Vertex Models of Epithelial Morphogenesis

The dynamic behavior of epithelial cell sheets plays a central role during numerous developmental processes. Genetic and imaging studies of epithelial morphogenesis in a wide range of organisms have led to increasingly detailed mechanisms of cell sheet dynamics. Computational models offer a useful means by which to investigate and test these mechanisms, and have played a key role in the study of cell-cell interactions. A variety of modeling approaches can be used to simulate the balance of forces within an epithelial sheet. Vertex models are a class of such models that consider cells as individual objects, approximated by two-dimensional polygons representing cellular interfaces, in which each vertex moves in response to forces due to growth, interfacial tension, and pressure within each cell. Vertex models are used to study cellular processes within epithelia, including cell motility, adhesion, mitosis, and delamination. This review summarizes how vertex models have been used to provide insight into developmental processes and highlights current challenges in this area, including progressing these models from two to three dimensions and developing new tools for model validation.     

Implementing vertex dynamics models of cell populations in biology within a consistent computational framework

The dynamic behaviour of epithelial cell sheets plays a central role during development, growth, disease and wound healing. These processes occur as a result of cell adhesion, migration, division, differentiation and death, and involve multiple processes acting at the cellular and molecular level. Computational models offer a useful means by which to investigate and test hypotheses about these processes, and have played a key role in the study of cell–cell interactions. However, the necessarily complex nature of such models means that it is difficult to make accurate comparison between different models, since it is often impossible to distinguish between differences in behaviour that are due to the underlying model assumptions, and those due to differences in the in silico implementation of the model. In this work, an approach is described for the implementation of vertex dynamics models, a discrete approach that represents each cell by a polygon (or polyhedron) whose vertices may move in response to forces. The implementation is undertaken in a consistent manner within a single open source computational framework, Chaste, which comprises fully tested, industrial-grade software that has been developed using an agile approach. This framework allows one to easily change assumptions regarding force generation and cell rearrangement processes within these models. The versatility and generality of this framework is illustrated using a number of biological examples. In each case we provide full details of all technical aspects of our model implementations, and in some cases provide extensions to make the models more generally applicable.     

Apical Junctional Fluctuations Lead to Cell Flow while Maintaining Epithelial Integrity

Epithelial sheet integrity is robustly maintained during morphogenesis, which is essential to shape organs and embryos. While maintaining the planar monolayer in three-dimensional space, cells dynamically flow via rearranging their connections between each other. However, little is known about how cells maintain the plane sheet integrity in three-dimensional space and provide cell flow in the in-plane sheet. In this study, using a three-dimensional vertex model, we demonstrate that apical junctional fluctuations allow stable cell rearrangements while ensuring monolayer integrity. In addition to the fluctuations, direction-dependent contraction on the apical cell boundaries, which corresponds to forces from adherens junctions, induces cell flow in a definite direction. We compared the kinematic behaviors of this apical-force-driven cell flow with those of typical cell flow that is driven by forces generated on basal regions and revealed the characteristic differences between them. These differences can be used to distinguish the mechanism of epithelial cell flow observed in experiments, i.e., whether it is apical- or basal-force-driven. Our numerical simulations suggest that cells actively generate fluctuations and use them to regulate both epithelial integrity and plasticity during morphogenesis.     

Mechanics of animal development

Morphogenetic movements are active processes created by forces located within the moving cells themselves. As a rule, these forces are generated by cytoskeleton structures (contraction of actin microfilaments organized as subcortical bundles or actine gel) and by the membranes and vacuole mediated processes of osmotic water transport. The intercellular forces lead to contraction and thus give rise to long-range mechanical stresses, mostly tensile ones. Tensile stresses create the regularly space/time arranged fields which remain topologically invariable within certain developmental periods, which then change drastically. The model of epithelial morphogenesis is discussed which postulates the segregation of an initially homogeneous cell sheet to the proportional domains of polarized and tangentially stretched cells as a result of self-organization. Some other models which tend to explain the different kinds of fold formation are also suggested. One of the models implies a simple "curvature increasing rule" which derives a common trefoiled archetype as a fundamental trend of development of an epithelial rudiment.     

