Computer simulations of cell sorting due to differential adhesion

The actions of cell adhesion molecules, in particular, cadherins during embryonic development and morphogenesis more generally, regulate many aspects of cellular interactions, regulation and signaling. Often, a gradient of cadherin expression levels drives collective and relative cell motions generating macroscopic cell sorting. Computer simulations of cell sorting have focused on the interactions of cells with only a few discrete adhesion levels between cells, ignoring biologically observed continuous variations in expression levels and possible nonlinearities in molecular binding. In this paper, we present three models relating the surface density of cadherins to the net intercellular adhesion and interfacial tension for both discrete and continuous levels of cadherin expression. We then use then the Glazier-Graner-Hogeweg (GGH) model to investigate how variations in the distribution of the number of cadherins per cell and in the choice of binding model affect cell sorting. We find that an aggregate with a continuous variation in the level of a single type of cadherin molecule sorts more slowly than one with two levels. The rate of sorting increases strongly with the interfacial tension, which depends both on the maximum difference in number of cadherins per cell and on the binding model. Our approach helps connect signaling at the molecular level to tissue-level morphogenesis.     

Tensile forces govern germ-layer organization in zebrafish

Understanding the factors that direct tissue organization during development is one of the most fundamental goals in developmental biology. Various hypotheses explain cell sorting and tissue organization on the basis of the adhesive and mechanical properties of the constituent cells. However, validating these hypotheses has been difficult due to the lack of appropriate tools to measure these parameters. Here we use atomic force microscopy (AFM) to quantify the adhesive and mechanical properties of individual ectoderm, mesoderm and endoderm progenitor cells from gastrulating zebrafish embryos. Combining these data with tissue self-assembly in vitro and the sorting behaviour of progenitors in vivo, we have shown that differential actomyosin-dependent cell-cortex tension, regulated by Nodal/TGFbeta-signalling (transforming growth factor beta), constitutes a key factor that directs progenitor-cell sorting. These results demonstrate a previously unrecognized role for Nodal-controlled cell-cortex tension in germ-layer organization during gastrulation.     

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.     

Decreased cell adhesion promotes angiogenesis in a Pyk2-dependent manner

Angiogenesis is regulated by both soluble growth factors and cellular interactions with the extracellular matrix (ECM). While cell adhesion via integrins has been shown to be required for angiogenesis, the effects of quantitative changes in cell adhesion and spreading against the ECM remain less clear. Here, we show that angiogenic sprouting in natural and engineered three-dimensional matrices exhibited a biphasic response, with peak sprouting when adhesion to the matrix was limited to intermediate levels. Examining changes in global gene expression to determine a genetic basis for this response, we demonstrate a vascular endothelial growth factor (VEGF)-induced upregulation of genes associated with vascular invasion and remodeling when cell adhesion was limited, whereas cells on highly adhesive surfaces upregulated genes associated with proliferation. To explore a mechanistic basis for this effect, we turned to focal adhesion kinase (FAK), a central player in adhesion signaling previously implicated in angiogenesis, and its homologue, proline-rich tyrosine kinase 2 (Pyk2). While FAK signaling had some impact, our results suggested that Pyk2 can regulate both gene expression and endothelial sprouting through its enhanced activation by VEGF in limited adhesion contexts. We also demonstrate decreased sprouting of tissue explants from Pyk2-null mice as compared to wild type mice as further confirmation of the role of Pyk2 in angiogenic sprouting. These results suggest a surprising finding that limited cell adhesion can enhance endothelial responsiveness to VEGF and demonstrate a novel role for Pyk2 in the adhesive regulation of angiogenesis.     

A Point-Wise Model of Adhesion Suitable for Real-Time Applications of Bio-Inspired Climbing Robots

Bio-inspired climbing robots relying on adhesion systems are believed to become essential tools for several industrial applications in the near future. In recent years, research has mainly focused on modeling micro-scale adhesion phenomena; a macro-scale adhesion model has however to be developed for the design of macro-scale systems. In this paper a macro-model of adhesion suitable for real-time applications is presented; it relies on a continuous representation of adhesion. An extension of the von Mises criterion is proposed as failure adhesion criterion in order to estimate the occurrence of detachment at any point of the contacting surface. An experimental set up has been designed in order to define the parameters of the model. A semi-automatic process has been developed to ensure repeatability and accuracy of the results. Polydimethylsiloxane (PDMS), which has revealed promising adhesive features for robotic use, has been used during the experimental phase. The macro-model of adhesion has been implemented in a multi-body dynamics environment based on Open Dynamics Engine (ODE) to simulate a spider-inspired robot. Simulations based on this model are suitable to represent the behaviour of climbing robots and also to optimize their design.     

