Computational analysis of three-dimensional epithelial morphogenesis using vertex models.
ABSTRACT: The folding of epithelial sheets, accompanied by cell shape changes and rearrangements, gives rise to three-dimensional structures during development. Recently, some aspects of epithelial morphogenesis have been modeled using vertex models, in which each cell is approximated by a polygon; however, these models have been largely confined to two dimensions. Here, we describe an adaptation of these models in which the classical two-dimensional vertex model is embedded in three dimensions. This modification allows for the construction of complex three-dimensional shapes from simple sheets of cells. We describe algorithmic, computational, and biophysical aspects of our model, with the view that it may be useful for formulating and testing hypotheses regarding the mechanical forces underlying a wide range of morphogenetic processes.
Project description:Epithelial tissue, in which cells adhere tightly to each other and to the underlying substrate, is one of the four major tissue types in adult organisms. In embryos, epithelial sheets serve as versatile substrates during the formation of developing organs. Some aspects of epithelial morphogenesis can be adequately described using vertex models, in which the two-dimensional arrangement of epithelial cells is approximated by a polygonal lattice with an energy that has contributions reflecting the properties of individual cells and their interactions. Previous studies with such models have largely focused on dynamics confined to two spatial dimensions and analyzed them numerically. We show how these models can be extended to account for three-dimensional deformations and studied analytically. Starting from the extended model, we derive a continuum plate description of cell sheets, in which the effective tissue properties, such as bending rigidity, are related explicitly to the parameters of the vertex model. To derive the continuum plate model, we duly take into account a microscopic shift between the two sublattices of the hexagonal network, which has been ignored in previous work. As an application of the continuum model, we analyze tissue buckling by a line tension applied along a circular contour, a simplified set-up relevant to several situations in the developmental contexts. The buckling thresholds predicted by the continuum description are in good agreement with the results of stability calculations based on the vertex model. Our results establish a direct connection between discrete and continuum descriptions of cell sheets and can be used to probe a wide range of morphogenetic processes in epithelial tissues.
Project description: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'.
Project description:Carboranes are a class of carbon-boron molecular clusters with three-dimensional aromaticity, and inherent robustness. These endowments enable carboranes as valuable building blocks for applications ranging from functional materials to pharmaceuticals. Thus, the chemistry of carboranes has received tremendous research interest, and significant progress has been made in the past decades. However, many attempts to the synthesis of carboranes with more than 14 vertices had been unsuccessful since the report of a 14-vertex carborane in 2005. The question arises as to whether these long sought-after molecules exist. We describe in this article the synthesis and structural characterization of 15- and 16-vertex closo-carboranes as well as 16-vertex ruthenacarborane. Such a success relies on the introduction of silyl groups to both cage carbons, stabilizing the corresponding nido-carborane dianions and promoting the capitation reaction with HBBr2·SMe2. This work would shed some light on the preparation of carboranes with 17 vertices or more, and open the door for studying supercarborane chemistry.
Project description:Epithelial folding transforms simple sheets of cells into complex three-dimensional tissues and organs during animal development. Epithelial folding has mainly been attributed to mechanical forces generated by an apically localized actomyosin network, however, contributions of forces generated at basal and lateral cell surfaces remain largely unknown. Here we show that a local decrease of basal tension and an increased lateral tension, but not apical constriction, drive the formation of two neighboring folds in developing Drosophila wing imaginal discs. Spatially defined reduction of extracellular matrix density results in local decrease of basal tension in the first fold; fluctuations in F-actin lead to increased lateral tension in the second fold. Simulations using a 3D vertex model show that the two distinct mechanisms can drive epithelial folding. Our combination of lateral and basal tension measurements with a mechanical tissue model reveals how simple modulations of surface and edge tension drive complex three-dimensional morphological changes.
Project description:Dynamic covalent chemistry (DCC) is a widely used method for the self-assembly of three-dimensional molecular architectures. The orthogonality of dynamic reactions is emerging as a versatile strategy for controlling product distributions in DCC, yet the application of this approach to the synthesis of 3D organic molecular cages is limited. We report the first system which employs the orthogonality of alkyne metathesis and dynamic imine exchange to prepare a molecular cage with a reversibly removable vertex. This study demonstrates the rational and controlled application of chemical orthogonality in DCC to prepare organic cages of expanded functionality which respond to chemical stimuli.
