Segment-Specific Adhesion as a Driver of Convergent Extension

Convergent extension, the simultaneous extension and narrowing of tissues, is a crucial event in the formation of the main body axis during embryonic development. It involves processes on multiple scales: the sub-cellular, cellular and tissue level, which interact via explicit or intrinsic feedback mechanisms. Computational modelling studies play an important role in unravelling the multiscale feedbacks underlying convergent extension. Convergent extension usually operates in tissue which has been patterned or is currently being patterned into distinct domains of gene expression. How such tissue patterns are maintained during the large scale tissue movements of convergent extension has thus far not been investigated. Intriguingly, experimental data indicate that in certain cases these tissue patterns may drive convergent extension rather than requiring safeguarding against convergent extension. Here we use a 2D Cellular Potts Model (CPM) of a tissue prepatterned into segments, to show that convergent extension tends to disrupt this pre-existing segmental pattern. However, when cells preferentially adhere to cells of the same segment type, segment integrity is maintained without any reduction in tissue extension. Strikingly, we demonstrate that this segment-specific adhesion is by itself sufficient to drive convergent extension. Convergent extension is enhanced when we endow our in silico cells with persistence of motion, which in vivo would naturally follow from cytoskeletal dynamics. Finally, we extend our model to confirm the generality of our results. We demonstrate a similar effect of differential adhesion on convergent extension in tissues that can only extend in a single direction (as often occurs due to the inertia of the head region of the embryo), and in tissues prepatterned into a sequence of domains resulting in two opposing adhesive gradients, rather than alternating segments.     

Large-scale simulations of biological cell sorting driven by differential adhesion follow diffusion-limited domain coalescence regime

Cell sorting, whereby a heterogeneous cell mixture segregates and forms distinct homogeneous tissues, is one of the main collective cell behaviors at work during development. Although differences in interfacial energies are recognized to be a possible driving source for cell sorting, no clear consensus has emerged on the kinetic law of cell sorting driven by differential adhesion. Using a modified Cellular Potts Model algorithm that allows for efficient simulations while preserving the connectivity of cells, we numerically explore cell-sorting dynamics over very large scales in space and time. For a binary mixture of cells surrounded by a medium, increase of domain size follows a power-law with exponent n = 1/4 independently of the mixture ratio, revealing that the kinetics is dominated by the diffusion and coalescence of rounded domains. We compare these results with recent numerical studies on cell sorting, and discuss the importance of algorithmic differences as well as boundary conditions on the observed scaling.     

Convergent extension by intercalation without mediolaterally fixed cell motion

We construct and implement a stochastic model of convergent extension, using a minimal set of assumptions on cell behavior. In addition to the basic assumptions of volume conservation, random cell motion, and cell-cell and cell-ECM adhesion, and a non-standard assumption that cytoskeletal polymerization generates an internal pressure tending to keep cells convex, we find that we need only two conditions for convergent extension. (1) Each cell type has a particular aspect ratio towards which it regulates its geometry. We do not require that cells align in a specific orientation, e.g. to be oriented mediolaterally. (2) The elongating tissue is composed of cells that prefer to be elongated, and these cells must be accompanied by cells which prefer to be round. The latter effectively provide a boundary to capture. In simulations, our model tissue extends and converges to a stacked arrangement of elongated cells one cell wide, an arrangement which is seen in ascidian notochords, but which has not been observed in other models. This arrangement is achieved without any direct mediolateral bias other than that which is provided by the physical edge of the adjacent tissue.     

Moving forward moving backward: directional sorting of chemotactic cells due to size and adhesion differences

Differential movement of individual cells within tissues is an important yet poorly understood process in biological development. Here we present a computational study of cell sorting caused by a combination of cell adhesion and chemotaxis, where we assume that all cells respond equally to the chemotactic signal. To capture in our model mesoscopic properties of biological cells, such as their size and deformability, we use the Cellular Potts Model, a multiscale, cell-based Monte Carlo model. We demonstrate a rich array of cell-sorting phenomena, which depend on a combination of mescoscopic cell properties and tissue level constraints. Under the conditions studied, cell sorting is a fast process, which scales linearly with tissue size. We demonstrate the occurrence of “absolute negative mobility”, which means that cells may move in the direction opposite to the applied force (here chemotaxis). Moreover, during the sorting, cells may even reverse the direction of motion. Another interesting phenomenon is “minority sorting”, where the direction of movement does not depend on cell type, but on the frequency of the cell type in the tissue. A special case is the cAMP-wave-driven chemotaxis of Dictyostelium cells, which generates pressure waves that guide the sorting. The mechanisms we describe can easily be overlooked in studies of differential cell movement, hence certain experimental observations may be misinterpreted.     

