Dynamics and mechanical stability of the developing dorsoventral organizer of the wing imaginal disc

Choice of friction coefficient deeply affects tissue behaviour in stochastic epithelial vertex models

To understand the mechanisms that coordinate the formation of biological tissues, the use of numerical implementations is necessary. The complexity of such models involves many assumptions and parameter choices that result in unpredictable consequences, obstructing the comparison with experimental data. Here, we focus on vertex models, a family of spatial models used extensively to simulate the dynamics of epithelial tissues. Usually, in the literature, the choice of the friction coefficient is not addressed using quasi-static deformation arguments that generally do not apply to realistic scenarios. In this manuscript, we discuss the role that the choice of friction coefficient has on the relaxation times and consequently in the conditions of cell cycle progression and division. We explore the effects that these changes have on the morphology, growth rate and topological transitions of the tissue dynamics. These results provide a deeper understanding of the role that an accurate mechanical description plays in the use of vertex models as inference tools. This article is part of a discussion meeting issue 'Causes and consequences of stochastic processes in development and disease'.

On the origins of developmental robustness: modeling buffering mechanisms against cell-level noise

During development, cells are subject to stochastic fluctuations in their positions (i.e. cell-level noise) that can potentially lead to morphological noise (i.e. stochastic differences between morphologies that are expected to be equal, e.g. the right and left sides of bilateral organisms). In this study, we explore new and existing hypotheses on buffering mechanisms against cell-level noise. Many of these hypotheses focus on how the boundaries between territories of gene expression remain regular and well defined, despite cell-level noise and division. We study these hypotheses and how irregular territory boundaries lead to morphological noise. To determine the consistency of the different hypotheses, we use a general computational model of development: EmbryoMaker. EmbryoMaker can implement arbitrary gene networks regulating basic cell behaviors (contraction, adhesion, etc.), signaling and tissue biomechanics. We found that buffering mechanisms based on the orientation of cell divisions cannot lead to regular boundaries but that other buffering mechanisms can (homotypic adhesion, planar contraction, non-dividing boundaries, constant signaling and majority rule hypotheses). We also explore the effects of the shape and size of the territories on morphological noise.

A quantitative biophysical principle to explain the 3D cellular connectivity in curved epithelia

Epithelial cell organization and the mechanical stability of tissues are closely related. In this context, it has been recently shown that packing optimization in bended or folded epithelia is achieved by an energy minimization mechanism that leads to a complex cellular shape: the "scutoid". Here, we focus on the relationship between this shape and the connectivity between cells. We use a combination of computational, experimental, and biophysical approaches to examine how energy drivers affect the three-dimensional (3D) packing of tubular epithelia. We propose an energy-based stochastic model that explains the 3D cellular connectivity. Then, we challenge it by experimentally reducing the cell adhesion. As a result, we observed an increment in the appearance of scutoids that correlated with a decrease in the energy barrier necessary to connect with new cells. We conclude that tubular epithelia satisfy a quantitative biophysical principle that links tissue geometry and energetics with the average cellular connectivity.

Image-based parameter inference for epithelial mechanics

Measuring mechanical parameters in tissues, such as the elastic modulus of cell-cell junctions, is essential to decipher the mechanical control of morphogenesis. However, their in vivo measurement is technically challenging. Here, we formulated an image-based statistical approach to estimate the mechanical parameters of epithelial cells. Candidate mechanical models are constructed based on force-cell shape correlations obtained from image data. Substitution of the model functions into force-balance equations at the cell vertex leads to an equation with respect to the parameters of the model, by which one can estimate the parameter values using a least-squares method. A test using synthetic data confirmed the accuracy of parameter estimation and model selection. By applying this method to Drosophila epithelial tissues, we found that the magnitude and orientation of feedback between the junction tension and shrinkage, which are determined by the spring constant of the junction, were correlated with the elevation of tension and myosin-II on shrinking junctions during cell rearrangement. Further, this method clarified how alterations in tissue polarity and stretching affect the anisotropy in tension parameters. Thus, our method provides a novel approach to uncovering the mechanisms governing epithelial morphogenesis.

Mechanics and self-organization in tissue development

Self-organization is an all-important feature of living systems that provides the means to achieve specialization and functionality at distinct spatio-temporal scales. Herein, we review this concept by addressing the packing organization of cells, the sorting/compartmentalization phenomenon of cell populations, and the propagation of organizing cues at the tissue level through traveling waves. We elaborate on how different theoretical models and tools from Topology, Physics, and Dynamical Systems have improved the understanding of self-organization by shedding light on the role played by mechanics as a driver of morphogenesis. Altogether, by providing a historical perspective, we show how ideas and hypotheses in the field have been revisited, developed, and/or rejected and what are the open questions that need to be tackled by future research.

