial cell monolayer mechanics. Unlike previous studies, we have been able to estimate in physical units the parameter values that match the experimental results. A key observation is that the model parameters must vary with the tissue strain. In particular, it was found that, while the perimeter contractility and the area elasticity of cells remain constant at lower strains (<20%), they must increase to respond to larger strains (>20%). However, above a threshold of 50% extension, the cells stop counteracting the tissue strain and reduce both their perimeter contractility and area elasticity.

Quantitative multivariate analysis of dynamic multicellular morphogenic trajectories

Interrogating fundamental cell biology principles that govern tissue morphogenesis is critical to better understanding of developmental biology and engineering novel multicellular systems. Recently, functional micro-tissues derived from pluripotent embryonic stem cell (ESC) aggregates have provided novel platforms for experimental investigation; however elucidating the factors directing emergent spatial phenotypic patterns remains a significant challenge. Computational modelling techniques offer a unique complementary approach to probe mechanisms regulating morphogenic processes and provide a wealth of spatio-temporal data, but quantitative analysis of simulations and comparison to experimental data is extremely difficult. Quantitative descriptions of spatial phenomena across multiple systems and scales would enable unprecedented comparisons of computational simulations with experimental systems, thereby leveraging the inherent power of computational methods to interrogate the mechanisms governing emergent properties of multicellular biology. To address these challenges, we developed a portable pattern recognition pipeline consisting of: the conversion of cellular images into networks, extraction of novel features via network analysis, and generation of morphogenic trajectories. This novel methodology enabled the quantitative description of morphogenic pattern trajectories that could be compared across diverse systems: computational modelling of multicellular structures, differentiation of stem cell aggregates, and gastrulation of cichlid fish. Moreover, this method identified novel spatio-temporal features associated with different stages of embryo gastrulation, and elucidated a complex paracrine mechanism capable of explaining spatiotemporal pattern kinetic differences in ESC aggregates of different sizes.

Par system components are asymmetrically localized in ectodermal epithelia, but not during early development in the sea anemone Nematostella vectensis

Background

The evolutionary origins of cell polarity in metazoan embryos are unclear. In most bilaterian animals, embryonic and cell polarity are set up during embryogenesis with the same molecules being utilized to regulate tissue polarity at different life stages. Atypical protein kinase C (aPKC), lethal giant larvae (Lgl), and Partitioning-defective (Par) proteins are conserved components of cellular polarization, and their role in establishing embryonic asymmetry and tissue polarity have been widely studied in model bilaterian groups. However, the deployment and role of these proteins in animals outside Bilateria has not been studied. We address this by characterizing the localization of different components of the Par system during early development of the sea anemone Nematostella vectensis, a member of the clade Cnidaria, the sister group to bilaterian animals.

Results

Immunostaining using specific N. vectensis antibodies and the overexpression of mRNA-reporter constructs show that components of the N. vectensis Par system (NvPar-1, NvPar-3, NvPar-6, NvaPKC, and NvLgl) distribute throughout the microtubule cytoskeleton of eggs and early embryos without clear polarization along any embryonic axis. However, they become asymmetrically distributed at later stages, when the embryo forms an ectodermal epithelial layer. NvLgl and NvPar-1 localize in the basolateral cortex, and NvaPKC, NvPar-6, and NvPar-3 at the apical zone of the cell in a manner seen in bilaterian animals.

Conclusions

The cnidarian N. vectensis exhibits clear polarity at all stages of early embryonic development, which appears to be established independent of the Par system reported in many bilaterian embryos. However, in N. vectensis, using multiple immunohistochemical and fluorescently labeled markers in vivo, components of this system are deployed to organize epithelial cell polarity at later stages of development. This suggests that Par system proteins were co-opted to organize early embryonic cell polarity at the base of the Bilateria and that, therefore, different molecular mechanisms operate in early cnidarian embryogenesis.

Electronic supplementary material

The online version of this article (doi:10.1186/s13227-015-0014-6) contains supplementary material, which is available to authorized users.

