The Differential Interfacial Tension Hypothesis (DITH): a comprehensive theory for the self-rearrangement of embryonic cells and tissues

A comprehensive theory, herein named the Differential Interfacial Tension Hypothesis for the self-rearrangement of embryonic cells and tissues is presented. These rearrangements include sorting, mixing and formation of checkerboard patterns in heterotypic aggregates of embryonic cells, and total or partial engulfment, separation and dissociation of tissues. This broadly-based theory accounts for the action of all currently known cytoskeletal components and cell adhesion mechanisms. The theory is used to derive conditions for the cell and tissue rearrangements named above. Finite element-based computer simulations involving two or more cell types confirm these conditions.     

The mechanics of cell sorting and envelopment

Aggregates of embryonic cells undergo a variety of intriguing processes including sorting by histological type and envelopment of cell masses of one type by another. It has long been held that these processes were driven by differential adhesions, as embodied in the famous differential adhesion hypothesis (DAH). Here, we use analytical mechanics to investigate the forces that are generated by various sub-cellular structures including microfilaments, cell membranes and their associated proteins, and by sources of cell-cell adhesions. We consider how these forces cause the triple junctions between cells to move, and how these motions ultimately give rise to phenomena such as cell sorting and tissue envelopment. The analyses show that, contrary to the widely accepted DAH, differential adhesions alone are unable to drive sorting and envelopment. They show, instead, that these phenomena are driven by the combined effect of several force generators, as embodied in an equivalent surface or interfacial tension. These unconventional findings follow directly from the relevant surface physics and mechanics, and are consistent with well-known cell sorting and envelopment experiments, and with recent computer simulations.     

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.     

Computer simulation of engulfment and other movements of embryonic tissues

Using a model proposed earlier by Goel et al. and a set of plausible motility rules, a computer simulation of engulfment of two or more intact embryonic tissues is successfully carried out. The same motility rules are used to simulate the rounding up of a tissue, centralization of one tissue within another tissue (a phenomenon not yet observed), and phase inversion, a process which may have relevance to differentiation. The finnal structures bear a good resemblance to those observed experimentally. The software, in conjunction with an appropriate hardware configuration, allows a visual display of the dynamics of cellular movement. These simulations indicate that the range of inter-cellular interactions controlling these tissue rearrangements extends only one or two cell diameters.     

Computer simulation of cellular movements: cell-sorting, cellular migration through a mass of cells and contact inhibition

The motility rules for cellular movement proposed earlier by Goel &; Rogers for engulfment of two or more intact embryonic tissues have been used to simulate on a computer the phenomena of cell-sorting, migration of individual cells through a mass of cells and contact inhibition of overlapping. These simulations in the most part are found to be consistent with the observations with real cells.     

Non-straight cell edges are important to invasion and engulfment as demonstrated by cell mechanics model

Computational models of cell–cell mechanical interactions typically simulate sorting and certain other motions well, but as demands on these models continue to grow, discrepancies between the cell shapes, contact angles and behaviours they predict and those that occur in real cells have come under increased scrutiny. To investigate whether these discrepancies are a direct result of the straight cell–cell edges generally assumed in these models, we developed a finite element model that approximates cell boundaries using polylines with an arbitrary number of segments. We then compared the predictions of otherwise identical polyline and monoline (straight-edge) models in a variety of scenarios, including annealing, single- and multi-cell engulfment, sorting, and two forms of mixing—invasion and checkerboard pattern formation. Keeping cell–cell edges straight influences cell motion, cell shape, contact angle, and boundary length, especially in cases where one cell type is pulled between or around cells of a different type, as in engulfment or invasion. These differences arise because monoline cells have restricted deformation modes. Polyline cells do not face these restrictions, and with as few as three segments per edge yielded realistic edge shapes and contact angle errors one-tenth of those produced by monoline models, making them considerably more suitable for situations where angles and shapes matter, such as validation of cellular force–inference techniques. The findings suggest that non-straight cell edges are important both in modelling and in nature.     

