Filopodial-Tension Model of Convergent-Extension of Tissues

Inferring active and passive mechanical drivers of epithelial convergent extension

What can we learn about the mechanical processes that shape tissues by simply watching? Several schemes suggest that static cell morphology or junctional connectivity can reveal where chains of cells transmit force or where force asymmetries drive cellular rearrangements. We hypothesize that dynamic cell shape changes from time lapse sequences can be used to distinguish specific mechanisms of tissue morphogenesis. Convergent extension (CE) is a crucial developmental motif wherein a planar tissue narrows in one direction and lengthens in the other. It is tempting to assume that forces driving CE reside within cells of the deforming tissue, as CE may reflect a variety of active processes or passive responses to forces generated by adjacent tissues. In this work, we first construct a simple model of epithelial cells capable of passive CE in response to external forces. We adapt this framework to simulate CE from active anisotropic processes in three different modes: crawling, contraction, and capture. We develop an image analysis pipeline for analysis of morphogenetic changes in both live cells and simulated cells using a panel of mechanical and statistical approaches. Our results allow us to identify how each simulated mechanism uniquely contributes to tissue morphology and provide insight into how force transmission is coordinated. We construct a MEchanism Index (MEI) to quantify how similar live cells are to simulated passive and active cells undergoing CE. Applying these analyses to live cell data of Xenopus neural CE reveals features of both passive motion and active forces. Furthermore, we find spatial variation across the neural plate. We compare the inferred mechanisms in the frog midline to tissues undergoing CE in both the mouse and fly. We find that distinct active modes may have different prevalences depending on the model system. Our modeling framework allows us to gain insight from tissue timelapse images and assess the relative contribution of specific cellular mechanisms to observed tissue phenotypes. This approach can be used to guide further experimental inquiry into how mechanics influences the shaping of tissues and organs during development.

Assessing mechanical agency during apical apoptotic cell extrusion

Homeostasis is necessary for epithelia to maintain barrier function and prevent the accumulation of defective cells. Unfit, excess, and dying cells in the larval zebrafish tail fin epidermis are removed via controlled cell death and extrusion. Extrusion coincides with oscillations of cell area, both in the extruding cell and its neighbors. Here, we develop a biophysical model of this process to explore the role of autonomous and non-autonomous mechanics. We vary biophysical properties and oscillatory behaviors of extruding cells and their neighbors along with tissue-wide cell density and viscosity. We find that cell autonomous processes are major contributors to the dynamics of extrusion, with the mechanical microenvironment providing a less pronounced contribution. We also find that some cells initially resist extrusion, influencing the duration of the expulsion process. Our model provides insights into the cellular dynamics and mechanics that promote elimination of unwanted cells from epithelia during homeostatic tissue maintenance.

Modeling the roles of cohesotaxis, cell-intercalation, and tissue geometry in collective cell migration of Xenopus mesendoderm

Collectively migrating Xenopus mesendoderm cells are arranged into leader and follower rows with distinct adhesive properties and protrusive behaviors. In vivo, leading row mesendoderm cells extend polarized protrusions and migrate along a fibronectin matrix assembled by blastocoel roof cells. Traction stresses generated at the leading row result in the pulling forward of attached follower row cells. Mesendoderm explants removed from embryos provide an experimentally tractable system for characterizing collective cell movements and behaviors, yet the cellular mechanisms responsible for this mode of migration remain elusive. We introduce a novel agent-based computational model of migrating mesendoderm in the Cellular-Potts computational framework to investigate the respective contributions of multiple parameters specific to the behaviors of leader and follower row cells. Sensitivity analyses identify cohesotaxis, tissue geometry, and cell intercalation as key parameters affecting the migration velocity of collectively migrating cells. The model predicts that cohesotaxis and tissue geometry in combination promote cooperative migration of leader cells resulting in increased migration velocity of the collective. Radial intercalation of cells towards the substrate is an additional mechanism contributing to an increase in migratory speed of the tissue. Model outcomes are validated experimentally using mesendoderm tissue explants.

Exploring the principles of embryonic mammary gland branching morphogenesis

Branching morphogenesis is a characteristic feature of many essential organs, such as the lung and kidney, and most glands, and is the net result of two tissue behaviors: branch point initiation and elongation. Each branched organ has a distinct architecture customized to its physiological function, but how patterning occurs in these ramified tubular structures is a fundamental problem of development. Here, we use quantitative 3D morphometrics, time-lapse imaging, manipulation of ex vivo cultured mouse embryonic organs and mice deficient in the planar cell polarity component Vangl2 to address this question in the developing mammary gland. Our results show that the embryonic epithelial trees are highly complex in topology owing to the flexible use of two distinct modes of branch point initiation: lateral branching and tip bifurcation. This non-stereotypy was contrasted by the remarkably constant average branch frequency, indicating a ductal growth invariant, yet stochastic, propensity to branch. The probability of branching was malleable and could be tuned by manipulating the Fgf10 and Tgfβ1 pathways. Finally, our in vivo data and ex vivo time-lapse imaging suggest the involvement of tissue rearrangements in mammary branch elongation.