Plithotaxis and emergent dynamics in collective cellular migration

For a monolayer sheet to migrate cohesively, it has long been suspected that each constituent cell must exert physical forces not only upon its extracellular matrix but also upon neighboring cells. The first comprehensive maps of these distinct force components reveal an unexpected physical picture. Rather than showing smooth and systematic variation within the monolayer, the distribution of physical forces is dominated by heterogeneity, both in space and in time, which emerges spontaneously, propagates over great distances, and cooperates over the span of many cell bodies. To explain the severe ruggedness of this force landscape and its role in collective cell guidance, the well known mechanisms of chemotaxis, durotaxis, haptotaxis are clearly insufficient. In a broad range of epithelial and endothelial cell sheets, collective cell migration is governed instead by a newly discovered emergent mechanism of innately collective cell guidance - plithotaxis.     

Planar cell polarity signaling in vertebrates

Planar cell polarity (PCP) refers to the polarization of a field of cells within the plane of a cell sheet. This form of polarization is required for diverse cellular processes in vertebrates, including convergent extension (CE), the establishment of PCP in epithelial tissues and ciliogenesis. Perhaps the most distinct example of vertebrate PCP is the uniform orientation of stereociliary bundles at the apices of sensory hair cells in the mammalian auditory sensory organ. The establishment of PCP in the mammalian cochlea occurs concurrently with CE in this ciliated epithelium, therefore linking three cellular processes regulated by the vertebrate PCP pathway in the same tissue and emerging as a model system for dissecting PCP signaling. This review summarizes the morphogenesis of this model system to assist the interpretation of the emerging data and proposes molecular mechanisms underlying PCP signaling in vertebrates.     

Epithelial morphogenesis in embryos: asymmetries, motors and brakes

Epithelial cells play a central role in many embryonic morphogenetic processes, during which they undergo highly coordinated cell shape changes. Here, we review some common principles that have recently emerged through genetic and cellular analyses performed mainly with invertebrate genetic models, focusing on morphogenetic processes involving epithelial sheets. All available data argue that myosin II is the main motor that induces cell shape changes during morphogenesis. We discuss the control of myosin II activity during epithelial morphogenesis, as well as the recently described involvement of microtubules in this process. Finally, we examine how forces unleashed by myosin II can be measured, how embryos use specific brakes to control molecular motors and the potential input of mechano-sensation in morphogenesis.     

The effects of mechanical forces on intestinal physiology and pathology

The epithelial and non-epithelial cells of the intestinal wall experience a myriad of physical forces including strain, shear, and villous motility during normal gut function. Pathologic conditions alter these forces, leading to changes in the biology of these cells. The responses of intestinal epithelial cells to forces vary with both the applied force and the extracellular matrix proteins with which the cells interact, with differing effects on proliferation, differentiation, and motility, and the regulation of these effects involves similar but distinctly different signal transduction mechanisms. Although normal epithelial cells respond to mechanical forces, malignant gastrointestinal epithelial cells also respond to forces, most notably by increased cell adhesion, a critical step in tumor metastasis. This review will focus on the phenomenon of mechanical forces influencing cell biology and the mechanisms by which the gut responds these forces in both the normal as well as pathophysiologic states when forces are altered. Although more is known about epithelial responses to force, information regarding mechanosensitivity of vascular, neural, and endocrine cells within the gut wall will also be discussed, as will, the mechanism by which forces can regulate epithelial tumor cell adhesion.     

Testing effects of signal transduction pathways on cadherin junctional complex assembly using quantitative image analysis

Cadherin adhesion molecules function in numerous cell biological processes that influence embryo development, normal cell physiology, and pathophysiology of many disease processes. Cadherins nucleate the assembly of the adherens junction, a cell-to-cell adhesion plaque that is prominent in simple epithelial cells and found in many cell types. Numerous cell biological approaches have been used to study this interesting class of molecules. Here, we outline methodology used in our studies of junctional complexes to examine effects of signaling molecules on assembly mechanisms. This is a quantitative method that allows the investigator to test the combined effect of two different signaling processes to determine whether these two signals act in concert within the same pathway. We discuss how this method could be generalized to other studies to examine consequences of various experimental manipulations on the assembly of cellular structures.     