The complex three-dimensional organization of epithelial tissues

Understanding the cellular organization of tissues is key to developmental biology. In order to deal with this complex problem, researchers have taken advantage of reductionist approaches to reveal fundamental morphogenetic mechanisms and quantitative laws. For epithelia, their two-dimensional representation as polygonal tessellations has proved successful for understanding tissue organization. Yet, epithelial tissues bend and fold to shape organs in three dimensions. In this context, epithelial cells are too often simplified as prismatic blocks with a limited plasticity. However, there is increasing evidence that a realistic approach, even from a reductionist perspective, must include apico-basal intercalations (i.e. scutoidal cell shapes) for explaining epithelial organization convincingly. Here, we present an historical perspective about the tissue organization problem. Specifically, we analyze past and recent breakthroughs, and discuss how and why simplified, but realistic, in silico models require scutoidal features to address key morphogenetic events.

Self-sustained planar intercalations due to mechanosignaling feedbacks lead to robust axis extension during morphogenesis

Tissue elongation is a necessary process in metazoans to implement their body plans that is not fully understood. Here we propose a mechanism based on the interplay between cellular mechanics and primordia patterning that results in self-sustained planar intercalations. Thus, we show that a location-dependent modulation of the mechanical properties of cells leads to robust axis extension. To illustrate the plausibility of this mechanism, we test it against different patterning models by means of computer simulations of tissues where we implemented mechano-signaling feedbacks. Our results suggest that robust elongation relies on a trade-off between cellular and tissue strains that is orchestrated through the cleavage orientation. In the particular context of axis extension in Turing-patterned tissues, we report that different directional cell activities cooperate synergetically to achieve elongation. Altogether, our findings help to understand how the axis extension phenomenon emerges from the dynamics of individual cells.

Neuronal differentiation influences progenitor arrangement in the vertebrate neuroepithelium

Cell division, movement and differentiation contribute to pattern formation in developing tissues. This is the case in the vertebrate neural tube, in which neurons differentiate in a characteristic pattern from a highly dynamic proliferating pseudostratified epithelium. To investigate how progenitor proliferation and differentiation affect cell arrangement and growth of the neural tube, we used experimental measurements to develop a mechanical model of the apical surface of the neuroepithelium that incorporates the effect of interkinetic nuclear movement and spatially varying rates of neuronal differentiation. Simulations predict that tissue growth and the shape of lineage-related clones of cells differ with the rate of differentiation. Growth is isotropic in regions of high differentiation, but dorsoventrally biased in regions of low differentiation. This is consistent with experimental observations. The absence of directional signalling in the simulations indicates that global mechanical constraints are sufficient to explain the observed differences in anisotropy. This provides insight into how the tissue growth rate affects cell dynamics and growth anisotropy and opens up possibilities to study the coupling between mechanics, pattern formation and growth in the neural tube.

Summary: A mechanical model of the vertebrate neuroepithelium, based on experimental observations, suggests that the rate of neuronal differentiation influences tissue growth and the shape of lineage-related clones.

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.

Approximate Bayesian computation reveals the importance of repeated measurements for parameterising cell-based models of growing tissues

The growth and dynamics of epithelial tissues govern many morphogenetic processes in embryonic development. A recent quantitative transition in data acquisition, facilitated by advances in genetic and live-imaging techniques, is paving the way for new insights to these processes. Computational models can help us understand and interpret observations, and then make predictions for future experiments that can distinguish between hypothesised mechanisms. Increasingly, cell-based modelling approaches such as vertex models are being used to help understand the mechanics underlying epithelial morphogenesis. These models typically seek to reproduce qualitative phenomena, such as cell sorting or tissue buckling. However, it remains unclear to what extent quantitative data can be used to constrain these models so that they can then be used to make quantitative, experimentally testable predictions. To address this issue, we perform an in silico study to investigate whether vertex model parameters can be inferred from imaging data, and explore methods to quantify the uncertainty of such estimates. Our approach requires the use of summary statistics to estimate parameters. Here, we focus on summary statistics of cellular packing and of laser ablation experiments, as are commonly reported from imaging studies. We find that including data from repeated experiments is necessary to generate reliable parameter estimates that can facilitate quantitative model predictions.

Finite cell-size effects on protein variability in Turing patterned tissues

Herein we present a framework to characterize different sources of protein expression variability in Turing patterned tissues. In this context, we introduce the concept of granular noise to account for the unavoidable fluctuations due to finite cell-size effects and show that the nearest-neighbours autocorrelation function provides the means to measure it. To test our findings, we perform in silico experiments of growing tissues driven by a generic activator-inhibitor dynamics. Our results show that the relative importance of different sources of noise depends on the ratio between the characteristic size of cells and that of the pattern domains and on the ratio between the pattern amplitude and the effective intensity of the biochemical fluctuations. Importantly, our framework provides the tools to measure and distinguish different stochastic contributions during patterning: granularity versus biochemical noise. In addition, our analysis identifies the protein species that buffer the stochasticity the best and, consequently, it can help to determine key instructive signals in systems driven by a Turing instability. Altogether, we expect our study to be relevant in developmental processes leading to the formation of periodic patterns in tissues.