Project description:OBJECTIVE:To estimate the contributions of patient and health care provider-hospital characteristics to the variation in the frequency of nulliparous, term, singleton, vertex cesarean delivery in a multi-institutional U.S. cohort. METHODS:We performed a secondary analysis of the multicenter Assessment of Perinatal Excellence cohort of 115,502 mother and neonatal pairs who were delivered at 25 hospitals between March 2008 and February 2011. Women met inclusion criteria if they were nulliparous and delivered a singleton in vertex presentation at term. Hospital ranks for nulliparous, term, singleton, vertex cesarean delivery frequency were determined after risk adjustment. The fraction of variation in nulliparous, term, singleton, vertex cesarean delivery frequency attributable to patient and health care provider-hospital characteristics was assessed using hierarchical logistic regression. RESULTS:Of the 115,502 deliveries in the initial cohort, 38,275 nulliparous, term, singleton, vertex deliveries met inclusion criteria. The median hospital nulliparous, term, singleton, vertex cesarean delivery frequency was 25.3% with a range from 15.0% to 35.2%. The majority of hospitals (16/25) changed rank quintiles after risk adjustment; overall the changes in rank were not statistically significant (P=.53). Patient characteristics accounted for 24% of the nulliparous, term, singleton, vertex cesarean delivery variation. The analyzed health care provider-hospital characteristics were not significantly associated with cesarean delivery frequency. CONCLUSION:Although patient characteristics accounted for some of the variation in nulliparous, term, singleton, vertex cesarean delivery frequency and accounting for case mix had implications for hospital cesarean delivery rankings, the majority of the variation was not explained by the characteristics evaluated. These findings emphasize the importance of continued efforts to understand aspects of obstetric care, including case mix, that contribute to cesarean delivery variation.
Project description:The cerebral cortex is fundamental to the functioning of the mind and body. <i>In vivo</i> cortical morphology can be studied through magnetic resonance imaging in several ways, including reconstructing surface-based models of the cortex. However, existing software for surface-based statistical analyses cannot accommodate "big data" or commonly used statistical methods such as the imputation of missing data, extensive bias correction, and non-linear modeling. To address these shortcomings, we developed the QDECR package, a flexible and extensible R package for group-level statistical analysis of cortical morphology. QDECR was written with large population-based epidemiological studies in mind and was designed to fully utilize the extensive modeling options in R. QDECR currently supports vertex-wise linear regression. Design matrix generation can be done through simple, familiar R formula specification, and includes user-friendly extensions for R options such as polynomials, splines, interactions and other terms. QDECR can handle unimputed and imputed datasets with thousands of participants. QDECR has a modular design, and new statistical models can be implemented which utilize several aspects from other generic modules which comprise QDECR. In summary, QDECR provides a framework for vertex-wise surface-based analyses that enables flexible statistical modeling and features commonly used in population-based and clinical studies, which have until now been largely absent from neuroimaging research.
Project description:We introduce an Active Vertex Model (AVM) for cell-resolution studies of the mechanics of confluent epithelial tissues consisting of tens of thousands of cells, with a level of detail inaccessible to similar methods. The AVM combines the Vertex Model for confluent epithelial tissues with active matter dynamics. This introduces a natural description of the cell motion and accounts for motion patterns observed on multiple scales. Furthermore, cell contacts are generated dynamically from positions of cell centres. This not only enables efficient numerical implementation, but provides a natural description of the T1 transition events responsible for local tissue rearrangements. The AVM also includes cell alignment, cell-specific mechanical properties, cell growth, division and apoptosis. In addition, the AVM introduces a flexible, dynamically changing boundary of the epithelial sheet allowing for studies of phenomena such as the fingering instability or wound healing. We illustrate these capabilities with a number of case studies.
Project description:Epithelial folding is a universal biological phenomenon in morphogenesis, typical examples being brain gyri, villi of the intestinal tract, and imaginal discs in invertebrates. During epithelial morphogenesis, the physical constraints imposed by the surrounding microenvironment on epithelial tissue play critical roles in folding morphology. In this study, we focused on the asymmetry of the environmental constraints sandwiching the epithelial sheet and introduced the degree of asymmetry, which indicates whether the basal or apical side of the epithelium is closer to the constraint wall. Then, we investigated the relationship between the degree of asymmetry and epithelial folding morphology using three-dimensional vertex simulations. The results show that the folding patterns of the epithelial sheets change from spot patterns to labyrinth patterns and then to hole patterns as the degree of asymmetry changes. Furthermore, we examined the pattern formation in terms of the equation of out-of-plane displacement of the sheet derived from the mechanical energy functional.
Project description:This study demonstrates computational simulations of multicellular deformation coupled with chemical patterning in the three-dimensional (3D) space. To address these aspects, we proposes a novel mathematical model, where a reaction-diffusion system is discretely expressed at a single cell level and combined with a 3D vertex model. To investigate complex phenomena emerging from the coupling of patterning and deformation, as an example, we employed an activator-inhibitor system and converted the activator concentration of individual cells into their growth rate. Despite the simplicity of the model, by growing a monolayer cell vesicle, the coupling system provided rich morphological dynamics such as undulation, tubulation, and branching. Interestingly, the morphological variety depends on the difference in time scales between patterning and deformation, and can be partially understood by the intrinsic hysteresis in the activator-inhibitor system with domain growth. Importantly, the model can be applied to 3D multicellular dynamics that couple the reaction-diffusion patterning with various cell behaviors, such as deformation, rearrangement, division, apoptosis, differentiation, and proliferation. Thus, the results demonstrate the significant advantage of the proposed model as well as the biophysical importance of exploring spatiotemporal dynamics of the coupling phenomena of patterning and deformation in 3D space.