The emergence of geometric order in proliferating metazoan epithelia

The interplay between cell signalling and mechanics in developmental processes

Force production and the propagation of stress and strain within embryos and organisms are crucial physical processes that direct morphogenesis. In addition, there is mounting evidence that biomechanical cues created by these processes guide cell behaviours and cell fates. In this Review we discuss key roles for biomechanics during development to directly shape tissues, to provide positional information for cell fate decisions and to enable robust programmes of development. Several recently identified molecular mechanisms suggest how cells and tissues might coordinate their responses to biomechanical cues. Finally, we outline long-term challenges in integrating biomechanics with genetic analysis of developing embryos.

Investigating biocomplexity through the agent-based paradigm

Capturing the dynamism that pervades biological systems requires a computational approach that can accommodate both the continuous features of the system environment as well as the flexible and heterogeneous nature of component interactions. This presents a serious challenge for the more traditional mathematical approaches that assume component homogeneity to relate system observables using mathematical equations. While the homogeneity condition does not lead to loss of accuracy while simulating various continua, it fails to offer detailed solutions when applied to systems with dynamically interacting heterogeneous components. As the functionality and architecture of most biological systems is a product of multi-faceted individual interactions at the sub-system level, continuum models rarely offer much beyond qualitative similarity. Agent-based modelling is a class of algorithmic computational approaches that rely on interactions between Turing-complete finite-state machines--or agents--to simulate, from the bottom-up, macroscopic properties of a system. In recognizing the heterogeneity condition, they offer suitable ontologies to the system components being modelled, thereby succeeding where their continuum counterparts tend to struggle. Furthermore, being inherently hierarchical, they are quite amenable to coupling with other computational paradigms. The integration of any agent-based framework with continuum models is arguably the most elegant and precise way of representing biological systems. Although in its nascence, agent-based modelling has been utilized to model biological complexity across a broad range of biological scales (from cells to societies). In this article, we explore the reasons that make agent-based modelling the most precise approach to model biological systems that tend to be non-linear and complex.

Topological progression in proliferating epithelia is driven by a unique variation in polygon distribution

Morphogenesis is consequence of lots of small coordinated variations that occur during development. In proliferating stages, tissue growth is coupled to changes in shape and organization. A number of studies have analyzed the topological properties of proliferating epithelia using the Drosophila wing disc as a model. These works are based in the existence of a fixed distribution of these epithelial cells according to their number of sides. Cell division, cell rearrangements or a combination of both mechanisms have been proposed to be responsible for this polygonal assembling. Here, we have used different system biology methods to compare images from two close proliferative stages that present high morphological similarity. This approach enables us to search for traces of epithelial organization. First, we show that geometrical and network characteristics of individual cells are mainly dependent on their number of sides. Second, we find a significant divergence between the distribution of polygons in epithelia from mid-third instar larva versus early prepupa. We show that this alteration propagates into changes in epithelial organization. Remarkably, only the variation in polygon distribution driven by morphogenesis leads to progression in epithelial organization. In addition, we identify the relevant features that characterize these rearrangements. Our results reveal signs of epithelial homogenization during the growing phase, before the planar cell polarity pathway leads to the hexagonal packing of the epithelium during pupal stages.

Differential proliferation rates generate patterns of mechanical tension that orient tissue growth

Orientation of cell divisions is a key mechanism of tissue morphogenesis. In the growing Drosophila wing imaginal disc epithelium, most of the cell divisions in the central wing pouch are oriented along the proximal-distal (P-D) axis by the Dachsous-Fat-Dachs planar polarity pathway. However, cells at the periphery of the wing pouch instead tend to orient their divisions perpendicular to the P-D axis despite strong Dachs polarization. Here, we show that these circumferential divisions are oriented by circumferential mechanical forces that influence cell shapes and thus orient the mitotic spindle. We propose that this circumferential pattern of force is not generated locally by polarized constriction of individual epithelial cells. Instead, these forces emerge as a global tension pattern that appears to originate from differential rates of cell proliferation within the wing pouch. Accordingly, we show that localized overgrowth is sufficient to induce neighbouring cell stretching and reorientation of cell division. Our results suggest that patterned rates of cell proliferation can influence tissue mechanics and thus determine the orientation of cell divisions and tissue shape.

