Is cell sorting caused by differences in the work of intercellular adhesion? A critique of the steinberg hypothesis

The differential adhesion hypothesis, developed by Malcolm Steinberg, proposes that the histotypic sorting out behavior of aggregated cells is mechanistically equivalent to certain aspects of liquid surface tension, specifically the spontaneous separation of immiscible liquids of differing surface tension. According to Steinberg's hypothesis, the adhesive forces between aggregated cells play essentially the same role in cell sorting as are played by intermolecular attractive forces in liquid surface tension.In this paper I discuss a number of crucial distinctions between intermolecular attraction (in liquids) and intercellular adhesion (in aggregates). First, liquid drops are closed systems thermodynamically whereas aggregates of living cells can generate an indeterminate amount of metabolic energy capable of altering cell positions and adhesions. Secondly, intercellular adhesions are more than just close range attractions since cells can be held together by forces in addition to those which originally pulled them together. Third, the breakage of intercellular adhesions need not be simply the reverse, thermodynamically, of the formation of those adhesions. And fourthly, because intercellular adhesion is generally concentrated at relatively small foci such as desmosomes, a maximization of intercellular adhesion does not necessarily require a maximization of intercellular contact area, or vice versa.In addition, several alternative hypotheses are proposed, each of which is theoretically capable of explaining cell sorting and the other surface tension-like aspects of cell aggregate behavior which Steinberg has sought to explain as consequences of differential adhesion. In particular, a differential surface contraction hypothesis is proposed, according to which cell sorting and related phenomena are the results of cell surface contractions induced to occur over those portions of the cell surface which are exposed to the surrounding culture medium. Because of the evidence that various invagination type movements of embryonic epithelia are caused by cell surface contractions, it is suggested that differential surface contraction is the most likely explanation of histotypic cell sorting. A number of experiments are suggested by which these various hypotheses might be tested.     

The mechanics of heterotypic cell aggregates: insights from computer simulations

Finite element-based computer simulations are used to investigate a number of phenomena, including tissue engulfment, cell sorting, and checkerboard-pattern formation, exhibited by heterotypic cell aggregates. The simulations show that these phenomena can be driven by a single equivalent force, namely a surface (or interfacial) tension, that results from cytoskeletal components and cell-cell adhesions. They also reveal that tissue engulfment, cell sorting, and checkerboard-pattern formation involve several discernible mechanical features or stages. With the aid of analytical arguments, we identify the conditions necessary for each of these phenomena. These findings are consistent with previous experimental investigations and computer simulations, but pose significant challenges to current theories of cell sorting and tissue engulfment.     

The differential adhesion hypothesis: a direct evaluation

The differential adhesion hypothesis (DAH), advanced in the 1960s, proposed that the liquid-like tissue-spreading and cell segregation phenomena of development arise from tissue surface tensions that in turn arise from differences in intercellular adhesiveness. Our earlier measurements of liquid-like cell aggregate surface tensions have shown that, without exception, a cell aggregate of lower surface tension tends to envelop one of higher surface tension to which it adheres. We here measure the surface tensions of L cell aggregates transfected to express N-, P- or E-cadherin in varied, measured amounts. We report that in these aggregates, in which cadherins are essentially the only cell-cell adhesion molecules, the aggregate surface tensions are a direct, linear function of cadherin expression level. Taken together with our earlier results, the conclusion follows that the liquid-like morphogenetic cell and tissue rearrangements of cell sorting, tissue spreading and segregation represent self-assembly processes guided by the diminution of adhesive-free energy as cells tend to maximize their mutual binding. This conclusion relates to the physics governing these morphogenetic phenomena and applies independently of issues such as the specificities of intercellular adhesives.     