Interplay of cell shape and division orientation promotes robust morphogenesis of developing epithelia

Epithelial cells acquire functionally important shapes (e.g., squamous, cuboidal, columnar) during development. Here, we combine theory, quantitative imaging, and perturbations to analyze how tissue geometry, cell divisions, and mechanics interact to shape the presumptive enveloping layer (pre-EVL) on the zebrafish embryonic surface. We find that, under geometrical constraints, pre-EVL flattening is regulated by surface cell number changes following differentially oriented cell divisions. The division pattern is, in turn, determined by the cell shape distribution, which forms under geometrical constraints by cell-cell mechanical coupling. An integrated mathematical model of this shape-division feedback loop recapitulates empirical observations. Surprisingly, the model predicts that cell shape is robust to changes of tissue surface area, cell volume, and cell number, which we confirm in vivo. Further simulations and perturbations suggest the parameter linking cell shape and division orientation contributes to epithelial diversity. Together, our work identifies an evolvable design logic that enables robust cell-level regulation of tissue-level development.

In vivo imaging of Nematostella vectensis embryogenesis and late development using fluorescent probes

BACKGROUND

Cnidarians are the closest living relatives to bilaterians and have been instrumental to studying the evolution of bilaterian properties. The cnidarian model, Nematostella vectensis, is a unique system in which embryology and regeneration are both studied, making it an ideal candidate to develop in vivo imaging techniques. Live imaging is the most direct way for quantitative and qualitative assessment of biological phenomena. Actin and tubulin are cytoskeletal proteins universally important for regulating many embryological processes but so far studies in Nematostella primarily focused on the localization of these proteins in fixed embryos.

RESULTS

We used fluorescent probes expressed in vivo to investigate the dynamics of Nematostella development. Lifeact-mTurquoise2, a fluorescent cyan F-actin probe, can be visualized within microvilli along the cellular surface throughout embryonic development and is stable for two months after injection. Co-expression of Lifeact-mTurquoise2 with End-Binding protein1 (EB1) fused to mVenus or tdTomato-NLS allows for the visualization of cell-cycle properties in real time. Utilizing fluorescent probes in vivo helped to identify a concentrated 'flash' of Lifeact-mTurquoise2 around the nucleus, immediately prior to cytokinesis in developing embryos. Moreover, Lifeact-mTurquoise2 expression in adult animals allowed the identification of various cell types as well as cellular boundaries.

CONCLUSION

The methods developed in this manuscript provide an alternative protocol to investigate Nematostella development through in vivo cellular analysis. This study is the first to utilize the highly photo-stable florescent protein mTurquoise2 as a marker for live imaging. Finally, we present a clear methodology for the visualization of minute temporal events during cnidarian development.

Current directions and future perspectives from the third Nematostella research conference

The third Nematostella vectensis Research Conference took place in December 2013 in Eilat, Israel, as a satellite to the 8th International Conference on Coelenterate Biology. The starlet sea anemone, N. vectensis, has emerged as a powerful cnidarian model, in large part due to the extensive genomic and transcriptomic resources and molecular approaches that are becoming available for Nematostella, which were the focus of several presentations. In addition, research was presented highlighting the broader utility of this species for studies of development, circadian rhythms, signal transduction, and gene-environment interactions.

A diploblastic radiate animal at the dawn of cambrian diversification with a simple body plan: distinct from Cnidaria?

Background

Microfossils of the genus Punctatus include developmental stages such as blastula, gastrula, and hatchlings, and represent the most complete developmental sequence of animals available from the earliest Cambrian. Despite the extremely well-preserved specimens, the evolutionary position of Punctatus has relied only on their conical remains and they have been tentatively assigned to cnidarians. We present a new interpretation of the Punctatus body plan based on the developmental reconstruction aided by recent advances in developmental biology.

Results

Punctatus developed from a rather large egg, gastrulated in a mode of invagination from a coeloblastura, and then formed a mouth directly from the blastopore. Spiny benthic hatchlings were distinguishable from swimming or crawling ciliate larvae found in cnidarians and sponges. A mouth appeared at the perihatching embryonic stage and was renewed periodically during growth, and old mouths transformed into the body wall, thus elongating the body. Growing animals retained a small blind gut in a large body cavity without partitioning by septa and did not form tentacles, pedal discs or holdfasts externally. A growth center at the oral pole was sufficient for body patterning throughout life, and the body patterning did not show any bias from radial symmetry.