The shapes of elongating gastruloids are consistent with convergent extension driven by a combination of active cell crawling and differential adhesion

Gastruloids have emerged as highly useful in vitro models of mammalian gastrulation. One of the most striking features of 3D gastruloids is their elongation, which mimics the extension of the embryonic anterior-posterior axis. Although axis extension is crucial for development, the underlying mechanism has not been fully elucidated in mammalian species. Gastruloids provide an opportunity to study this morphogenic process in vitro. Here, we measure and quantify the shapes of elongating gastruloids and show, by Cellular Potts model simulations based on a novel, optimized algorithm, that convergent extension, driven by a combination of active cell crawling and differential adhesion can explain the observed shapes. We reveal that differential adhesion alone is insufficient and also directly observe hallmarks of convergent extension by time-lapse imaging of gastruloids. Finally, we show that gastruloid elongation can be abrogated by inhibition of the Rho kinase pathway, which is involved in convergent extension in vivo. All in all, our study demonstrates, how gastruloids can be used to elucidate morphogenic processes in embryonic development.

Assessing mechanical agency during apical apoptotic cell extrusion

Epithelial tissues maintain homeostasis through the continual addition and removal of cells. Homeostasis is necessary for epithelia to maintain barrier function and prevent the accumulation of defective cells. Unfit, excess, and dying cells can be removed from epithelia by the process of extrusion. Controlled cell death and extrusion in the epithelium of the larval zebrafish tail fin coincides with oscillation of cell area, both in the extruding cell and its neighbors. Both cell-autonomous and non-autonomous factors have been proposed to contribute to extrusion but have been challenging to test by experimental approaches. Here we develop a dynamic cell-based biophysical model that recapitulates the process of oscillatory cell extrusion to test and compare the relative contributions of these factors. Our model incorporates the mechanical properties of individual epithelial cells in a two-dimensional simulation as repelling active particles. The area of cells destined to extrude oscillates with varying durations or amplitudes, decreasing their mechanical contribution to the epithelium and surrendering their space to surrounding cells. Quantitative variations in cell shape and size during extrusion are visualized by a hybrid weighted Voronoi tessellation technique that renders individual cell mechanical properties directly into an epithelial sheet. To explore the role of autonomous and non-autonomous mechanics, we vary the biophysical properties and behaviors of extruding cells and neighbors such as the period and amplitude of repulsive forces, cell density, and tissue viscosity. Our data suggest that cell autonomous processes are major contributors to the dynamics of extrusion, with the mechanical microenvironment providing a less pronounced contribution. Our computational model based on in vivo data serves as a tool to provide insights into the cellular dynamics and localized changes in mechanics that promote elimination of unwanted cells from epithelia during homeostatic tissue maintenance.

Modeling the roles of cohesotaxis, cell-intercalation, and tissue geometry in collective cell migration of Xenopus mesendoderm

Collectively migrating Xenopus mesendoderm cells are arranged into leader and follower rows with distinct adhesive properties and protrusive behaviors. In vivo, leading row mesendoderm cells extend polarized protrusions and migrate along a fibronectin matrix assembled by blastocoel roof cells. Traction stresses generated at the leading row result in the pulling forward of attached follower row cells. Mesendoderm explants removed from embryos provide an experimentally tractable system for characterizing collective cell movements and behaviors, yet the cellular mechanisms responsible for this mode of migration remain elusive. We introduce an agent-based computational model of migrating mesendoderm in the Cellular-Potts computational framework to investigate the relative contributions of multiple parameters specific to the behaviors of leader and follower row cells. Sensitivity analyses identify cohesotaxis, tissue geometry, and cell intercalation as key parameters affecting the migration velocity of collectively migrating cells. The model predicts that cohesotaxis and tissue geometry in combination promote cooperative migration of leader cells resulting in increased migration velocity of the collective. Radial intercalation of cells towards the substrate is an additional mechanism to increase migratory speed of the tissue.

Summary Statement

We present a novel Cellular-Potts model of collective cell migration to investigate the relative roles of cohesotaxis, tissue geometry, and cell intercalation on migration velocity of Xenopus mesendoderm.