Transition from Actin-Driven to Water-Driven Cell Migration Depends on External Hydraulic Resistance

Cells in vivo can reside in diverse physical and biochemical environments. For example, epithelial cells typically live in a two-dimensional (2D) environment, whereas metastatic cancer cells can move through dense three-dimensional matrices. These distinct environments impose different kinds of mechanical forces on cells and thus potentially can influence the mechanism of cell migration. For example, cell movement on 2D flat surfaces is mostly driven by forces from focal adhesion and actin polymerization, whereas in confined geometries, it can be driven by water permeation. In this work, we utilize a two-phase model of the cellular cytoplasm in which the mechanics of the cytosol and the F-actin network are treated on an equal footing. Using conservation laws and simple force balance considerations, we are able to describe the contributions of water flux, actin polymerization and flow, and focal adhesions to cell migration both on 2D surfaces and in confined spaces. The theory shows how cell migration can seamlessly transition from a focal adhesion- and actin-based mechanism on 2D surfaces to a water-based mechanism in confined geometries.     

DO MORPHOGENETIC TISSUE REARRANGEMENTS REQUIRE ACTIVE CELL MOVEMENTS? : The Reversible Inhibition of Cell Sorting and Tissue Spreading by Cytochalasin B

Previous studies have indicated that cell sorting and tissue spreading are caused by cell combination-specific differences in intercellular adhesive energies, acting in a system of motile cells. We wished to determine whether these adhesive energies could drive cell rearrangements as well as guide them. Accordingly, aggregates of intermixed embryonic cells were cultured in solutions of the drug cytochalasin B (CCB) at a concentration shown to inhibit the locomotion of cells on a solid surface. In addition, spherical aggregates of several kinds were cultured in mutual contact under similar conditions. Both cell sorting and tissue spreading were found to be inhibited. The prompt release of this inhibition upon removal of the CCB showed that the inhibited cells were not merely injured. Moreover, aggregation experiments showed that CCB did not prevent cells of several kinds from initiating mutual adhesions. In fact, heart cell aggregation was enhanced by CCB. We conclude that interfacial forces, originating outside the cell, act together with forces originating inside it in bringing about the morphogenetic movements of cell sorting and tissue spreading. We propose the term "cooperative cell locomotion" to describe translational movements of cells arising from such a combination of intrinsic and extrinsic forces.     

Genetic control of intercellular adhesion or how cadherins shape the fruitfly Drosophila melanogaster

The beauty and diversity of cell shapes have always fascinated both biologists and physicists. In the early 1950, J. Holtfreter coined the term "tissue affinities" to describe the forces behind the spontaneous shaping of groups of cells. These tissue affinites were later on related to adhesive properties of cell membranes. In the 1960, Malcom Steinberg proposed the differential adhesion hypothesis (DAH) as a physical explanation of the liquid-like behaviour of tissues and cells during morphogenesis. However, the link between the cellular properties of adhesion molecules, such as the cadherins, and the physical rules that shape the body, has remained unclear. Recent in vitro studies have now shown that surface tensions, which drive the spontaneous liquid-like behaviour of cell rearrangements, are a direct and linear function of cadherin expression levels. Tissue surface tensions thus arise from differences in intercellular adhesiveness, which validates the DAH in vitro. The DAH was also vindicated in vivo by stunning experiments in Drosophila. The powerful genetic tools available in Drosophila allow to manipulate the levels and patterns of expression of several cadherins and to create artificially differences in intercellular adhesiveness. The results showed that simple laws of thermodynamics, as well as quantitative and qualitative differences in cadherins expression were sufficient to explain processes as complex as the establishment of the anterior-posterior axis and the formation of the compound eye in Drosophila.     