Cadherin-mediated cell sorting not determined by binding or adhesion specificity.

Cadherin adhesion molecules play important roles in the establishment of tissue boundaries. Cells expressing different cadherins sort out from each other in cell aggregation assays. To determine the contribution of cadherin binding and adhesion specificity to the sorting process, we examined the adhesion of cells to different purified cadherin proteins. Chinese hamster ovary cell lines expressing one of four different cadherins were allowed to bind to the purified cadherin extracellular domains of either human E-cadherin or Xenopus C-cadherin, and the specificity of adhesion was compared with cell-sorting assays. None of the different cadherin-expressing cells exhibited any adhesive specificity toward either of the two purified cadherin substrates, even though these cadherins differ considerably in their primary sequence. In addition, all cells exhibited similar strengthening of adhesion on both substrates. However, this lack of adhesive specificity did not determine whether different cadherin-expressing cells would sort from each other, and the tendency to sort was not predictable by the extent of sequence diversity in their extracellular domains. These results show that cadherins are far more promiscuous in their adhesive-binding capacity than had been expected and that the ability to sort out must be determined by mechanisms other than simple adhesive-binding specificity.     

Ankyrin-G Inhibits Endocytosis of Cadherin Dimers

Dynamic regulation of endothelial cell adhesion is central to vascular development and maintenance. Furthermore, altered endothelial adhesion is implicated in numerous diseases. Therefore, normal vascular patterning and maintenance require tight regulation of endothelial cell adhesion dynamics. However, the mechanisms that control junctional plasticity are not fully understood. Vascular endothelial cadherin (VE-cadherin) is an adhesive protein found in adherens junctions of endothelial cells. VE-cadherin mediates adhesion through trans interactions formed by its extracellular domain. Trans binding is followed by cis interactions that laterally cluster the cadherin in junctions. VE-cadherin is linked to the actin cytoskeleton through cytoplasmic interactions with β- and α-catenin, which serve to increase adhesive strength. Furthermore, p120-catenin binds to the cytoplasmic tail of cadherin and stabilizes it at the plasma membrane. Here we report that induced cis dimerization of VE-cadherin inhibits endocytosis independent of both p120 binding and trans interactions. However, we find that ankyrin-G, a protein that links membrane proteins to the spectrin-actin cytoskeleton, associates with VE-cadherin and inhibits its endocytosis. Ankyrin-G inhibits VE-cadherin endocytosis independent of p120 binding. We propose a model in which ankyrin-G associates with and inhibits the endocytosis of VE-cadherin cis dimers. Our findings support a novel mechanism for regulation of VE-cadherin endocytosis through ankyrin association with cadherin engaged in lateral interactions.     

Modeling concurrent binding of multiple molecular species in cell adhesion

Cell adhesion provides not only physical linkage but also communication between the cell and its environment. As such, it is important to many cellular functions. Recently, the probability distribution of forming a low number of specific adhesive bonds in a short-duration contact has been described (Chesla et al., Biophys. J. , 1998, 75:1553-1572). This model assumes that binding occurs between a single receptor species and a single ligand species. However, cell adhesion molecules rarely work alone in physiological settings. To account for these in vivo situations, we extended the previous model to include concurrent interactions of multiple receptor-ligand species, introducing the concept of independent binding. Closed-form solutions have been obtained for cases where competition is absent or can be neglected. In two companion papers (Williams et al., Biophys. J., 2000, 79:1858-1866; 2000, 79:1867-1875), the model developed herein has been applied to analyze two sets of experiments designed such that the validity of the theory was also tested.     

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.     

