Development of a New 3D Hybrid Model for Epithelia Morphogenesis

Deciphering the interplay between biology and physics with a finite element method-implemented vertex organoid model: A tool for the mechanical analysis of cell behavior on a spherical organoid shell

Understanding the interplay between biology and mechanics in tissue architecture is challenging, particularly in terms of 3D tissue organization. Addressing this challenge requires a biological model enabling observations at multiple levels from cell to tissue, as well as theoretical and computational approaches enabling the generation of a synthetic model that is relevant to the biological model and allowing for investigation of the mechanical stresses experienced by the tissue. Using a monolayer human colon epithelium organoid as a biological model, freely available tools (Fiji, Cellpose, Napari, Morphonet, or Tyssue library), and the commercially available Abaqus FEM solver, we combined vertex and FEM approaches to generate a comprehensive viscoelastic finite element model of the human colon organoid and demonstrated its flexibility. We imaged human colon organoid development for 120 hours, following the evolution of the organoids from an immature to a mature morphology. According to the extracted architectural/geometric parameters of human colon organoids at various stages of tissue architecture establishment, we generated organoid active vertex models. However, this approach did not consider the mechanical aspects involved in the organoids' morphological evolution. Therefore, we applied a finite element method considering mechanical loads mimicking osmotic pressure, external solicitation, or active contraction in the vertex model by using the Abaqus FEM solver. Integration of finite element analysis (FEA) into the vertex model achieved a better fit with the biological model. Therefore, the FEM model provides a basis for depicting cell shape, tissue deformation, and cellular-level strain due to imposed stresses. In conclusion, we demonstrated that a combination of vertex and FEM approaches, combining geometrical and mechanical parameters, improves modeling of alterations in organoid morphology over time and enables better assessment of the mechanical cues involved in establishing the architecture of the human colon epithelium.

Interplay of geometry and mechanics in epithelial wound healing

Wound healing is a complex biological process critical for maintaining an organism's structural integrity and tissue repair following an infection or injury. Recent studies have unveiled the mechanisms involving the coordination of biochemical and mechanical responses in the tissue in wound healing. In this article, we focus on the healing property of an epithelial tissue as a material while the effects of biological mechanisms such as cell proliferation, tissue intercalation, cellular migration, cell crawling, and filopodia protrusion is minimal. We present a mathematical framework that predicts the fate of a wounded tissue based on the wound's geometrical features and the tissue's mechanical properties. Precisely, adapting the vertex model of tissue mechanics, we predict whether a wound of a specific size in an epithelial monolayer characterized by certain levels of actomyosin contractility and cell-cell adhesion will heal (i.e., close), shrink in size, or rupture the tissue further. Moreover, we show how tissue-mediated mechanisms such as purse-string tension at the wound boundary facilitate wound healing. Finally, we validate the predictions of our model by designing an experimental setup that enables us to create wounds of specific sizes in kidney epithelial cells (MDCK) monolayers. Altogether, this work sets up a basis for interpreting the interplay of mechanical and geometrical features of a tissue in the process of wound healing.

Endogenous OptoRhoGEFs reveal biophysical principles of epithelial tissue furrowing

During development, epithelia function as malleable substrates that undergo extensive remodeling to shape developing embryos. Optogenetic control of Rho signaling provides an avenue to investigate the mechanisms of epithelial morphogenesis, but transgenic optogenetic tools can be limited by variability in tool expression levels and deleterious effects of transgenic overexpression on development. Here, we use CRISPR/Cas9 to tag Drosophila RhoGEF2 and Cysts/Dp114RhoGEF with components of the iLID/SspB optogenetic heterodimer, permitting light-dependent control over endogenous protein activities. Using quantitative optogenetic perturbations, we uncover a dose-dependence of tissue furrow depth and bending behavior on RhoGEF recruitment, revealing mechanisms by which developing embryos can shape tissues into particular morphologies. We show that at the onset of gastrulation, furrows formed by cell lateral contraction are oriented and size-constrained by a stiff basal actomyosin layer. Our findings demonstrate the use of quantitative, 3D-patterned perturbations of cell contractility to precisely shape tissue structures and interrogate developmental mechanics.