Polarity, cell division, and out-of-equilibrium dynamics control the growth of epithelial structures

The growth of a well-formed epithelial structure is governed by mechanical constraints, cellular apico-basal polarity, and spatially controlled cell division. Here we compared the predictions of a mathematical model of epithelial growth with the morphological analysis of 3D epithelial structures. In both in vitro cyst models and in developing epithelial structures in vivo, epithelial growth could take place close to or far from mechanical equilibrium, and was determined by the hierarchy of time-scales of cell division, cell-cell rearrangements, and lumen dynamics. Equilibrium properties could be inferred by the analysis of cell-cell contact topologies, and the nonequilibrium phenotype was altered by inhibiting ROCK activity. The occurrence of an aberrant multilumen phenotype was linked to fast nonequilibrium growth, even when geometric control of cell division was correctly enforced. We predicted and verified experimentally that slowing down cell division partially rescued a multilumen phenotype induced by altered polarity. These results improve our understanding of the development of epithelial organs and, ultimately, of carcinogenesis.

Mechanical control of organ size in the development of the Drosophila wing disc

Control of cessation of growth in developing organs has recently been proposed to be influenced by mechanical forces acting on the tissue due to its growth. In particular, it was proposed that stretching of the tissue leads to an increase in cell proliferation. Using the model system of the Drosophila wing imaginal disc, we directly stretch the tissue finding a significant increase in cell proliferation, thus confirming this hypothesis. In addition, we characterize the growth over the entire growth period of the wing disc finding a correlation between the apical cell area and cell proliferation rate.

PACS numbers: 87.19.lx, 87.18.Nq, 87.80.Ek, 87.17.Ee, 87.85.Xd

A global pattern of mechanical stress polarizes cell divisions and cell shape in the growing Drosophila wing disc

Organismal development is under genetic control. Ultimately, mechanical forces shape embryos. If we want to understand the precise regulation of size and shape in animals, we must dissect how forces are distributed in developing tissues, and how they drive cell behavior to shape organs. This has not been addressed fully in the context of growing tissues. As cells grow and divide, they exert a pressure on their neighbors. How these local stresses add up or dissipate as the tissue grows is an unanswered question. We address this issue in the growing wing imaginal disc of Drosophila larvae, the precursor of the adult wing. We used a quantitative approach to analyze the strains and stresses of cells of the wing pouch, and found a global pattern of stress whereby cells in the periphery of the tissue are mechanically stretched and cells in the center are compressed. This pattern has important consequences on cell shape in the wing pouch: cells respond to it by polarizing their acto-myosin cortex, and aligning their divisions with the main axis of cell stretch, thereby polarizing tissue growth. Ectopic perturbations of tissue growth by the Hippo signaling pathway reorganize this pattern in a non-autonomous manner, suggesting a synergy between tissue mechanics and growth control during wing disc morphogenesis.

Epithelial junctions maintain tissue architecture by directing planar spindle orientation

During epithelial cell proliferation, planar alignment of the mitotic spindle coordinates the local process of symmetric cell cleavage with the global maintenance of polarized tissue architecture. Although the disruption of planar spindle alignment is proposed to cause epithelial to mesenchymal transition and cancer, the in vivo mechanisms regulating mitotic spindle orientation remain elusive. Here we demonstrate that the actomyosin cortex and the junction-localized neoplastic tumour suppressors Scribbled and Discs large 1 have essential roles in planar spindle alignment and thus the control of epithelial integrity in the Drosophila imaginal disc. We show that defective alignment of the mitotic spindle correlates with cell delamination and apoptotic death, and that blocking the death of misaligned cells is sufficient to drive the formation of basally localized tumour-like masses. These findings indicate a key role for junction-mediated spindle alignment in the maintenance of epithelial integrity, and also reveal a previously unknown cell-death-mediated tumour-suppressor function inherent in the polarized architecture of epithelia.

Mechanics of epithelial tissue homeostasis and morphogenesis

Epithelia are robust tissues that support the structure of embryos and organs and serve as effective barriers against pathogens. Epithelia also chemically separate different physiological environments. These vital functions require tight association between cells through the assembly of junctions that mechanically stabilize the tissue. Remarkably, epithelia are also dynamic and can display a fluid behavior. Cells continuously die or divide, thereby allowing functional tissue homeostasis. Epithelial cells can change shape or intercalate as tissues deform during morphogenesis. We review the mechanical basis of tissue robustness and fluidity, with an emphasis on the pivotal role of junction dynamics. Tissue fluidity emerges from local active stresses acting at cell interfaces and allows the maintenance of epithelial organization during morphogenesis and tissue renewal.