Contact response of cells can mediate morphogenetic pattern formation

Theories of morphogenetic pattern formation have included Turing's chemical prepatterns, mechanochemical interactions, cell sorting, and other mechanisms involving guided motion or signalling of cells. Many of these theories presuppose long-range cellular communication or other controls such as chemical concentration fields. However, the possibility that direct interactions between cells can lead to order and structure has not been seriously investigated in mathematical models. In this paper we consider this possibility, with emphasis on cells that reorient and align with each other when they come into contact. We show that such contact responses can account for the formation of multicellular patterns called parallel arrays. These patterns typically occur in tissue cultures of fibroblasts, and consist of clusters of cells sharing a common axis of orientation. Using predictions of a mathematical model and computer simulations of cell motion and interactions we show that contact responses alone, in the absence of other global controls, can promote the formation of these patterns. We suggest other situations in which patterns may result from direct cellular communication. Previous theories of morphogenesis are briefly reviewed and compared with this proposed mechanism.     

A model of cell sorting

Voronoi polygons are introduced as a suitable representation for a two-dimensional cell sheet. These polygons are defined in terms of a finite number of points, making numerical simulations tractable and yet allowing cells to change neighbors and their shape in response to deforming forces without leaving gaps in the tissue. Using this geometry and an extension of the equilibrium theory proposed by Steinberg to drive the motion, simulations of rounding of uneven tissue and engulfment of two intact tissues are carried out.     

Evidence for a conserved role for CRKII and Rac in engulfment of apoptotic cells

Apoptosis or programmed cell death occurs in multicellular organisms throughout life. The removal of apoptotic cells by phagocytes prevents secondary necrosis and inflammation and also plays a key role in tissue remodeling and regulating immune responses. The molecular mechanisms that regulate the engulfment of apoptotic cells are just beginning to be elucidated. Recent genetic studies in the nematode Caenorhabditis elegans have implicated at least six genes in the removal of apoptotic cell corpses. The gene products of ced-2, ced-5, and ced-10 are thought to be part of a pathway that regulates the reorganization of the cytoskeleton during engulfment. The adapter proteins CrkII and Dock180 and the small GTPase Rac represent the mammalian orthologues of the ced-2, ced-5 and ced-10 gene products, respectively. It is not known whether CrkII, Dock180, or Rac proteins have any role during engulfment in mammalian cells. Here we show, using stable cell lines and transient transfections, that overexpression of wild-type CrkII or an activated form of Rac1 enhances engulfment. Mutants of CrkII failed to mediate this increased engulfment. The higher CrkII-mediated uptake was inhibited by coexpression of a dominant negative form of Rac1 but not by a dominant a negative Rho protein; this suggested that Rac functions downstream of CrkII in this process, which is consistent with genetic studies in the worm that place ced-10 (rac) downstream of ced-2 (crk) in cell corpse removal. Taken together, these data suggest that CED-2/CrkII and CED-10/Rac are part of an evolutionarily conserved pathway in engulfment of apoptotic cells.     

Mechanics of enveloped virus entry into host cells

Enveloped viruses such as HIV-1 enter their hosts by first establishing a contact region at the cell surface, which is stabilized by the formation of receptor-ligand complexes. We show that the favorable contact energy stemming from the formation of the receptor complexes in the interaction zone is sufficient to drive the engulfment of the virus by the cell. Using a continuum model, we show that the equilibrium engulfment depth and the force driving the engulfment are functions of the virus size and the complex formation energy. Resistance to engulfment is dominated by the elastic deformation of the cytoskeleton.     

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.     