EphA4 is required for cell adhesion and rhombomere-boundary formation in the zebrafish

The formation of boundaries between or within tissues is a fundamental aspect of animal development. In the developing vertebrate hindbrain, boundaries separate molecularly and neuroanatomically distinct segments called rhombomeres. Transplantation studies have suggested that rhombomere boundaries form by the local sorting out of cells with different segmental identities. This sorting-out process has been shown to involve repulsive interactions between cells expressing an Eph receptor tyrosine kinase, EphA4, and cells expressing its ephrinB ligands. Although a model for rhombomere-boundary formation based on repulsive Eph-ephrin signaling is well established in the literature, the predictions of this model have not been tested in loss-of-function experiments. Here, we eliminate EphA4 and ephrinB2a proteins in zebrafish with antisense morpholinos (MO) and find that rhombomere boundaries are disrupted in EphA4MO embryos, consistent with a requirement for Eph-ephrin signaling in boundary formation. However, in mosaic embryos, we observe that EphA4MO cells and EphA4-expressing cells sort from one another, an observation that is not predicted by the Eph-ephrin repulsion model but instead suggests that EphA4 promotes cell adhesion within the rhombomeres in which it is expressed. Differential cell adhesion is known to be an effective mechanism for cell sorting. We therefore propose that the well-known EphA4-dependent repulsion between rhombomeres operates in parallel with the EphA4-dependent adhesion within rhombomeres described here to drive the cell sorting that underlies rhombomere-boundary formation.     

A complex of Protocadherin-19 and N-cadherin mediates a novel mechanism of cell adhesion

During embryonic morphogenesis, adhesion molecules are required for selective cell-cell interactions. The classical cadherins mediate homophilic calcium-dependent cell adhesion and are founding members of the large and diverse cadherin superfamily. The protocadherins are the largest subgroup within this superfamily, yet their participation in calcium-dependent cell adhesion is uncertain. In this paper, we demonstrate a novel mechanism of adhesion, mediated by a complex of Protocadherin-19 (Pcdh19) and N-cadherin (Ncad). Although Pcdh19 alone is only weakly adhesive, the Pcdh19-Ncad complex exhibited robust adhesion in bead aggregation assays, and Pcdh19 appeared to play the dominant role. Adhesion by the Pcdh19-Ncad complex was unaffected by mutations that disrupt Ncad homophilic binding but was inhibited by a mutation in Pcdh19. In addition, the complex exhibited homophilic specificity, as beads coated with Pcdh19-Ncad did not intermix with Ncad- or Pcdh17-Ncad-coated beads. We propose a model in which association of a protocadherin with Ncad acts as a switch, converting between distinct binding specificities.     

Mixed extracellular matrix ligands synergistically modulate integrin adhesion and signaling

Cell adhesion to extracellular matrix (ECM) components through cell-surface integrin receptors is essential to the formation, maintenance and repair of numerous tissues, and therefore represents a central theme in the design of bioactive materials that successfully interface with the body. While the adhesive responses associated with a single ligand have been extensively analyzed, the effects of multiple integrin subtypes binding to multivalent ECM signals remain poorly understood. In the present study, we generated a high throughput platform of non-adhesive surfaces presenting well-defined, independent densities of two integrin-specific engineered ligands for the type I collagen (COL-I) receptor alpha(2)beta(1) and the fibronectin (FN) receptor alpha(5)beta(1) to evaluate the effects of integrin cross-talk on adhesive responses. Engineered surfaces displayed ligand density-dependent adhesive effects, and mixed ligand surfaces significantly enhanced cell adhesion strength and focal adhesion assembly compared to single FN and COL-I ligand surfaces. Moreover, surfaces presenting mixed COL-I/FN ligands synergistically enhanced FAK activation compared to the single ligand substrates. The enhanced adhesive activities of the mixed ligand surfaces also promoted elevated proliferation rates. Our results demonstrate interplay between multivalent ECM ligands in adhesive responses and downstream cellular signaling.     

Modelling and simulation of substrate elasticity sensing in stem cells

Recently, we have developed a multiscale soft matter cell model aiming at improving the understanding of mechanotransduction mechanism of stem cells, which is responsible for information exchange between cells and their extracellular environment. In this paper, we report the preliminary results of our research on multiscale modelling and simulation of soft contact and adhesion of stem cells. The proposed multiscale soft matter cell model may be used to model soft contact and adhesion between cells and their extracellular substrates. To the authors' best knowledge, this may be the first time that a soft matter model has been developed for cell contact and adhesion. Moreover, we have developed and implemented a Lagrange-type meshfree Galerkin formulation and related computational algorithms for the proposed cell model. Comparison study with experimental data has been conducted to validate the parameters of the cell model. By using the soft matter cell model, we have simulated the soft adhesive contact process between cells and extracellular substrates. The simulation shows that the cell can sense substrate elasticity by responding it in different manners from cell spreading to cell contact configuration and molecular conformation changes.     