Cooperation and competition in the dynamics of tissue architecture during homeostasis and tumorigenesis

The construction of a network of cell-to-cell contacts makes it possible to characterize the patterns and spatial organization of tissues. Such networks are highly dynamic, depending on the changes of the tissue architecture caused by cell division, death and migration. Local competitive and cooperative cell-to-cell interactions influence the choices cells make. We review the literature on quantitative data of epithelial tissue topology and present a dynamical network model that can be used to explore the evolutionary dynamics of a two dimensional tissue architecture with arbitrary cell-to-cell interactions. In particular, we show that various forms of experimentally observed types of interactions can be modelled using game theory. We discuss a model of cooperative and non-cooperative cell-to-cell communication that can capture the interplay between cellular competition and tissue dynamics. We conclude with an outlook on the possible uses of this approach in modelling tumorigenesis and tissue homeostasis.

PTEN controls junction lengthening and stability during cell rearrangement in epithelial tissue

Planar cell rearrangements control epithelial tissue morphogenesis and cellular pattern formation. They lead to the formation of new junctions whose length and stability determine the cellular pattern of tissues. Here, we show that during Drosophila wing development the loss of the tumor suppressor PTEN disrupts cell rearrangements by preventing the lengthening of newly formed junctions that become unstable and keep on rearranging. We demonstrate that the failure to lengthen and to stabilize is caused by the lack of a decrease of Myosin II and Rho-kinase concentration at the newly formed junctions. This defect results in a heterogeneous cortical contractility at cell junctions that disrupts regular hexagonal pattern formation. By identifying PTEN as a specific regulator of junction lengthening and stability, our results uncover how a homogenous distribution of cortical contractility along the cell cortex is restored during cell rearrangement to control the formation of epithelial cellular pattern.

A high-throughput template for optimizing Drosophila organ culture with response-surface methods

The Drosophila wing imaginal disc is a key model organ for molecular developmental genetics. Wing disc studies are generally restricted to end-point analyses of fixed tissues. Recently several studies have relied on limited data from discs cultured in uncharacterized conditions. Systematic efforts towards developing Drosophila organ culture techniques are becoming crucial for further progress. Here, we have designed a multi-tiered, high-throughput pipeline that employs design-of-experiment methods to design a culture medium for wing discs. The resulting formula sustains high levels of proliferation for more than 12 hours. This approach results in a statistical model of proliferation as a function of extrinsic growth supplements and identifies synergies that improve insulin-stimulated growth. A more dynamic view of organogenesis emerges from the optimized culture system that highlights important facets of growth: spatiotemporal clustering of cell divisions and cell junction rearrangements. The same approach could be used to improve culture conditions for other organ systems.

Simulation of cellular packing in non-proliferative epithelia

The physical laws governing the morphogenesis of biological tissues remain largely misunderstood. In particular, the role of the mechanical interactions occurring in this process needs to be better understood and studied. Inner follicular cells surrounding the oocytes of Ciona intestinalis form an epithelial monolayer resulting from an accretion process (without mitosis or apoptosis). This epithelium is elementary and useful for morphogenesis studies: the cells exhibit polygon packing with a specific but non-systematically repeatable topology (i.e. the distribution of pentagons, hexagons and heptagons changes). To understand the role of mechanical forces in tissue formation, we propose an innovative "2D spherical" model based on the physics of divided media. This approach simulates the cellular mechanical behavior and epithelium structuration by allowing cells to adopt a large variety of shapes and to self-organize in response to mechanical interactions. The numerical parameters considered in the model are derived from experimental data in order to perform pertinent and realistic simulations. The results obtained are compared to biological observations using the same counting method to characterize epithelium topology. Numerical and experimental data appear close enough to validate the model. It is then used for exploratory studies dealing with "Tissue Development Speed" variation, which is not easily attainable by experimentation. We show that the formation speed of the tissue influences its topology and hence its packing organization.

Crocodile Head Scales Are Not Developmental Units But Emerge from Physical Cracking

Various lineages of amniotes display keratinized skin appendages (feathers, hairs, and scales) that differentiate in the embryo from genetically controlled developmental units whose spatial organization is patterned by reaction-diffusion mechanisms (RDMs). We show that, contrary to skin appendages in other amniotes (as well as body scales in crocodiles), face and jaws scales of crocodiles are random polygonal domains of highly keratinized skin, rather than genetically controlled elements, and emerge from a physical self-organizing stochastic process distinct from RDMs: cracking of the developing skin in a stress field. We suggest that the rapid growth of the crocodile embryonic facial and jaw skeleton, combined with the development of a very keratinized skin, generates the mechanical stress that causes cracking.