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.

Contact inhibition of locomotion and mechanical cross-talk between cell-cell and cell-substrate adhesion determine the pattern of junctional tension in epithelial cell aggregates

A computational approach is used to analyze the biomechanics of epithelial cells based on their capacity to adhere to one another and to the substrate and exhibit contact inhibition of locomotion. This approach reproduces emergent properties of epithelial cell aggregates and makes predictions for experimental validation.

We used a computational approach to analyze the biomechanics of epithelial cell aggregates—islands, stripes, or entire monolayers—that combines both vertex and contact-inhibition-of-locomotion models to include cell–cell and cell–substrate adhesion. Examination of the distribution of cell protrusions (adhesion to the substrate) in the model predicted high-order profiles of cell organization that agree with those previously seen experimentally. Cells acquired an asymmetric distribution of basal protrusions, traction forces, and apical aspect ratios that decreased when moving from the edge to the island center. Our in silico analysis also showed that tension on cell–cell junctions and apical stress is not homogeneous across the island. Instead, these parameters are higher at the island center and scale up with island size, which we confirmed experimentally using laser ablation assays and immunofluorescence. Without formally being a three-dimensional model, our approach has the minimal elements necessary to reproduce the distribution of cellular forces and mechanical cross-talk, as well as the distribution of principal stress in cells within epithelial cell aggregates. By making experimentally testable predictions, our approach can aid in mechanical analysis of epithelial tissues, especially when local changes in cell–cell and/or cell–substrate adhesion drive collective cell behavior.

Qualitative Dynamical Modelling Can Formally Explain Mesoderm Specification and Predict Novel Developmental Phenotypes

Given the complexity of developmental networks, it is often difficult to predict the effect of genetic perturbations, even within coding genes. Regulatory factors generally have pleiotropic effects, exhibit partially redundant roles, and regulate highly interconnected pathways with ample cross-talk. Here, we delineate a logical model encompassing 48 components and 82 regulatory interactions involved in mesoderm specification during Drosophila development, thereby providing a formal integration of all available genetic information from the literature. The four main tissues derived from mesoderm correspond to alternative stable states. We demonstrate that the model can predict known mutant phenotypes and use it to systematically predict the effects of over 300 new, often non-intuitive, loss- and gain-of-function mutations, and combinations thereof. We further validated several novel predictions experimentally, thereby demonstrating the robustness of model. Logical modelling can thus contribute to formally explain and predict regulatory outcomes underlying cell fate decisions.

Capabilities and Limitations of Tissue Size Control through Passive Mechanical Forces

Embryogenesis is an extraordinarily robust process, exhibiting the ability to control tissue size and repair patterning defects in the face of environmental and genetic perturbations. The size and shape of a developing tissue is a function of the number and size of its constituent cells as well as their geometric packing. How these cellular properties are coordinated at the tissue level to ensure developmental robustness remains a mystery; understanding this process requires studying multiple concurrent processes that make up morphogenesis, including the spatial patterning of cell fates and apoptosis, as well as cell intercalations. In this work, we develop a computational model that aims to understand aspects of the robust pattern repair mechanisms of the Drosophila embryonic epidermal tissues. Size control in this system has previously been shown to rely on the regulation of apoptosis rather than proliferation; however, to date little work has been done to understand the role of cellular mechanics in this process. We employ a vertex model of an embryonic segment to test hypotheses about the emergence of this size control. Comparing the model to previously published data across wild type and genetic perturbations, we show that passive mechanical forces suffice to explain the observed size control in the posterior (P) compartment of a segment. However, observed asymmetries in cell death frequencies across the segment are demonstrated to require patterning of cellular properties in the model. Finally, we show that distinct forms of mechanical regulation in the model may be distinguished by differences in cell shapes in the P compartment, as quantified through experimentally accessible summary statistics, as well as by the tissue recoil after laser ablation experiments.

Making quantitative morphological variation from basic developmental processes: Where are we? The case of the Drosophila wing

One of the aims of evolutionary developmental biology is to discover the developmental origins of morphological variation. The discipline has mainly focused on qualitative morphological differences (e.g., presence or absence of a structure) between species. Studies addressing subtle, quantitative variation are less common. The Drosophila wing is a model for the study of development and evolution, making it suitable to investigate the developmental mechanisms underlying the subtle quantitative morphological variation observed in nature. Previous reviews have focused on the processes involved in wing differentiation, patterning and growth. Here, we investigate what is known about how the wing achieves its final shape, and what variation in development is capable of generating the variation in wing shape observed in nature. Three major developmental stages need to be considered: larval development, pupariation, and pupal development. The major cellular processes involved in the determination of tissue size and shape are cell proliferation, cell death, oriented cell division and oriented cell intercalation. We review how variation in temporal and spatial distribution of growth and transcription factors affects these cellular mechanisms, which in turn affects wing shape. We then discuss which aspects of the wing morphological variation are predictable on the basis of these mechanisms. Developmental Dynamics 244:1058-1073, 2015. © 2015 Wiley Periodicals, Inc.