Conclusions

Contrary to proposed cnidarian affinity, the Punctatus body plan has basic differences from that of cnidarians, especially concerning a spacious body cavity separating ectoderm from endoderm. The lack of many basic cnidarian characters in the body patterning of Punctatus leads us to consider its own taxonomic group, potentially outside of Cnidaria.

Physiology-based model of cell viscoelasticity

The measured viscoelastic properties of biological tissues is the result of the passive and active response of the cells. We propose an evolution law of the remodeling process in the cytoskeleton which is able to mimic the viscous properties of biological cellular tissues. Our model is based on dynamical changes of the resting length. We show that under the small strain regime, the linear rheology models are recovered, with the relaxation time being replaced by the cell resistance to remodel. We implement the one-dimensional model into network systems of two and three dimensions, and show that the same conclusions may be drawn for those systems.

A biomechanical analysis of ventral furrow formation in the Drosophila melanogaster embryo

The article provides a biomechanical analysis of ventral furrow formation in the Drosophila melanogaster embryo. Ventral furrow formation is the first large-scale morphogenetic movement in the fly embryo. It involves deformation of a uniform cellular monolayer formed following cellularisation, and has therefore long been used as a simple system in which to explore the role of mechanics in force generation. Here we use a quantitative framework to carry out a systematic perturbation analysis to determine the role of each of the active forces observed. The analysis confirms that ventral furrow invagination arises from a combination of apical constriction and apical–basal shortening forces in the mesoderm, together with a combination of ectodermal forces. We show that the mesodermal forces are crucial for invagination: the loss of apical constriction leads to a loss of the furrow, while the mesodermal radial shortening forces are the primary cause of the internalisation of the future mesoderm as the furrow rises. Ectodermal forces play a minor but significant role in furrow formation: without ectodermal forces the furrow is slower to form, does not close properly and has an aberrant morphology. Nevertheless, despite changes in the active mesodermal and ectodermal forces lead to changes in the timing and extent of furrow, invagination is eventually achieved in most cases, implying that the system is robust to perturbation and therefore over-determined.

Modeling cellular processes in 3D

Recent advances in photonic imaging and fluorescent protein technology offer unprecedented views of molecular space-time dynamics in living cells. At the same time, advances in computing hardware and software enable modeling of ever more complex systems, from global climate to cell division. As modeling and experiment become more closely integrated we must address the issue of modeling cellular processes in 3D. Here, we highlight recent advances related to 3D modeling in cell biology. While some processes require full 3D analysis, we suggest that others are more naturally described in 2D or 1D. Keeping the dimensionality as low as possible reduces computational time and makes models more intuitively comprehensible; however, the ability to test full 3D models will build greater confidence in models generally and remains an important emerging area of cell biological modeling.

Spatial organization of mesenchymal stem cells in vitro--results from a new individual cell-based model with podia

Therapeutic application of mesenchymal stem cells (MSC) requires their extensive in vitro expansion. MSC in culture typically grow to confluence within a few weeks. They show spindle-shaped fibroblastoid morphology and align to each other in characteristic spatial patterns at high cell density. We present an individual cell-based model (IBM) that is able to quantitatively describe the spatio-temporal organization of MSC in culture. Our model substantially improves on previous models by explicitly representing cell podia and their dynamics. It employs podia-generated forces for cell movement and adjusts cell behavior in response to cell density. At the same time, it is simple enough to simulate thousands of cells with reasonable computational effort. Experimental sheep MSC cultures were monitored under standard conditions. Automated image analysis was used to determine the location and orientation of individual cells. Our simulations quantitatively reproduced the observed growth dynamics and cell-cell alignment assuming cell density-dependent proliferation, migration, and morphology. In addition to cell growth on plain substrates our model captured cell alignment on micro-structured surfaces. We propose a specific surface micro-structure that according to our simulations can substantially enlarge cell culture harvest. The 'tool box' of cell migratory behavior newly introduced in this study significantly enhances the bandwidth of IBM. Our approach is capable of accommodating individual cell behavior and collective cell dynamics of a variety of cell types and tissues in computational systems biology.