A mechanical model of cell segregation driven by differential adhesion

From simulations that begin with a random mix of two cell types, we monitor progress towards segregation driven by contact-mediated linkage of model cells, which is equivalent to the cell-cell adhesion of real cells. In comparison with real cell experiments, we show that this mechanical model can account for the observed extent of segregation obtained by differential adhesion in a 2D cell culture assay of cells with differentially expressed cadherin molecules. Calibration of virtual to real time allowed us to estimate a time course for these experiments that was within 50% agreement for the simulations compared to differential adhesion of cells. In contrast, simulations of differential adhesion do not account for the rate of segregation driven by interactions between EphB2 receptor and ephrinB1 expressing cells which occurs an order of magnitude faster. The latter result suggests that mechanisms additional or alternative to differential adhesion contribute to Eph-ephrin mediated cell segregation.     

A cell-based model exhibiting branching and anastomosis during tumor-induced angiogenesis

This work describes the first cell-based model of tumor-induced angiogenesis. At the extracellular level, the model describes diffusion, uptake, and decay of tumor-secreted pro-angiogenic factor. At the cellular level, the model uses the cellular Potts model based on system-energy reduction to describe endothelial cell migration, growth, division, cellular adhesion, and the evolving structure of the stroma. Numerical simulations show: 1), different tumor-secreted pro-angiogenic factor gradient profiles dramatically affect capillary sprout morphology; 2), average sprout extension speeds depend on the proximity of the proliferating region to the sprout tip, and the coordination of cellular functions; and 3), inhomogeneities in the extravascular tissue lead to sprout branching and anastomosis, phenomena that emerge without any prescribed rules. This model provides a quantitative framework to test hypotheses on the biochemical and biomechanical mechanisms that control tumor-induced angiogenesis.     

Integrin-ECM interactions regulate cadherin-dependent cell adhesion and are required for convergent extension in Xenopus

BACKGROUND: Convergence extension movements are conserved tissue rearrangements implicated in multiple morphogenetic events. While many of the cell behaviors involved in convergent extension are known, the molecular interactions required for this process remain elusive. However, past evidence suggests that regulation of cell adhesion molecule function is a key step in the progression of these behaviors. RESULTS: Antibody blocking of fibronectin (FN) adhesion or dominant-negative inhibition of integrin beta 1 function alters cadherin-mediated cell adhesion, promotes cell-sorting behaviors in reaggregation assays, and inhibits medial-lateral cell intercalation and axial extension in gastrulating embryos and explants. Embryo explants were used to demonstrate that normal integrin signaling is required for morphogenetic movements within defined regions but not for cell fate specification. The binding of soluble RGD-containing fragments of fibronectin to integrins promotes the reintegration of dissociated single cells into intact tissues. The changes in adhesion observed are independent of cadherin or integrin expression levels. CONCLUSIONS: We conclude that integrin modulation of cadherin adhesion influences cell intercalation behaviors within boundaries defined by extracellular matrix. We propose that this represents a fundamental mechanism promoting localized cell rearrangements throughout development.     

The planar cell polarity gene strabismus regulates convergence and extension and neural fold closure in Xenopus

We cloned Xenopus Strabismus (Xstbm), a homologue of the Drosophila planar cell or tissue polarity gene. Xstbm encodes four transmembrane domains in its N-terminal half and a PDZ-binding motif in its C-terminal region, a structure similar to Drosophila and mouse homologues. Xstbm is expressed strongly in the deep cells of the anterior neural plate and at lower levels in the posterior notochordal and neural regions during convergent extension. Overexpression of Xstbm inhibits convergent extension of mesodermal and neural tissues, as well as neural tube closure, without direct effects on tissue differentiation. Expression of Xstbm(DeltaPDZ-B), which lacks the PDZ-binding region of Xstbm, inhibits convergent extension when expressed alone but rescues the effect of overexpressing Xstbm, suggesting that Xstbm(DeltaPDZ-B) acts as a dominant negative and that both increase and decrease of Xstbm function from an optimum retards convergence and extension. Recordings show that cells expressing Xstbm or Xstbm(DeltaPDZ-B) fail to acquire the polarized protrusive activity underlying normal cell intercalation during convergent extension of both mesodermal and neural and that this effect is population size-dependent. These results further characterize the role of Xstbm in regulating the cell polarity driving convergence and extension in Xenopus.     