[Regulation of intercellular adhesion during epithelial morphogenesis]

The epithelium is one of the most abundant tissues in metazoans. It is required to generate stable chemical and mechanical barriers between physiological compartments (fluid matrix/external environment). This function is based on multiple intercellular junctions, which insulate and stabilize cell-cell contacts in the tissue. Despite this apparent robustness, epithelia can be extensively remodeled during wound healing, embryogenesis and tumor progression. The capacity to be remodeled while keeping tissue cohesion requires a perfect balance between stability and plasticity of intercellular junctions. The balance is partially regulated by intercellular adhesion, which is mostly based on adherens junctions and the transmembrane protein E-cadherin. The aim of this review is to report the molecular basis of the balance between plasticity and robustness in the epithelium. We will first present the minimal physical framework used to describe epithelial cell shape. We will then describe the main processes involved in intercellular adhesion regulation and their functions during epithelial morphogenesis. Eventually, we will analyze the relationship and the coupling between adhesive forces and cortical tension.

A mathematical model to study the dynamics of epithelial cellular networks

Epithelia are sheets of connected cells that are essential across the animal kingdom. Experimental observations suggest that the dynamical behavior of many single-layered epithelial tissues has strong analogies with that of specific mechanical systems, namely large networks consisting of point masses connected through spring-damper elements and undergoing the influence of active and dissipating forces. Based on this analogy, this work develops a modeling framework to enable the study of the mechanical properties and of the dynamic behavior of large epithelial cellular networks. The model is built first by creating a network topology that is extracted from the actual cellular geometry as obtained from experiments, then by associating a mechanical structure and dynamics to the network via spring-damper elements. This scalable approach enables running simulations of large network dynamics: the derived modeling framework in particular is predisposed to be tailored to study general dynamics (for example, morphogenesis) of various classes of single-layered epithelial cellular networks. In this contribution, we test the model on a case study of the dorsal epithelium of the Drosophila melanogaster embryo during early dorsal closure (and, less conspicuously, germband retraction).

Epithelial machines of morphogenesis and their potential application in organ assembly and tissue engineering

Sheets of embryonic epithelial cells coordinate their efforts to create diverse tissue structures such as pits, grooves, tubes, and capsules that lead to organ formation. Such cells can use a number of cell behaviors including contractility, proliferation, and directed movement to create these structures. By contrast, tissue engineers and researchers in regenerative medicine seeking to produce organs for repair or replacement therapy can combine cells with synthetic polymeric scaffolds. Tissue engineers try to achieve these goals by shaping scaffold geometry in such a way that cells embedded within these scaffold self-assemble to form a tissue, for instance aligning to synthetic fibers, and assembling native extracellular matrix to form the desired tissue-like structure. Although self-assembly is a dominant process that guides tissue assembly both within the embryo and within artificial tissue constructs, we know little about these critical processes. Here, we compare and contrast strategies of tissue assembly used by embryos to those used by engineers during epithelial morphogenesis and highlight opportunities for future applications of developmental biology in the field of tissue engineering.

Statistical topology of cellular networks in two and three dimensions

Cellular networks may be found in a variety of natural contexts, from soap foams to biological tissues to grain boundaries in a polycrystal, and the characterization of these structures is therefore a subject of interest to a range of disciplines. An approach to describe the topology of a cellular network in two and three dimensions is presented. This allows for the quantification of a variety of features of the cellular network, including a quantification of topological disorder and a robust measure of the statistical similarity or difference of a set of structures. The results of this analysis are presented for numerous simulated systems including the Poisson-Voronoi and the steady-state grain growth structures in two and three dimensions.

In-vivo imaging of the Drosophila wing imaginal disc over time: novel insights on growth and boundary formation

In developmental biology, the sequence of gene induction and pattern formation is best studied over time as an organism develops. However, in the model system of Drosophila larvae this oftentimes proves difficult due to limitations in imaging capabilities. Using the larval wing imaginal disc, we show that both overall growth, as well as the creation of patterns such as the distinction between the anterior(A) and posterior(P) compartments and the dorsal(D) and ventral(V) compartments can be studied directly by imaging the wing disc as it develops inside a larva. Imaged larvae develop normally, as can be seen by the overall growth curve of the wing disc. Yet, the fact that we can follow the development of individual discs through time provides the opportunity to simultaneously assess individual variability. We for instance find that growth rates can vary greatly over time. In addition, we observe that mechanical forces act on the wing disc within the larva at times when there is an increase in growth rates. Moreover, we observe that A/P boundary formation follows the established sequence and a smooth boundary is present from the first larval instar on. The division of the wing disc into a dorsal and a ventral compartment, on the other hand, develops quite differently. Contrary to expectation, the specification of the dorsal compartment starts with only one or two cells in the second larval instar and a smooth boundary is not formed until the third larval instar.