Brushes,cables, and anchors: Recent insights into multiscale assembly and mechanics of cellular structural networks

The remarkable ability of living cells to sense, process, and respond to mechanical stimuli in their environment depends on the rapid and efficient interconversion of mechanical and chemical energy at specific times and places within the cell. For example, application of force to cells leads to conformational changes in specific mechanosensitive molecules which then trigger cellular signaling cascades that may alter cellular structure, mechanics, and migration and profoundly influence gene expression. Similarly, the sensitivity of cells to mechanical stresses is governed by the composition, architecture, and mechanics of the cellular cytoskeleton and extracellular matrix (ECM), which are in turn driven by molecular-scale forces between the constituent biopolymers. Understanding how these mechanochemical systems coordinate over multiple length and time scales to produce orchestrated cell behaviors represents a fundamental challenge in cell biology. Here, we review recent advances in our understanding of these complex processes in three experimental systems: the assembly of axonal neurofilaments, generation of tensile forces by actomyosin stress fiber bundles, and mechanical control of adhesion assembly.     

A phenomenological cohesive model for the macroscopic simulation of cell–matrix adhesions

Cell adhesion is crucial for cells to not only physically interact with each other but also sense their microenvironment and respond accordingly. In fact, adherent cells can generate physical forces that are transmitted to the surrounding matrix, regulating the formation of cell–matrix adhesions. The main purpose of this work is to develop a computational model to simulate the dynamics of cell–matrix adhesions through a cohesive formulation within the framework of the finite element method and based on the principles of continuum damage mechanics. This model enables the simulation of the mechanical adhesion between cell and extracellular matrix (ECM) as regulated by local multidirectional forces and thus predicts the onset and growth of the adhesion. In addition, this numerical approach allows the simulation of the cell as a whole, as it models the complete mechanical interaction between cell and ECM. As a result, we can investigate and quantify how different mechanical conditions in the cell (e.g., contractile forces, actin cytoskeletal properties) or in the ECM (e.g., stiffness, external forces) can regulate the dynamics of cell–matrix adhesions.     

Differential adhesion in morphogenesis: a modern view

The spreading of one embryonic tissue over another, the sorting out of their cells when intermixed and the formation of intertissue boundaries respected by the motile border cells all have counterparts in the behavior of immiscible liquids. The 'differential adhesion hypothesis' (DAH) explains these liquid-like tissue behaviors as consequences of the generation of tissue surface and interfacial tensions arising from the adhesion energies between motile cells. The experimental verification of the DAH, the recent computational models simulating adhesion-mediated morphogenesis, and the evidence concerning the role of differential adhesion in a number of morphodynamic events, including teleost epiboly, the specification of boundaries between rhombomeres in the developing vertebrate hindbrain, epithelial-mesenchymal transitions in embryos, and malignant invasion are reviewed here.     

Dynamics of cellular focal adhesions on deformable substrates: consequences for cell force microscopy

Cell focal adhesions are micrometer-sized aggregates of proteins that anchor the cell to the extracellular matrix. Within the cell, these adhesions are connected to the contractile, actin cytoskeleton; this allows the adhesions to transmit forces to the surrounding matrix and makes the adhesion assembly sensitive to the rigidity of their environment. In this article, we predict the dynamics of focal adhesions as a function of the rigidity of the substrate. We generalize previous theories and include the fact that the dynamics of proteins that adsorb to adhesions are also driven by their coupling to cell contractility and the deformation of the matrix. We predict that adhesions reach a finite size that is proportional to the elastic compliance of the substrate, on a timescale that also scales with the compliance: focal adhesions quickly reach a relatively small, steady-state size on soft materials. However, their apparent sliding is not sensitive to the rigidity of the substrate. We also suggest some experimental probes of these ideas and discuss the nature of information that can be extracted from cell force microscopy on deformable substrates.     