Spatial modelling of brief and long interactions between T cells and dendritic cells

In the early phases of an immune response, T cells of appropriate antigen specificity become activated by antigen-presenting cells in secondary lymphoid organs. Two-photon microscopy imaging experiments have shown that this stimulation occurs in distinct stages during which T cells exhibit different motilities and interactions with dendritic cells (DCs). In this paper, we utilize the Cellular Potts Model, a model formalism that takes cell shapes and cellular interactions explicitly into account, to simulate the dynamics of, and interactions between, T cells and DCs in the lymph node paracortex. Our three-dimensional simulations suggest that the initial decrease in T-cell motility after antigen appearance is due to "stop signals" transmitted by activated DCs to T cells. The long-lived interactions that occur at a later stage can only be explained by the presence of both stop signals and a high adhesion between specific T cells and antigen-bearing DCs. Furthermore, our results indicate that long-lasting contacts with T cells are promoted when DCs retract dendrites that detect a specific contact at lower velocities than other dendrites. Finally, by performing long simulations (after prior fitting to short time scale data) we are able to provide an estimate of the average contact duration between T cells and DCs.     

Computational modeling of epithelial–mesenchymal transformations

An epithelial–mesenchymal transformation (EMT) involves alterations in cell–cell and cell–matrix adhesion, the detachment of epithelial cells from their neighbors, the degradation of the basal lamina and acquisition of mesenchymal phenotype. Here we present Monte Carlo simulations for a specific EMT in early heart development: the formation of cardiac cushions. Cell rearrangements are described in accordance with Steinberg's differential adhesion hypothesis, which states that cells possess a type-dependent adhesion apparatus and are sufficiently motile to give rise to the tissue conformation with the largest number of strong bonds. We also implement epithelial and mesenchymal cell proliferation, cell type change and extracellular matrix production by mesenchymal cells. Our results show that an EMT is promoted more efficiently by an increase in cell–substrate adhesion than by a decrease in cell–cell adhesion. In addition to cushion tissue formation, the model also accounts for the phenomena of matrix invasion and mesenchymal condensation. We conclude that in order to maintain epithelial integrity during EMT the number of epithelial cells must increase at a controlled rate. Our model predictions are in qualitative agreement with available experimental data.     

CompuCell, a multi-model framework for simulation of morphogenesis

MOTIVATION: CompuCell is a multi-model software framework for simulation of the development of multicellular organisms known as morphogenesis. It models the interaction of the gene regulatory network with generic cellular mechanisms, such as cell adhesion, division, haptotaxis and chemotaxis. A combination of a state automaton with stochastic local rules and a set of differential equations, including subcellular ordinary differential equations and extracellular reaction-diffusion partial differential equations, model gene regulation. This automaton in turn controls the differentiation of the cells, and cell-cell and cell-extracellular matrix interactions that give rise to cell rearrangements and pattern formation, e.g. mesenchymal condensation. The cellular Potts model, a stochastic model that accurately reproduces cell movement and rearrangement, models cell dynamics. All these models couple in a controllable way, resulting in a powerful and flexible computational environment for morphogenesis, which allows for simultaneous incorporation of growth and spatial patterning. RESULTS: We use CompuCell to simulate the formation of the skeletal architecture in the avian limb bud. AVAILABILITY: Binaries and source code for Microsoft Windows, Linux and Solaris are available for download from http://sourceforge.net/projects/compucell/     

Convergent extension and the hexahedral cell

During development, embryonic cells sculpt three-dimensional tissues. Although cell polarity is commonly analysed along one, and sometimes two, dimensions, this perspective illustrates how higher-order cell polarity regulates convergent extension - the coordinated cell rearrangement that produces solid tissue elongation.     

Emergent morphogenesis: Elastic mechanics of a self-deforming tissue

Multicellular organisms are generated by coordinated cell movements during morphogenesis. Convergent extension is a key tissue movement that organizes mesoderm, ectoderm, and endoderm in vertebrate embryos. The goals of researchers studying convergent extension, and morphogenesis in general, include understanding the molecular pathways that control cell identity, establish fields of cell types, and regulate cell behaviors. Cell identity, the size and boundaries of tissues, and the behaviors exhibited by those cells shape the developing embryo; however, there is a fundamental gap between understanding the molecular pathways that control processes within single cells and understanding how cells work together to assemble multicellular structures. Theoretical and experimental biomechanics of embryonic tissues are increasingly being used to bridge that gap. The efforts to map molecular pathways and the mechanical processes underlying morphogenesis are crucial to understanding: (1) the source of birth defects, (2) the formation of tumors and progression of cancer, and (3) basic principles of tissue engineering. In this paper, we first review the process of tissue convergent extension of the vertebrate axis and then review models used to study the self-organizing movements from a mechanical perspective. We conclude by presenting a relatively simple “wedge-model” that exhibits key emergent properties of convergent extension such as the coupling between tissue stiffness, cell intercalation forces, and tissue elongation forces.     