An octapeptide in the juxtamembrane domain of VE-cadherin is important for p120ctn binding and cell proliferation

The cadherins are a family of adhesive proteins involved in cell-cell homophilic interactions. VE-cadherin, expressed in endothelial cells, is involved in morphogenesis, regulation of permeability, and cellular proliferation. The cytoplasmic tails of cadherins contain two major domains, the juxtamembrane domain that plays a role in the intercellular localization of the protein and also serves for binding of p120ctn, and a C-terminal domain that associates with beta- or gamma-catenin. A highly conserved region present in the juxtamembrane domain of the cadherins has been shown to be necessary for p120ctn binding in E-cadherin. Using a mutant VE-cadherin lacking a highly conserved octapeptide, we demonstrated that it is required for p120ctn binding to VE-cadherin as determined by immunoprecipitation and colocalization studies. By immunofluorescence, this mutant protein has a topographical distribution similar to that of the wild-type VE-cadherin and, therefore, we conclude that the topographical distribution of VE-cadherin is independent of this motif. In addition, although cell-cell association is present in cells expressing this mutant form of VE-cadherin, we found that the strength of adhesion is decreased. Finally, our results for the first time demonstrate that the interaction of VE-cadherin with p120 catenin plays an important role in cellular growth, suggesting that the binding of p120 catenin to cadherins may regulate cell proliferation.     

Paraxial protocadherin mediates cell sorting and tissue morphogenesis by regulating C-cadherin adhesion activity

Little is known about how protocadherins function in cell adhesion and tissue development. Paraxial protocadherin (PAPC) controls cell sorting and morphogenetic movements in the Xenopus laevis embryo. We find that PAPC mediates these functions by down-regulating the adhesion activity of C-cadherin. Expression of exogenous C-cadherin reverses PAPC-induced cell sorting and gastrulation defects. Moreover, loss of endogenous PAPC results in elevated C-cadherin adhesion activity in the dorsal mesoderm and interferes with the normal blastopore closure, a defect that can be rescued by a dominant-negative C-cadherin mutant. Importantly, activin induces PAPC expression, and PAPC is required for activin-induced regulation of C-cadherin adhesion activity and explant morphogenesis. Signaling through Frizzled-7 is not required for PAPC regulation of C-cadherin, suggesting that C-cadherin regulation and Frizzled-7 signaling are two distinct branches of the PAPC pathway that induce morphogenetic movements. Thus, spatial regulation of classical cadherin adhesive function by local expression of a protocadherin is a novel mechanism for controlling cell sorting and tissue morphogenesis.     

The adhesive binding site of cadherins revisited

Cadherins are single-pass transmembrane proteins that, through their homophilic specificity, function in selective cell adhesion and sorting. They have a modular structure that includes an ectodomain composed of tandem 'cadherin domains,' which have a beta-sandwich topology similar to that of immunoglobulin domains. Some early experiments suggest that, for the 'classical' cadherins, the adhesive specificity is encoded in the membrane-distal amino-terminal cadherin domain. Here, we review these data, and present new data that supports this idea.     

Cadherin-directed actin assembly: E-cadherin physically associates with the Arp2/3 complex to direct actin assembly in nascent adhesive contacts

Cadherin cell adhesion molecules are major determinants of tissue patterning which function in cooperation with the actin cytoskeleton. In the context of stable adhesion, cadherin/catenin complexes are often envisaged to passively scaffold onto cortical actin filaments. However, cadherins also form dynamic adhesive contacts during wound healing and morphogenesis. Here actin polymerization has been proposed to drive cell surfaces together, although F-actin reorganization also occurs as cell contacts mature. The interaction between cadherins and actin is therefore likely to depend on the functional state of adhesion. We sought to analyze the relationship between cadherin homophilic binding and cytoskeletal activity during early cadherin adhesive contacts. Dissecting the specific effect of cadherin ligation alone on actin regulation is difficult in native cell-cell contacts, due to the range of juxtacrine signals that can arise when two cell surfaces adhere. We therefore activated homophilic ligation using a specific functional recombinant protein. We report the first evidence that E-cadherin associates with the Arp2/3 complex actin nucleator and demonstrate that cadherin binding can exert an active, instructive influence on cells to mark sites for actin assembly at the cell surface.     