Pinching and pushing: fold formation in the Drosophila dorsal epidermis

Epithelial folding is a fundamental morphogenetic process that shapes planar epithelial sheets into complex three-dimensional structures. Multiple mechanisms can generate epithelial folds, including apical constriction, which acts locally at the cellular level, differential growth on the tissue scale, or buckling because of compression from neighboring tissues. Here, we investigate the formation of dorsally located epithelial folds at segment boundaries during the late stages of Drosophila embryogenesis. We found that the fold formation at the segment boundaries occurs through the juxtaposition of two key morphogenetic processes: local apical constriction and tissue-level compressive forces from posterior segments. Further, we found that epidermal spreading and fold formation are accompanied by spatiotemporal pulses of Hedgehog (Hh) signaling. A computational model that incorporates the local forces generated from the differential tensions of the apical, basal, and lateral sides of the cell and active forces generated within the whole tissue recapitulates the overall fold formation process in wild-type and Hh overexpression conditions. In sum, this work demonstrates how epithelial folding depends on multiple, separable physical mechanisms to generate the final morphology of the dorsal epidermis. This work illustrates the modularity of morphogenetic unit operations that occur during epithelial morphogenesis.     

Divide and polarize: recent advances in the molecular mechanism regulating epithelial tubulogenesis

Epithelial organs are generated from groups of non-polarized cells by a combination of processes that induce the acquisition of cell polarity, lumen formation, and the subsequent steps required for tubulogenesis. The subcellular mechanisms associated to these processes are still poorly understood. The extracellular environment provides a cue for the initial polarization, while cytoskeletal rearrangements build up the three-dimensional architecture that supports the central lumen. The proper orientation of cell division in the epithelium has been found to be required for the normal formation of the central lumen in epithelial morphogenesis. Moreover, recent data in cellular models and in vivo have shed light into the underlying mechanisms that connect the spindle orientation machinery with cell polarity. In addition, recent work has clarified the core molecular components of the vesicle trafficking machinery in epithelial morphogenesis, including Rab-GTPases and the Exocyst, as well as an increasing list of microtubule-binding and actin-binding proteins and motors, most of which are conserved from yeast to humans. In this review we will focus on the discussion of novel findings that have unveiled important clues for the mechanisms that regulate epithelial tubulogenesis.     

Techniques for assessing 3-D cell–matrix mechanical interactions in vitro and in vivo

Cellular interactions with extracellular matrices (ECM) through the application of mechanical forces mediate numerous biological processes including developmental morphogenesis, wound healing and cancer metastasis. They also play a key role in the cellular repopulation and/or remodeling of engineered tissues and organs. While 2-D studies can provide important insights into many aspects of cellular mechanobiology, cells reside within 3-D ECMs in vivo, and matrix structure and dimensionality have been shown to impact cell morphology, protein organization and mechanical behavior. Global measurements of cell-induced compaction of 3-D collagen matrices can provide important insights into the regulation of overall cell contractility by various cytokines and signaling pathways. However, to understand how the mechanics of cell spreading, migration, contraction and matrix remodeling are regulated at the molecular level, these processes must also be studied in individual cells. Here we review the evolution and application of techniques for imaging and assessing local cell–matrix mechanical interactions in 3-D culture models, tissue explants and living animals.     

Enhanced serine palmitoyltransferase expression in proliferating fibroblasts, transformed cell lines, and human tumors.