Effect of cellular rearrangement time delays on the rheology of vertex models for confluent tissues

Large-scale tissue deformation during biological processes such as morphogenesis requires cellular rearrangements. The simplest rearrangement in confluent cellular monolayers involves neighbor exchanges among four cells, called a T1 transition, in analogy to foams. But unlike foams, cells must execute a sequence of molecular processes, such as endocytosis of adhesion molecules, to complete a T1 transition. Such processes could take a long time compared to other timescales in the tissue. In this work, we incorporate this idea by augmenting vertex models to require a fixed, finite time for T1 transitions, which we call the “T1 delay time”. We study how variations in T1 delay time affect tissue mechanics, by quantifying the relaxation time of tissues in the presence of T1 delays and comparing that to the cell-shape based timescale that characterizes fluidity in the absence of any T1 delays. We show that the molecular-scale T1 delay timescale dominates over the cell shape-scale collective response timescale when the T1 delay time is the larger of the two. We extend this analysis to tissues that become anisotropic under convergent extension, finding similar results. Moreover, we find that increasing the T1 delay time increases the percentage of higher-fold coordinated vertices and rosettes, and decreases the overall number of successful T1s, contributing to a more elastic-like—and less fluid-like—tissue response. Our work suggests that molecular mechanisms that act as a brake on T1 transitions could stiffen global tissue mechanics and enhance rosette formation during morphogenesis.     

Computational Modeling Reveals that a Combination of Chemotaxis and Differential Adhesion Leads to Robust Cell Sorting during Tissue Patterning

Robust tissue patterning is crucial to many processes during development. The "French Flag" model of patterning, whereby naïve cells in a gradient of diffusible morphogen signal adopt different fates due to exposure to different amounts of morphogen concentration, has been the most widely proposed model for tissue patterning. However, recently, using time-lapse experiments, cell sorting has been found to be an alternative model for tissue patterning in the zebrafish neural tube. But it remains unclear what the sorting mechanism is. In this article, we used computational modeling to show that two mechanisms, chemotaxis and differential adhesion, are needed for robust cell sorting. We assessed the performance of each of the two mechanisms by quantifying the fraction of correct sorting, the fraction of stable clusters formed after correct sorting, the time needed to achieve correct sorting, and the size variations of the cells having different fates. We found that chemotaxis and differential adhesion confer different advantages to the sorting process. Chemotaxis leads to high fraction of correct sorting as individual cells will either migrate towards or away from the source depending on its cell type. However after the cells have sorted correctly, there is no interaction among cells of the same type to stabilize the sorted boundaries, leading to cell clusters that are unstable. On the other hand, differential adhesion results in low fraction of correct clusters that are more stable. In the absence of morphogen gradient noise, a combination of both chemotaxis and differential adhesion yields cell sorting that is both accurate and robust. However, in the presence of gradient noise, the simple combination of chemotaxis and differential adhesion is insufficient for cell sorting; instead, chemotaxis coupled with delayed differential adhesion is required to yield optimal sorting.     

The cellular basis of cell sorting kinetics

Cell sorting is a dynamical cooperative phenomenon that is fundamental for tissue morphogenesis and tissue homeostasis. According to Steinberg's differential adhesion hypothesis, the structure of sorted cell aggregates is determined by physical characteristics of the respective tissues, the tissue surface tensions. Steinberg postulated that tissue surface tensions result from quantitative differences in intercellular adhesion. Several experiments in cell cultures as well as in developing organisms support this hypothesis.The question of how tissue surface tension might result from differential adhesion was addressed in some theoretical models. These models describe the cellular interdependence structure once the temporal evolution has stabilized. In general, these models are capable of reproducing sorted patterns. However, the model dynamics at the cellular scale are defined implicitly and are not well-justified. The precise mechanism describing how differential adhesion generates the observed sorting kinetics at the tissue level is still unclear.It is necessary to formulate the concepts of cell level kinetics explicitly. Only then it is possible to understand the temporal development at the cellular and tissue scales. Here we argue that individual cell mobility is reduced the more the cells stick to their neighbors. We translate this assumption into a precise mathematical model which belongs to the class of stochastic interacting particle systems. Analyzing this model, we are able to predict the emergent sorting behavior at the population level. We describe qualitatively the geometry of cell segregation depending on the intercellular adhesion parameters. Furthermore, we derive a functional relationship between intercellular adhesion and surface tension and highlight the role of cell mobility in the process of sorting. We show that the interaction between the cells and the boundary of a confining vessel has a major impact on the sorting geometry.     