Cell-center-based model for simulating three-dimensional monolayer tissue deformation

The shape of the epithelial monolayer can be depicted as a curved tissue in three-dimensional (3D) space, where individual cells are tightly adhered to one another. The 3D morphogenesis of these tissues is governed by cell dynamics, and a variety of mathematical modeling and simulation studies have been conducted to investigate this process. One promising approach is the cell-center model, which can account for the discreteness of cells. The cell nucleus, which is considered to correspond to the cell center, can be observed experimentally. However, there has been a shortage of cell-center models specifically tailored for simulating 3D monolayer tissue deformation. In this study, we developed a mathematical model based on the cell-center model to simulate 3D monolayer tissue deformation. Our model was confirmed by simulating the in-plane deformation, out-of-plane deformation, and invagination due to apical constriction.

Why Animal Experiments Are Still Indispensable in Bone Research: A Statement by the European Calcified Tissue Society

Major achievements in bone research have always relied on animal models and in vitro systems derived from patient and animal material. However, the use of animals in research has drawn intense ethical debate and the complete abolition of animal experimentation is demanded by fractions of the population. This phenomenon is enhanced by the reproducibility crisis in science and the advance of in vitro and in silico techniques. 3D culture, organ-on-a-chip, and computer models have improved enormously over the last few years. Nevertheless, the overall complexity of bone tissue cross-talk and the systemic and local regulation of bone physiology can often only be addressed in entire vertebrates. Powerful genetic methods such as conditional mutagenesis, lineage tracing, and modeling of the diseases enhanced the understanding of the entire skeletal system. In this review endorsed by the European Calcified Tissue Society (ECTS), a working group of investigators from Europe and the US provides an overview of the strengths and limitations of experimental animal models, including rodents, fish, and large animals, as well the potential and shortcomings of in vitro and in silico technologies in skeletal research. We propose that the proper combination of the right animal model for a specific hypothesis and state-of-the-art in vitro and/or in silico technology is essential to solving remaining important questions in bone research. This is crucial for executing most efficiently the 3R principles to reduce, refine, and replace animal experimentation, for enhancing our knowledge of skeletal biology, and for the treatment of bone diseases that affect a large part of society. © 2023 The Authors. Journal of Bone and Mineral Research published by Wiley Periodicals LLC on behalf of American Society for Bone and Mineral Research (ASBMR).

Arrested coalescence of multicellular aggregates

Multicellular aggregates are known to exhibit liquid-like properties. The fusion process of two cell aggregates is commonly studied as the coalescence of two viscous drops. However, tissues are complex materials and can exhibit viscoelastic behaviour. It is known that elastic effects can prevent the complete fusion of two drops, a phenomenon known as arrested coalescence. Here we study this phenomenon in stem cell aggregates and provide a theoretical framework which agrees with the experiments. In addition, agent-based simulations show that active cell fluctuations can control a solid-to-fluid phase transition, revealing that arrested coalescence can be found in the vicinity of an unjamming transition. By analysing the dynamics of the fusion process and combining it with nanoindentation measurements, we obtain the effective viscosity, shear modulus and surface tension of the aggregates. More generally, our work provides a simple, fast and inexpensive method to characterize the mechanical properties of viscoelastic materials.

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.

Mechanical Regulation of Limb Bud Formation

Early limb bud development has been of considerable interest for the study of embryological development and especially morphogenesis. The focus has long been on biochemical signalling and less on cell biomechanics and mechanobiology. However, their importance cannot be understated since tissue shape changes are ultimately controlled by active forces and bulk tissue rheological properties that in turn depend on cell-cell interactions as well as extracellular matrix composition. Moreover, the feedback between gene regulation and the biomechanical environment is still poorly understood. In recent years, novel experimental techniques and computational models have reinvigorated research on this biomechanical and mechanobiological side of embryological development. In this review, we consider three stages of early limb development, namely: outgrowth, elongation, and condensation. For each of these stages, we summarize basic biological regulation and examine the role of cellular and tissue mechanics in the morphogenetic process.

Mechanical heterogeneity along single cell-cell junctions is driven by lateral clustering of cadherins during vertebrate axis elongation

Morphogenesis is governed by the interplay of molecular signals and mechanical forces across multiple length scales. The last decade has seen tremendous advances in our understanding of the dynamics of protein localization and turnover at subcellular length scales, and at the other end of the spectrum, of mechanics at tissue-level length scales. Integrating the two remains a challenge, however, because we lack a detailed understanding of the subcellular patterns of mechanical properties of cells within tissues. Here, in the context of the elongating body axis of Xenopus embryos, we combine tools from cell biology and physics to demonstrate that individual cell-cell junctions display finely-patterned local mechanical heterogeneity along their length. We show that such local mechanical patterning is essential for the cell movements of convergent extension and is imparted by locally patterned clustering of a classical cadherin. Finally, the patterning of cadherins and thus local mechanics along cell-cell junctions are controlled by Planar Cell Polarity signaling, a key genetic module for CE that is mutated in diverse human birth defects.