Metastatic processes, including cell invasion, extracellular matrix degradation, and tissue remodeling, require cellular reorganization and proliferation. The cell signaling molecules required and the proteins involved in cell restructuring have not been completely elucidated. We have been studying the role of sphingolipids in normal cell activity and in several pathophysiological states. In this study we used immunohistochemistry to observe the presence of the two known subunits of serine palmitoyltransferase (SPT) in proliferating cells, in an in vitro model of wound repair, and in human malignant tissue. We report increased expression of the two subunits, SPT1 and SPT2, in the proliferating cells in these models. We also demonstrate a change in subcellular localization of the SPT subunits from predominantly cytosolic in quiescent cells to nuclear in proliferating cells. In addition, we observed SPT1 and SPT2 immunoreactivity in reactive stromal fibroblasts surrounding the carcinoma cells of some of the tumors. This enhanced SPT expression was absent in the stromal fibroblasts surrounding normal epithelial cells. Our results suggest a potential role for overexpression of SPT in the processes of cell metastasis.     

Big roles for small GTPases in the control of directed cell movement

Small GTPases are involved in the control of diverse cellular behaviours, including cellular growth, differentiation and motility. In addition, recent studies have revealed new roles for small GTPases in the regulation of eukaryotic chemotaxis. Efficient chemotaxis results from co-ordinated chemoattractant gradient sensing, cell polarization and cellular motility, and accumulating data suggest that small GTPase signalling plays a central role in each of these processes as well as in signal relay. The present review summarizes these recent findings, which shed light on the molecular mechanisms by which small GTPases control directed cell migration.     

Epithelial morphogenesis.

The identification of protein factors, such as epimorphin, scatter factor, and activin, that induce epithelial branching and convergent extension-like movements in embryonic tissues are important breakthroughs in our understanding of the role of mesenchyme in epithelial morphogenesis. Moreover, the development of simple in vitro epithelial cell systems that undergo morphogenesis in response to these factors should provide a means to investigate the cellular and molecular bases of the morphogenetic movements themselves. Although many different cellular processes are involved in such morphogenetic behaviors, cell rearrangement is a particularly intriguing one that will be important to study further. Several considerations lead to the prediction that a dynamic regulation of cell-cell adhesion is likely to play a central role in cell rearrangements and epithelial morphogenesis. Ultimately, a greater issue to be addressed is how the different cellular mechanisms participating in epithelial morphogenesis are coordinated and regulated, so as to generate the diverse patterns found in various epithelia.     

Phosphoinositides in cell architecture

Inositol phospholipids have been implicated in almost all aspects of cellular physiology including spatiotemporal regulation of cellular signaling, acquisition of cellular polarity, specification of membrane identity, cytoskeletal dynamics, and regulation of cellular adhesion, motility, and cytokinesis. In this review, we examine the critical role phosphoinositides play in these processes to execute the establishment and maintenance of cellular architecture. Epithelial tissues perform essential barrier and transport functions in almost all major organs. Key to their development and function is the establishment of epithelial cell polarity. We place a special emphasis on highlighting recent studies demonstrating phosphoinositide regulation of epithelial cell polarity and how individual cells use phosphoinositides to further organize into epithelial tissues.     

Isolation of Mammary Epithelial Cells from Three-dimensional Mixed-cell Spheroid Co-culture