Apoptotic cells are cleared by directional migration and elmo1- dependent macrophage engulfment

Apoptotic cell death is essential for development and tissue homeostasis. Failure to clear apoptotic cells can ultimately cause inflammation and autoimmunity. Apoptosis has primarily been studied by staining of fixed tissue sections, and a clear understanding of the behavior of apoptotic cells in living tissue has been elusive. Here, we use a newly developed technique to track apoptotic cells in real time as they emerge and are cleared from the zebrafish brain. We find that apoptotic cells are remarkably motile, frequently migrating several cell diameters to the periphery of living tissues. F-actin remodeling occurs in surrounding cells, but also within the apoptotic cells themselves, suggesting a cell-autonomous component of motility. During the first 2 days of development, engulfment is rare, and most apoptotic cells lyse at the brain periphery. By 3 days postfertilization, most cell corpses are rapidly engulfed by macrophages. This engulfment requires the guanine nucleotide exchange factor elmo1. In elmo1-deficient macrophages, engulfment is rare and may occur through macropinocytosis rather than directed engulfment. These findings suggest that clearance of apoptotic cells in living vertebrates is accomplished by the combined actions of apoptotic cell migration and elmo1-dependent macrophage engulfment.     

Computer simulation of compartment maintenance in the Drosophila wing imaginal disc

A new method for modelling cell division is reported which uses a cellular representation based on graph theory. This allows us to model the adjacencies of non-regular dividing cells accurately, avoiding the rigid geometrical constraints present in earlier simulations. We use this system to simulate compartment boundary maintenance in the Drosophila wing imaginal disc. We show that a boundary of minimum length between two growing polyclones of cells could depend on sorting between cells in the different polyclones. We also investigate the response of the model to differential cell division rates within polyclones. This is the first demonstration that cell sorting can generate a smooth boundary in a dividing cell mass. We suggest that biological analogs of our computer sorting rules are responsible for the similar straight polyclone borders seen in the real wing disc. A possible strategy for showing the existence of these analogs is also given.     

Requirement for the cell division protein DivIB in polar cell division and engulfment during sporulation in Bacillus subtilis

During spore formation in Bacillus subtilis, cell division occurs at the cell pole and is believed to require essentially the same division machinery as vegetative division. Intriguingly, although the cell division protein DivIB is not required for vegetative division at low temperatures, it is essential for efficient sporulation under these conditions. We show here that at low temperatures in the absence of DivIB, formation of the polar septum during sporulation is delayed and less efficient. Furthermore, the polar septa that are complete are abnormally thick, containing more peptidoglycan than a normal polar septum. These results show that DivIB is specifically required for the efficient and correct formation of a polar septum. This suggests that DivIB is required for the modification of sporulation septal peptidoglycan, raising the possibility that DivIB either regulates hydrolysis of polar septal peptidoglycan or is a hydrolase itself. We also show that, despite the significant number of completed polar septa that form in this mutant, it is unable to undergo engulfment. Instead, hydrolysis of the peptidoglycan within the polar septum, which occurs during the early stages of engulfment, is incomplete, producing a similar phenotype to that of mutants defective in the production of sporulation-specific septal peptidoglycan hydrolases. We propose a role for DivIB in sporulation-specific peptidoglycan remodelling or its regulation during polar septation and engulfment.     

Forespore engulfment mediated by a ratchet-like mechanism

A key step in bacterial endospore formation is engulfment, during which one bacterial cell engulfs another in a phagocytosis-like process that normally requires SpoIID, SpoIIM, and SpoIIP (DMP). We here describe a second mechanism involving the zipper-like interaction between the forespore protein SpoIIQ and its mother cell ligand SpoIIIAH, which are essential for engulfment when DMP activity is reduced or SpoIIB is absent. They are also required for the rapid engulfment observed during the enzymatic removal of peptidoglycan, a process that does not require DMP. These results suggest the existence of two separate engulfment machineries that compensate for one another in intact cells, thereby rendering engulfment robust. Photobleaching analysis demonstrates that SpoIIQ assembles a stationary structure, suggesting that SpoIIQ and SpoIIIAH function as a ratchet that renders forward membrane movement irreversible. We suggest that ratchet-mediated engulfment minimizes the utilization of chemical energy during this dramatic cellular reorganization, which occurs during starvation.     