Mechanisms of regulating tissue elongation in Drosophila wing: impact of oriented cell divisions, oriented mechanical forces, and reduced cell size

Regulation of cell growth and cell division plays fundamental roles in tissue morphogenesis. However, the mechanisms of regulating tissue elongation through cell growth and cell division are still not well understood. The wing imaginal disc of Drosophila provides a model system that has been widely used to study tissue morphogenesis. Here we use a recently developed two-dimensional cellular model to study the mechanisms of regulating tissue elongation in Drosophila wing. We simulate the effects of directional cues on tissue elongation. We also computationally analyze the role of reduced cell size. Our simulation results indicate that oriented cell divisions, oriented mechanical forces, and reduced cell size can all mediate tissue elongation, but they function differently. We show that oriented cell divisions and oriented mechanical forces act as directional cues during tissue elongation. Between these two directional cues, oriented mechanical forces have a stronger influence than oriented cell divisions. In addition, we raise the novel hypothesis that reduced cell size may significantly promote tissue elongation. We find that reduced cell size alone cannot drive tissue elongation. However, when combined with directional cues, such as oriented cell divisions or oriented mechanical forces, reduced cell size can significantly enhance tissue elongation in Drosophila wing. Furthermore, our simulation results suggest that reduced cell size has a short-term effect on cell topology by decreasing the frequency of hexagonal cells, which is consistent with experimental observations. Our simulation results suggest that cell divisions without cell growth play essential roles in tissue elongation.

The Leaf Adaxial-Abaxial Boundary and Lamina Growth

In multicellular organisms, boundaries have a role in preventing the intermingling of two different cell populations and in organizing the morphogenesis of organs and the entire organism. Plant leaves have two different cell populations, the adaxial (or upper) and abaxial (or lower) cell populations, and the boundary is considered to be important for lamina growth. At the boundary between the adaxial and abaxial epidermis, corresponding to the margin, margin-specific structures are developed and structurally separate the adaxial and abaxial epidermis from each other. The adaxial and abaxial cells are determined by the adaxial and abaxial regulatory genes (including transcription factors and small RNAs), respectively. Among many lamina-growth regulators identified by recent genetic analyses, it has been revealed that the phytohormone, auxin, and the WOX family transcription factors act at the adaxial-abaxial boundary downstream of the adaxial-abaxial pattern. Furthermore, mutant analyses of the WOX genes shed light on the role of the adaxial-abaxial boundary in preventing the mixing of the adaxial and abaxial features during lamina growth. In this review, we highlight the recent studies on the dual role of the adaxial-abaxial boundary.

Developmental biology: a growing role for computer simulations

Keeping cells separated in well-defined domains is essential for development. A new computational-experimental study elucidates the physical mechanisms that establish and maintain the dorsal-ventral compartment boundary in the Drosophila wing disc and demonstrates the increasing value of computer simulations in developmental biology.

Physical mechanisms shaping the Drosophila dorsoventral compartment boundary

BACKGROUND

Separating cells with distinct identities and fates by straight and sharp compartment boundaries is important for growth and pattern formation during animal development. The physical mechanisms shaping compartment boundaries, however, are not fully understood.

RESULTS

We combine theory and quantitative experiments to investigate the roles of different mechanisms to shape compartment boundaries. Our theoretical work shows that cell elongation created by anisotropic stress, cell proliferation rate, orientation of cell division, and cell bond tension all have distinct effects on the morphology of compartment boundaries during tissue growth. Our experiments using the developing Drosophila wing reveal that the roughness of the dorsoventral compartment boundary is dynamic and that it decreases during development. By measuring tissue relaxation in response to laser ablation of cell bonds at different developmental times, we demonstrate that decreased boundary roughness correlates with increased cell bond tension along the compartment boundary. Finally, by using experimentally determined values for cell bond tension, cell elongation and bias in orientation of cell division in simulations of tissue growth, we can reproduce the main features of the time evolution of the dorsoventral compartment boundary shape.

CONCLUSIONS

Local increase of cell bond tension along the boundary as well as global anisotropies in the tissue contribute to shaping boundaries in cell networks. We propose a simple scenario that combines time-dependent cell bond tension at the boundary, oriented cell division, and cell elongation in the tissue that can account for the main features of the dynamics of the shape of the dorsoventral compartment boundary.