While enormous efforts have gone into identifying signaling pathways and molecules involved in normal and malignant cell behaviors^1-2, much of this work has been done using classical two-dimensional cell culture models, which allow for easy cell manipulation. It has become clear that intracellular signaling pathways are affected by extracellular forces, including dimensionality and cell surface tension^3-4. Multiple approaches have been taken to develop three-dimensional models that more accurately represent biologic tissue architecture³. While these models incorporate multi-dimensionality and architectural stresses, study of the consequent effects on cells is less facile than in two-dimensional tissue culture due to the limitations of the models and the difficulty in extracting cells for subsequent analysis.The important role of the microenvironment around tumors in tumorigenesis and tumor behavior is becoming increasingly recognized⁴. Tumor stroma is composed of multiple cell types and extracellular molecules. During tumor development there are bidirectional signals between tumor cells and stromal cells⁵. Although some factors participating in tumor-stroma co-evolution have been identified, there is still a need to develop simple techniques to systematically identify and study the full array of these signals⁶. Fibroblasts are the most abundant cell type in normal or tumor-associated stromal tissues, and contribute to deposition and maintenance of basement membrane and paracrine growth factors⁷.Many groups have used three dimensional culture systems to study the role of fibroblasts on various cellular functions, including tumor response to therapies, recruitment of immune cells, signaling molecules, proliferation, apoptosis, angiogenesis, and invasion^8-15. We have optimized a simple method for assessing the effects of mammary fibroblasts on mammary epithelial cells using a commercially available extracellular matrix model to create three-dimensional cultures of mixed cell populations (co-cultures)^16-22. With continued co-culture the cells form spheroids with the fibroblasts clustering in the interior and the epithelial cells largely on the exterior of the spheroids and forming multi-cellular projections into the matrix. Manipulation of the fibroblasts that leads to altered epithelial cell invasiveness can be readily quantified by changes in numbers and length of epithelial projections²³. Furthermore, we have devised a method for isolating epithelial cells out of three-dimensional co-culture that facilitates analysis of the effects of fibroblast exposure on epithelial behavior. We have found that the effects of co-culture persist for weeks after epithelial cell isolation, permitting ample time to perform multiple assays. This method is adaptable to cells of varying malignant potential and requires no specialized equipment. This technique allows for rapid evaluation of in vitro cell models under multiple conditions, and the corresponding results can be compared to in vivo animal tissue models as well as human tissue samples.     

The mechanical basis of cell rearrangement. I. Epithelial morphogenesis during Fundulus epiboly

Many morphogenetic processes are accomplished by coordinated cell rearrangements. These rearrangements are accompanied by substantial shifts in the neighbor relationships between cells. Here we propose a model for studying morphogenesis in epithelial sheets by directed cell neighbor change. Our model describes cell rearrangements by accounting for the balance of forces between neighboring cells within an epithelium. Cell rearrangement and cell shape changes occur when these forces are not in mechanical equilibrium. We will show that cell rearrangement within the epidermal enveloping layer (EVL) of the teleost fish Fundulus during epiboly can be explained solely in terms of the balance of forces generated among constituent epithelial cells. Within a cell, we account for circumferential elastic forces and the force generated by hydrostatic and osmotic pressure. The model treats epithelial cells as two-dimensional polygons where the mechanical forces are applied to the polygonal nodes. A cell node protrudes or contracts when the nodal forces are not in mechanical equilibrium. In an epithelial sheet, adjacent cells share common boundary nodes; in this way, mechanical force is transmitted from cell to cell, mimicking junctional coupling. These junctional nodes can slide, and nodes may appear or disappear, so that the number of polygonal sides is variable. Computer graphics allows us to compare numerical simulations of the model with time-lapse cinemicroscopy of cell rearrangements in the living embryo, and data obtained from fixed and silver stained embryos. By manipulating the mechanical properties of the model cells we can study the conditions necessary to reproduce normal cell behavior during Fundulus epiboly. We find that simple stress relaxation is sufficient to account for cell rearrangements among interior cells of the EVL when they are isotropically contractile. Experimental observations show that the number of EVL marginal cells continuously decreases throughout epiboly. In order for the simulation to reproduce this behavior, cells at the EVL boundary must generate protrusive forces rather than contractile tension forces. Therefore, the simulation results suggest that the mechanical properties of EVL marginal cells at their leading edge must be quite different from EVL interior cells.     

Epithelial machines that shape the embryo

Embryonic form and the shape of many organs are the product of forces acting within and on epithelial sheets. Analysis of these processes requires both consideration of the mechanical operation of these multicellular machines and an understanding of how epithelial sheets are integrated with surrounding tissues. From the diverse array of epithelial morphogenetic movements seen during embryogenesis we review examples of epithelial sheet bending, Drosophila ventral furrow formation and ascidian gastrulation, and direct measurements of epithelial mechanics from Xenopus laevis. We present these examples as works-in-progress and highlight opportunities for future studies into both the direct consequence of force production and embryonic tissue mechanics and potential roles of signaling from biomechanical processes.