Cell adhesive affinity does not dictate primitive endoderm segregation and positioning during murine embryoid body formation

The classical cell sorting experiments undertaken by Townes and Holtfreter described the intrinsic propensity of dissociated embryonic cells to self‐organize and reconcile into their original embryonic germ layers with characteristic histotypic positioning. Steinberg presented the differential adhesion hypothesis to explain these patterning phenomena. Here, we have reappraised these issues by implementing embryoid bodies to model the patterning of epiblast and primitive endoderm layers. We have used combinations of embryonic stem (ES) cells and their derivatives differentiated by retinoic acid treatment to model epiblast and endoderm cells, and wild‐type or E‐cadherin null cells to represent strongly or weakly adherent cells, respectively. One cell type was fluorescently labeled and reconstituted with another heterotypically to generate chimeric embryoid bodies, and cell sorting was tracked by time‐lapse video microscopy and confirmed by immunostaining. When undifferentiated wild‐type and E‐cadherin null ES cells were mixed, the resulting cell aggregates consisted of a core of wild‐type cells surrounded by loosely associated E‐cadherin null cells, consistent with the differential adhesion hypothesis. However, when mixed with undifferentiated ES cells, the differentiated primitive endoderm‐like cells sorted to the surface to form a primitive endoderm layer irrespective of cell‐adhesive strength, contradicting the differential adhesion hypothesis. We propose that the primitive endoderm cells reach the surface by random movement, and subsequently the cells generate an apical/basal polarity that prevents reentry. Thus, the ability to generate epithelial polarity, rather than adhesive affinity, determines the surface positioning of the primitive endoderm cells. genesis 47:579–589, 2009. © 2009 Wiley‐Liss, Inc.     

New information from cell aggregate compression tests and its implications for theories of cell sorting

In order to verify theories about the mechanics of cell sorting, tissue spreading and checkerboard pattern formation, it is necessary to measure certain cell properties such as surface tension and adhesiveness. The purpose of this work is to clarify the relationship between these two important properties and to use computer simulations and analytical calculations to extract additional information from parallel plate compression tests. This paper shows that compression tests can be used to determine not only the surface tension between the aggregate and the surrounding medium, but also the effective viscosity of the cell cytoplasm and the interfacial tension that acts between the cells that make up the aggregate. The findings reported here also support a novel, differential interfacial tension-based theory for cell sorting, tissue spreading and checkerboard pattern formation, and pose further challenges to current differential adhesion-based models.     

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.     

A thermodynamical model of cell distributions in the slug of cellular slime mold

A theoretical model is proposed for the formation of cell distribution patterns in the slug stage of the cellular slime moldDictyostelium discoideum. The equilibrium distribution of two types of cells, prestalk and prespore, is obtained by minimizing the free energy, which is defined in terms of differential chemotaxis, differential cell adhesion and randomness of cell movement. Resulting distributions show various segregation patterns of cell types. The condition for cell sorting is obtained from stability analysis of the set of diffusion equations governing the evolution of cell type distribution and the concentration of chemoattractant. The intensities of differential chemotaxis and random cell movement are quantitatively evaluated from experimental data to show that two cell types can sort themselves completely by these forces.     

Traction force microscopy in rapidly moving cells reveals separate roles for ROCK and MLCK in the mechanics of retraction

Retraction is a major rate-limiting step in cell motility, particularly in slow moving cell types that form large stable adhesions. Myosin II dependent contractile forces are thought to facilitate detachment by physically pulling up the rear edge. However, retraction can occur in the absence of myosin II activity in cell types that form small labile adhesions. To investigate the role of contractile force generation in retraction, we performed traction force microscopy during the movement of fish epithelial keratocytes. By correlating changes in local traction stress at the rear with the area retracted, we identified four distinct modes of retraction. “Recoil” retractions are preceded by a rise in local traction stress, while rear edge is temporarily stuck, followed by a sharp drop in traction stress upon detachment. This retraction type was most common in cells generating high average traction stress. In “pull” type retractions local traction stress and area retracted increase concomitantly. This was the predominant type of retraction in keratocytes and was observed mostly in cells generating low average traction stress. “Continuous” type retractions occur without any detectable change in traction stress, and are seen in cells generating low average traction stress. In contrast, to many other cell types, “release” type retractions occur in keratocytes following a decrease in local traction stress. Our identification of distinct modes of retraction suggests that contractile forces may play different roles in detachment that are related to rear adhesion strength. To determine how the regulation of contractility via MLCK or Rho kinase contributes to the mechanics of detachment, inhibitors were used to block or augment these pathways. Modulation of MLCK activity led to the most rapid change in local traction stress suggesting its importance in regulating attachment strength. Surprisingly, Rho kinase was not required for detachment, but was essential for localizing retraction to the rear. We suggest that in keratocytes MLCK and Rho kinase play distinct, complementary roles in the respective temporal and spatial control of rear detachment that is essential for maintaining rapid motility.     