Active viscoelastic models for cell and tissue mechanics

Living cells are out of equilibrium active materials. Cell-generated forces are transmitted across the cytoskeleton network and to the extracellular environment. These active force interactions shape cellular mechanical behaviour, trigger mechano-sensing, regulate cell adaptation to the microenvironment and can affect disease outcomes. In recent years, the mechanobiology community has witnessed the emergence of many experimental and theoretical approaches to study cells as mechanically active materials. In this review, we highlight recent advancements in incorporating active characteristics of cellular behaviour at different length scales into classic viscoelastic models by either adding an active tension-generating element or adjusting the resting length of an elastic element in the model. Summarizing the two groups of approaches, we will review the formulation and application of these models to understand cellular adaptation mechanisms in response to various types of mechanical stimuli, such as the effect of extracellular matrix properties and external loadings or deformations.

Forced back into shape: Mechanics of epithelial wound repair

Wound repair, the closing of a hole, is inherently a physical process that requires the change of shape of materials, in this case, cells and tissues. Not only is efficient and accurate wound repair critical for restoring barrier function and reducing infection, but it is also critical for restoring the complex three-dimensional architecture of an organ. This re-sculpting of tissues requires the complex coordination of cell behaviours in multiple dimensions, in space and time, to ensure that the repaired structure can continue functioning optimally. Recent evidence highlights the importance of cell and tissue mechanics in 2D and 3D to achieve such seamless wound repair.

Geometric control by active mechanics of epithelial gap closure

Epithelial wound healing is one of the most important biological processes occurring during the lifetime of an organism. It is a self-repair mechanism closing wounds or gaps within tissues to restore their functional integrity. In this work we derive a new diffuse interface approach for modelling the gap closure by means of a variational principle in the framework of non-equilibrium thermodynamics. We investigate the interplay between the crawling with lamellipodia protrusions and the supracellular tension exerted by the actomyosin cable on the closure dynamics. These active features are modeled as Korteweg forces into a generalised chemical potential. From an asymptotic analysis, we derive a pressure jump across the gap edge in the sharp interface limit. Moreover, the chemical potential diffuses as a Mullins-Sekerka system, and its interfacial value is given by a Gibbs-Thompson relation for its local potential driven by the curvature-dependent purse-string tension. The finite element simulations show an excellent quantitative agreement between the closure dynamics and the morphology of the edge with respect to existing biological experiments. The resulting force patterns are also in good qualitative agreement with existing traction force microscopy measurements. Our results shed light on the geometrical control of the gap closure dynamics resulting from the active forces that are chemically activated around the gap edge.

CartoCell, a high-content pipeline for 3D image analysis, unveils cell morphology patterns in epithelia

Decades of research have not yet fully explained the mechanisms of epithelial self-organization and 3D packing. Single-cell analysis of large 3D epithelial libraries is crucial for understanding the assembly and function of whole tissues. Combining 3D epithelial imaging with advanced deep-learning segmentation methods is essential for enabling this high-content analysis. We introduce CartoCell, a deep-learning-based pipeline that uses small datasets to generate accurate labels for hundreds of whole 3D epithelial cysts. Our method detects the realistic morphology of epithelial cells and their contacts in the 3D structure of the tissue. CartoCell enables the quantification of geometric and packing features at the cellular level. Our single-cell cartography approach then maps the distribution of these features on 2D plots and 3D surface maps, revealing cell morphology patterns in epithelial cysts. Additionally, we show that CartoCell can be adapted to other types of epithelial tissues.

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.

Growth orientations, rather than heterogeneous growth rates, dominate jaw joint morphogenesis in the larval zebrafish

In early limb embryogenesis, synovial joints acquire specific shapes which determine joint motion and function. The process by which the opposing cartilaginous joint surfaces are moulded into reciprocal and interlocking shapes, called joint morphogenesis, is one of the least understood aspects of joint formation and the cell-level dynamics underlying it are yet to be unravelled. In this research, we quantified key cellular dynamics involved in growth and morphogenesis of the zebrafish jaw joint and synthesised them in a predictive computational simulation of joint development. Cells in larval zebrafish jaw joints labelled with cartilage markers were tracked over a 48-h time window using confocal imaging. Changes in distance and angle between adjacent cell centroids resulting from cell rearrangement, volume expansion and extracellular matrix (ECM) deposition were measured and used to calculate the rate and direction of local tissue deformations. We observed spatially and temporally heterogeneous growth patterns with marked anisotropy over the developmental period assessed. There was notably elevated growth at the level of the retroarticular process of the Meckel's cartilage, a feature known to undergo pronounced shape changes during zebrafish development. Analysis of cell dynamics indicated a dominant role for cell volume expansion in growth, with minor influences from ECM volume increases and cell intercalation. Cell proliferation in the joint was minimal over the timeframe of interest. Synthesising the dynamic cell data into a finite element model of jaw joint development resulted in accurate shape predictions. Our biofidelic computational simulation demonstrated that zebrafish jaw joint growth can be reasonably approximated based on cell positional information over time, where cell positional information derives mainly from cell orientation and cell volume expansion. By modifying the input parameters of the simulation, we were able to assess the relative contributions of heterogeneous growth rates and of growth orientation. The use of uniform rather than heterogeneous growth rates only minorly impacted the shape predictions, whereas isotropic growth fields resulted in altered shape predictions. The simulation results suggest that growth anisotropy is the dominant influence on joint growth and morphogenesis. This study addresses the gap of the cellular processes underlying joint morphogenesis, with implications for understanding the aetiology of developmental joint disorders such as developmental dysplasia of the hip and arthrogryposis.