A mechanical model of early somite segmentation

Somitogenesis is often described using the clock-and-wavefront (CW) model, which does not explain how molecular signaling rearranges the pre-somitic mesoderm (PSM) cells into somites. Our scanning electron microscopy analysis of chicken embryos reveals a caudally-progressing epithelialization front in the dorsal PSM that precedes somite formation. Signs of apical constriction and tissue segmentation appear in this layer 3-4 somite lengths caudal to the last-formed somite. We propose a mechanical instability model in which a steady increase of apical contractility leads to periodic failure of adhesion junctions within the dorsal PSM and positions the future inter-somite boundaries. This model produces spatially periodic segments whose size depends on the speed of the activation front of contraction (F), and the buildup rate of contractility (Λ). The Λ/F ratio determines whether this mechanism produces spatially and temporally regular or irregular segments, and whether segment size increases with the front speed.

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Dorsal pre-somitic mesoderm of chicken embryos epithelializes before somite formation

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Dorsal epithelium shows signs of apical constriction and early segmentation

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A mechanical instability model can reproduce sequential segmentation

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A single ratio describes spatial and temporal patterns of segmentation

A direct role for SNX9 in the biogenesis of filopodia

Filopodia are finger-like actin-rich protrusions that extend from the cell surface and are important for cell-cell communication and pathogen internalization. The small size and transient nature of filopodia combined with shared usage of actin regulators within cells confounds attempts to identify filopodial proteins. Here, we used phage display phenotypic screening to isolate antibodies that alter the actin morphology of filopodia-like structures (FLS) in vitro. We found that all of the antibodies that cause shorter FLS interact with SNX9, an actin regulator that binds phosphoinositides during endocytosis and at invadopodia. In cells, we discover SNX9 at specialized filopodia in Xenopus development and that SNX9 is an endogenous component of filopodia that are hijacked by Chlamydia entry. We show the use of antibody technology to identify proteins used in filopodia-like structures, and a role for SNX9 in filopodia.

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.

Model to Link Cell Shape and Polarity with Organogenesis

How do flat sheets of cells form gut and neural tubes? Across systems, several mechanisms are at play: cells wedge, form actomyosin cables, or intercalate. As a result, the cell sheet bends, and the tube elongates. It is unclear to what extent each mechanism can drive tube formation on its own. To address this question, we computationally probe if one mechanism, either cell wedging or intercalation, may suffice for the entire sheet-to-tube transition. Using a physical model with epithelial cells represented by polarized point particles, we show that either cell intercalation or wedging alone can be sufficient and that each can both bend the sheet and extend the tube. When working in parallel, the two mechanisms increase the robustness of the tube formation. The successful simulations of the key features in Drosophila salivary gland budding, sea urchin gastrulation, and mammalian neurulation support the generality of our results.

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Cell wedging and intercalation are modeled using a polarized point-particle approach

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Cell intercalation is sufficient for tube budding

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Tube budding is more robust when intercalation is complemented by wedging

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Wedging and differential proliferation are sufficient for mammalian neurulation

Convergent extension in the amphibian, Xenopus laevis

This review is a comprehensive analysis of the cell biology and biomechanics of Convergent Extension in Xenopus.

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.

SpheroidSim-Preliminary evaluation of a new computational tool to predict the influence of cell cycle time and phase fraction on spheroid growth

BACKGROUND

There is a relative paucity of research that integrates materials science and bioengineering with computational simulations to decipher the intricate processes promoting cancer progression. Therefore, a first-generation computational model, SpheroidSim, was developed that includes a biological data set derived from a bioengineered spheroid model to obtain a quantitative description of cell kinetics.

RESULTS

SpheroidSim is a 3D agent-based model simulating the growth of multicellular cancer spheroids. Cell cycle time and phases mathematically motivated the population growth. SpheroidSim simulated the growth dynamics of multiple spheroids by individually defining a collection of specific phenotypic traits and characteristics for each cell. Experimental data derived from a hydrogel-based spheroid model were fit to the predictions providing insight into the influence of cell cycle time (CCT) and cell phase fraction (CPF) on the cell population. A comparison of the number of active cells predicted for each analysis showed that the value and method used to define CCT had a greater effect on the predicted cell population than CPF. The model predictions were similar to the experimental results for the number of cells, with the predicted total number of cells varying by 8% and 12%, respectively, compared to the experimental data.

CONCLUSIONS

SpheroidSim is a first step in developing a biologically based predictive tool capable of revealing fundamental elements in cancer cell physiology. This computational model may be applied to study the effect of the microenvironment on spheroid growth and other cancer cell types that demonstrate a similar multicellular clustering behavior as the population develops. © 2018 American Institute of Chemical Engineers Biotechnol. Prog., 34:1335-1343, 2018.

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'.