Cytoskeleton dynamics: fluctuations within the network

Out-of-equilibrium systems, such as the dynamics of a living cytoskeleton (CSK), are inherently noisy with fluctuations arising from the stochastic nature of the underlying biochemical and molecular events. Recently, such fluctuations within the cell were characterized by observing spontaneous nano-scale motions of an RGD-coated microbead bound to the cell surface [Bursac et al., Nat. Mater. 4 (2005) 557-561]. While these reported anomalous bead motions represent a molecular level reorganization (remodeling) of microstructures in contact with the bead, a precise nature of these cytoskeletal constituents and forces that drive their remodeling dynamics are largely unclear. Here, we focused upon spontaneous motions of an RGD-coated bead and, in particular, assessed to what extent these motions are attributable to (i) bulk cell movement (cell crawling), (ii) dynamics of focal adhesions, (iii) dynamics of lipid membrane, and/or (iv) dynamics of the underlying actin CSK driven by myosin motors.     

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 structure of cell-matrix adhesions: the new frontier

Adhesions between the cell and the extracellular matrix (ECM) are mechanosensitive multi-protein assemblies that transmit force across the cell membrane and regulate biochemical signals in response to the chemical and mechanical environment. These combined functions in force transduction, signaling and mechanosensing contribute to cellular phenotypes that span development, homeostasis and disease. These adhesions form, mature and disassemble in response to actin organization and physical forces that originate from endogenous myosin activity or external forces by the extracellular matrix. Despite advances in our understanding of the protein composition, interactions and regulation, our understanding of matrix adhesion structure and organization, how forces affect this organization, and how these changes dictate specific signaling events is limited. Insights across multiple structural levels are acutely needed to elucidate adhesion structure and ultimately the molecular basis of signaling and mechanotransduction. Here we describe the challenges and recent advances and prospects for unraveling the structure of cell-matrix adhesions and their response to force.     

Mechanical stress inference for two dimensional cell arrays

Many morphogenetic processes involve mechanical rearrangements of epithelial tissues that are driven by precisely regulated cytoskeletal forces and cell adhesion. The mechanical state of the cell and intercellular adhesion are not only the targets of regulation, but are themselves the likely signals that coordinate developmental process. Yet, because it is difficult to directly measure mechanical stress in vivo on sub-cellular scale, little is understood about the role of mechanics in development. Here we present an alternative approach which takes advantage of the recent progress in live imaging of morphogenetic processes and uses computational analysis of high resolution images of epithelial tissues to infer relative magnitude of forces acting within and between cells. We model intracellular stress in terms of bulk pressure and interfacial tension, allowing these parameters to vary from cell to cell and from interface to interface. Assuming that epithelial cell layers are close to mechanical equilibrium, we use the observed geometry of the two dimensional cell array to infer interfacial tensions and intracellular pressures. Here we present the mathematical formulation of the proposed Mechanical Inverse method and apply it to the analysis of epithelial cell layers observed at the onset of ventral furrow formation in the Drosophila embryo and in the process of hair-cell determination in the avian cochlea. The analysis reveals mechanical anisotropy in the former process and mechanical heterogeneity, correlated with cell differentiation, in the latter process. The proposed method opens a way for quantitative and detailed experimental tests of models of cell and tissue mechanics.