Adhesion of a chicken myeloblast cell line to fibrinogen and vitronectin through a beta 1-class integrin.

The adhesive interactions of circulating blood cells are tightly regulated, receptor-mediated events. To establish a model for studies on regulation of cell adhesion, we have examined the adhesive properties of the HD11 chick myeloblast cell line. Function-perturbing antibodies were used to show that integrins containing the beta 1 subunit mediate HD11 cell attachment to several distinct extracellular matrix proteins, specifically fibronectin, collagen, vitronectin, and fibrinogen. This is the first evidence that an integrin heterodimer in the beta 1 family functions as a receptor for fibrinogen. While the alpha v beta 1 heterodimer has been shown to function as a vitronectin receptor on some cells, this heterodimer could not be detected on HD11 cells. Instead, results suggest that the beta 1 subunit associates with different, unidentified alpha subunit(s) to form receptors for vitronectin and fibrinogen. Results using function-blocking antibodies also demonstrate that on these cells, additional receptors for vitronectin are formed by alpha v beta 3 and alpha v associated with an unidentified 100-kD beta subunit. The adhesive interactions of HD11 cells with these extracellular matrix ligands were shown to be regulated by lipopolysaccharide treatment, making the HD11 cell line attractive for studies of mechanisms regulating cell adhesion. In contrast to primary macrophage which rapidly exhibit enhanced adhesion to laminin and collagen upon activation, activated HD11 cells exhibited reduced adhesion to most extracellular matrix constituents.     

p120-catenin and β-catenin differentially regulate cadherin adhesive function

Vascular endothelial (VE)-cadherin, the major adherens junction adhesion molecule in endothelial cells, interacts with p120-catenin and β-catenin through its cytoplasmic tail. However, the specific functional contributions of the catenins to the establishment of strong adhesion are not fully understood. Here we use bioengineering approaches to identify the roles of cadherin–catenin interactions in promoting strong cellular adhesion and the ability of the cells to spread on an adhesive surface. Our results demonstrate that the domain of VE-cadherin that binds to β-catenin is required for the establishment of strong steady-state adhesion strength. Surprisingly, p120 binding to the cadherin tail had no effect on the strength of adhesion when the available adhesive area was limited. Instead, the binding of VE-cadherin to p120 regulates adhesive contact area in a Rac1-dependent manner. These findings reveal that p120 and β-catenin have distinct but complementary roles in strengthening cadherin-mediated adhesion.     

Can retinal adhesion mechanisms determine cell-sorting patterns: a test of the differential adhesion hypothesis

Embryonic chick neural retina cells possess two classes of adhesion mechanism, one Ca2+-independent, one Ca2+-dependent, responsible for short-term cell aggregation. This study investigates the role of these mechanisms in the long-term cell sorting potentially relevant to in vivo histogenesis. Retina cells are prepared either with both (E cells) or with only one mechanism (TC cells, CD; LTE cells, CI), respectively. The two types of cell preparations are differentially labelled using fluorescein or rhodamine isothiocyanate, mixed and allowed to aggregate in the presence or absence of cycloheximide at 0.5 microgram ml-1 to retard metabolic recovery of the removed adhesive mechanism. When observed by fluorescence and phase-contrast microscopy, the aggregates formed in cycloheximide show cell sorting, the cells with both mechanisms assuming a more interior position relative to those with a single adhesion mechanism. In parallel hanging-drop experiments, preformed aggregates of cells with a single adhesion mechanism are seen to spread upon aggregates of cells with both mechanisms. No sorting occurs amongst cells from a given stage prepared using any single dissociation protocol. The observed cell sorting would thus seem to derive exclusively from differential cell adhesiveness dependent upon the different dissociation conditions and maintained in the presence of cycloheximide. The experiments support the hypothesis that the dual CI and CD adhesion mechanisms in question can play a central role in governing cell-sorting behaviour during normal histogenesis.