The role of extracellular matrix in glioma invasion: a cellular Potts model approach

In this work, a cellular Potts model based on the differential adhesion hypothesis is employed to analyze the relative importance of select cell-cell and cell-extracellular matrix (ECM) contacts in glioma invasion. To perform these simulations, three types of cells and two ECM components are included. The inclusion of explicit ECM with an inhomogeneous fibrous component and a homogeneously dispersed afibrous component allows exploration of the importance of relative energies of cell-cell and cell-ECM contacts in a variety of environments relevant to in vitro and in vivo experimental investigations of glioma invasion. Simulations performed here focus chiefly on reproducing findings of in vitro experiments on glioma spheroids embedded in collagen I gels. For a given range and set ordering of energies associated with key cell-cell and cell-ECM interactions, our model qualitatively reproduces the dispersed glioma invasion patterns found for most glioma cell lines embedded as spheroids in collagen I gels of moderate concentration. In our model, we find that invasion is maximized at intermediate collagen concentrations, as occurs experimentally. This effect is seen more strongly in model gels composed of short collagen fibers than in those composed of long fibers, which retain significant connectivity even at low density. Additional simulations in aligned model matrices further elucidate how matrix structure dictates invasive patterns. Finally, simulations that allow invading cells to both dissolve and deposit ECM components demonstrate how Q-Potts models may be elaborated to allow active cell alteration of their surroundings. The model employed here provides a quantitative framework with which to bound the relative values of cell-cell and cell-ECM interactions and investigate how varying the magnitude and type of these interactions, as well as ECM structure, could potentially curtail glioma invasion.     

Xenopus Dishevelled signaling regulates both neural and mesodermal convergent extension: parallel forces elongating the body axis

During amphibian development, non-canonical Wnt signals regulate the polarity of intercalating dorsal mesoderm cells during convergent extension. Cells of the overlying posterior neural ectoderm engage in similar morphogenetic cell movements. Important differences have been discerned in the cell behaviors associated with neural and mesodermal cell intercalation, raising the possibility that different mechanisms may control intercalations in these two tissues. In this report, targeted expression of mutants of Xenopus Dishevelled (Xdsh) to neural or mesodermal tissues elicited different defects that were consistent with inhibition of either neural or mesodermal convergent extension. Expression of mutant Xdsh also inhibited elongation of neural tissues in vitro in Keller sandwich explants and in vivo in neural plate grafts. Targeted expression of other Wnt signaling antagonists also inhibited neural convergent extension in whole embryos. In situ hybridization indicated that these defects were not due to changes in cell fate. Examination of embryonic phenotypes after inhibition of convergent extension in different tissues reveals a primary role for mesodermal convergent extension in axial elongation, and a role for neural convergent extension as an equalizing force to produce a straight axis. This study demonstrates that non-canonical Wnt signaling is a common mechanism controlling convergent extension in two very different tissues in the Xenopus embryo and may reflect a general conservation of control mechanisms in vertebrate convergent extension.     

Xenopus p21-activated kinase 5 regulates blastomeres' adhesive properties during convergent extension movements

The p21-activated kinase (PAK) proteins regulate many cellular events including cell cycle progression, cell death and survival, and cytoskeleton rearrangements. We previously identified X-PAK5 that binds the actin and microtubule networks, and could potentially regulate their coordinated dynamics during cell motility. In this study, we investigated the functional importance of this kinase during gastrulation in Xenopus. X-PAK5 is mainly expressed in regions of the embryo that undergo extensive cell movements during gastrula such as the animal hemisphere and the marginal zone. Expression of a kinase-dead mutant inhibits convergent extension movements in whole embryos and in activin-treated animal cap by modifying behavior of cells. This phenotype is rescued in embryo by adding back X-PAK5 catalytic activity. The active kinase decreases cell adhesiveness when expressed in animal hemisphere and inhibits the calcium-dependent reassociation of cells, while dead X-PAK5 kinase localizes to cell-cell junctions and increases cell adhesion. In addition, endogenous X-PAK5 colocalizes with adherens junction proteins and its activity is regulated by extracellular calcium. Taken together, our results suggest that X-PAK5 regulates convergent extension movements in vivo by modulating the calcium-mediated cell-cell adhesion.