Quantitative modeling identifies critical cell mechanics driving bile duct lumen formation

Biliary ducts collect bile from liver lobules, the smallest functional and anatomical units of liver, and carry it to the gallbladder. Disruptions in this process caused by defective embryonic development, or through ductal reaction in liver disease have a major impact on life quality and survival of patients. A deep understanding of the processes underlying bile duct lumen formation is crucial to identify intervention points to avoid or treat the appearance of defective bile ducts. Several hypotheses have been proposed to characterize the biophysical mechanisms driving initial bile duct lumen formation during embryogenesis. Here, guided by the quantification of morphological features and expression of genes in bile ducts from embryonic mouse liver, we sharpened these hypotheses and collected data to develop a high resolution individual cell-based computational model that enables to test alternative hypotheses in silico. This model permits realistic simulations of tissue and cell mechanics at sub-cellular scale. Our simulations suggest that successful bile duct lumen formation requires a simultaneous contribution of directed cell division of cholangiocytes, local osmotic effects generated by salt excretion in the lumen, and temporally-controlled differentiation of hepatoblasts to cholangiocytes, with apical constriction of cholangiocytes only moderately affecting luminal size.

The initial step in bile duct development is the formation of a biliary lumen, a process which involves several cellular mechanisms, such as cell division and polarization, and secretion of fluid. However, how these mechanisms are orchestrated in time and space is difficult to understand. Here, we built a computational model of biliary lumen formation which represents every cell and its function in detail. With the model we can simulate the effect of biophysical aspects that affect duct formation. We have tested the individual and combined effects of directed cell division, apical constriction, and osmotic effects on lumen expansion by varying the parameters that control their relative strength. Our simulations suggest that successful bile duct lumen formation requires the simultaneous contribution of directed cell division of cholangiocytes, local osmotic effects generated by salt excretion in the lumen, and temporally-controlled differentiation of hepatoblasts to cholangiocytes, with apical constriction of cholangiocytes only moderately affecting luminal size.

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.

TiFoSi: an efficient tool for mechanobiology simulations of epithelia

MOTIVATION

Emerging phenomena in developmental biology and tissue engineering are the result of feedbacks between gene expression and cell biomechanics. In that context, in silico experiments are a powerful tool to understand fundamental mechanisms and to formulate and test hypotheses.

RESULTS

Here, we present TiFoSi, a computational tool to simulate the cellular dynamics of planar epithelia. TiFoSi allows to model feedbacks between cellular mechanics and gene expression (either in a deterministic or a stochastic way), the interaction between different cell populations, the custom design of the cell cycle and cleavage properties, the protein number partitioning upon cell division, and the modeling of cell communication (juxtacrine and paracrine signaling).

AVAILABILITY AND IMPLEMENTATION

http://tifosi.thesimbiosys.com.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Junctional and cytoplasmic contributions in wound healing

Wound healing is characterized by the re-epitheliation of a tissue through the activation of contractile forces concentrated mainly at the wound edge. While the formation of an actin purse string has been identified as one of the main mechanisms, far less is known about the effects of the viscoelastic properties of the surrounding cells, and the different contribution of the junctional and cytoplasmic contractilities. In this paper, we simulate the wound healing process, resorting to a hybrid vertex model that includes cell boundary and cytoplasmic contractilities explicitly, together with a differentiated viscoelastic rheology based on an adaptive rest-length. From experimental measurements of the recoil and closure phases of wounds in the Drosophila wing disc epithelium, we fit tissue viscoelastic properties. We then analyse in terms of closure rate and energy requirements the contributions of junctional and cytoplasmic contractilities. Our results suggest that reduction of junctional stiffness rather than cytoplasmic stiffness has a more pronounced effect on shortening closure times, and that intercalation rate has a minor effect on the stored energy, but contributes significantly to shortening the healing duration, mostly in the later stages.