The cell biology of cell-in-cell structures

For decades, authors have described unusual cell structures, referred to as cell-in-cell structures, in which whole cells are found in the cytoplasm of other cells. One well-characterized process that results in the transient appearance of such structures is the engulfment of apoptotic cells by phagocytosis. However, many other types of cell-in-cell structure have been described that involve viable non-apoptotic cells. Some of these structures seem to form by the invasion of one cell into another, rather than by engulfment. The mechanisms of cell-in-cell formation and the possible physiological roles of these processes will be discussed.     

Transitivity,pattern-reversal,engulfment and duality in exchange-type cell aggregation kinetics

Simulations of cell-sorting phenomena in embryogenesis describable by means of the differential adhesion mechanism are further studied using the exchange model. In this study, more than two cell-types are employed and results nicely complement the successes of earlier work with only two cell-types. Again, it is noticed that “central clumping” does not usually appear in final distributions. In addition, the phenomena of transitivity, pattern-reversal and the engulfment of one tissue by another are studied. The first is shown to be a trivial consequence of Steinberg's stochastic version of differential adhesion. Also, it is shown that the exchange model successfully simulates pattern-reversal by the reversal of the relative adhesion values due to the time-in-culture reversal of the effect of adhesivity of trypsin-assisted dissociation of tissues. The connection between the occurrence of pattern reversal and the absolute and relative positions of tissue types in the adhesion hierarchy is explained in terms on the exchange model. It is found that the model, as it stands, does not seem to give a satisfactory basis for the simulation of engulfment. Suggestions for the extension of the exchange principle are made which will perhaps rectify this limitation. It is felt that any real system which exhibits engulfment will also exhibit central clumping, and conversely. The importance of the figure-ground ambiguity we have called “duality” is again stressed. If this ambiguity is not taken into account in experimental work, interpretation of many results on cell-sorting are rendered meaningless.     

Lattice Boltzmann simulations of the time evolution of living multicellular systems

Embryonic tissues and multicellular aggregates of adult cells mimic the behavior of highly viscous liquids. The liquid analogy helps to understand morphogenetic phenomena, such as cell sorting and tissue fusion, observed in developmental biology and tissue engineering. Tissue fusion is vital in tissue printing, an emergent technique based on computer-controlled deposition of tissue fragments and biocompatible materials. Computer simulations proved useful in predicting post-printing shape changes of tissue constructs. The simulation methods available to date, however, are unable to describe the time evolution of living systems made of millions of cells. The Lattice Boltzmann (LB) approach allows the implementation of interaction forces between the constituents of the system and yields time evolution in terms of distribution functions. With tissue engineering applications in mind, we have developed a finite difference Lattice Boltzmann model of a multicellular system and applied it to simulate the sidewise fusion of two contiguous cylinders made of cohesive cells and embedded in a medium (hydrogel). We have identified a biologically relevant range of model parameters. The proposed LB model may be extended to describe the time evolution of more complex multicellular structures such as sheets or tubes produced by tissue printing.     

Cell wall synthesis is necessary for membrane dynamics during sporulation of Bacillus subtilis

During Bacillus subtilis sporulation, an endocytic‐like process called engulfment results in one cell being entirely encased in the cytoplasm of another cell. The driving force underlying this process of membrane movement has remained unclear, although components of the machinery have been characterized. Here we provide evidence that synthesis of peptidoglycan, the rigid, strength bearing extracellular polymer of bacteria, is a key part of the missing force‐generating mechanism for engulfment. We observed that sites of peptidoglycan synthesis initially coincide with the engulfing membrane and later with the site of engulfment membrane fission. Furthermore, compounds that block muropeptide synthesis or polymerization prevented membrane migration in cells lacking a component of the engulfment machinery (SpoIIQ), and blocked the membrane fission event at the completion of engulfment in all cells. In addition, these compounds inhibited bulge and vesicle formation that occur in spoIID mutant cells unable to initiate engulfment, as did genetic ablation of a protein that polymerizes muropeptides. This is the first report to our knowledge that peptidoglycan synthesis is necessary for membrane movements in bacterial cells and has implications for the mechanism of force generation during cytokinesis.