Mechanisms of regulating cell topology in proliferating epithelia: impact of division plane, mechanical forces, and cell memory

Regulation of cell growth and cell division has a fundamental role in tissue formation, organ development, and cancer progression. Remarkable similarities in the topological distributions were found in a variety of proliferating epithelia in both animals and plants. At the same time, there are species with significantly varied frequency of hexagonal cells. Moreover, local topology has been shown to be disturbed on the boundary between proliferating and quiescent cells, where cells have fewer sides than natural proliferating epithelia. The mechanisms of regulating these topological changes remain poorly understood. In this study, we use a mechanical model to examine the effects of orientation of division plane, differential proliferation, and mechanical forces on animal epithelial cells. We find that regardless of orientation of division plane, our model can reproduce the commonly observed topological distributions of cells in natural proliferating animal epithelia with the consideration of cell rearrangements. In addition, with different schemes of division plane, we are able to generate different frequency of hexagonal cells, which is consistent with experimental observations. In proliferating cells interfacing quiescent cells, our results show that differential proliferation alone is insufficient to reproduce the local changes in cell topology. Rather, increased tension on the boundary, in conjunction with differential proliferation, can reproduce the observed topological changes. We conclude that both division plane orientation and mechanical forces play important roles in cell topology in animal proliferating epithelia. Moreover, cell memory is also essential for generating specific topological distributions.

Integrating force-sensing and signaling pathways in a model for the regulation of wing imaginal disc size

The regulation of organ size constitutes a major unsolved question in developmental biology. The wing imaginal disc of Drosophila serves as a widely used model system to study this question. Several mechanisms have been proposed to have an impact on final size, but they are either contradicted by experimental data or they cannot explain a number of key experimental observations and may thus be missing crucial elements. We have modeled a regulatory network that integrates the experimentally confirmed molecular interactions underlying other available models. Furthermore, the network includes hypothetical interactions between mechanical forces and specific growth regulators, leading to a size regulation mechanism that conceptually combines elements of existing models, and can be understood in terms of a compression gradient model. According to this model, compression increases in the center of the disc during growth. Growth stops once compression levels in the disc center reach a certain threshold and the compression gradient drops below a certain level in the rest of the disc. Our model can account for growth termination as well as for the paradoxical observation that growth occurs uniformly in the presence of a growth factor gradient and non-uniformly in the presence of a uniform growth factor distribution. Furthermore, it can account for other experimental observations that argue either in favor or against other models. The model also makes specific predictions about the distribution of cell shape and size in the developing disc, which we were able to confirm experimentally.

Discontinuities in Rap1 activity determine epithelial cell morphology within the developing wing of Drosophila

Mechanisms that govern cell-fate specification within developing epithelia have been intensely investigated, with many of the critical intercellular signaling pathways identified, and well characterized. Much less is known, however, about downstream events that drive the morphological differentiation of these cells, once their fate has been determined. In the Drosophila wing-blade epithelium, two cell types predominate: vein and intervein. After cell proliferation is complete and adhesive cell-cell contacts have been refined, the vast majority of intervein cells adopt a hexagonal morphology. Within vein territories, however, cell-shape refinement results in trapezoids. Signaling events that differentiate between vein and intervein cell fates are well understood, but the genetic pathways underlying vein/intervein cyto-architectural differences remain largely undescribed. We show here that the Rap1 GTPase plays a critical role in determining cell-type-specific morphologies within the developing wing epithelium. Rap1, together with its effector Canoe, promotes symmetric distribution of the adhesion molecule DE-cadherin about the apicolateral circumference of epithelial cells. We provide evidence that in presumptive vein tissue Rap1/Canoe activity is down-regulated, resulting in adhesive asymmetries and non-hexagonal cell morphologies. In particular Canoe levels are reduced in vein cells as they morphologically differentiate. We also demonstrate that over-expression of Rap1 disrupts vein formation both in the developing epithelium and the adult wing blade. Therefore, vein/intervein morphological differences result, at least in part, from the patterned regulation of Rap1 activity.

Size-topology relations in packings of grains, emulsions, foams, and biological cells

Particulate packings in 3D are used to study the effects of compression and polydispersity on the geometry of the tiling in these systems. We find that the dependence of the neighbor number on cell size is quasilinear in the monodisperse case and becomes nonlinear above a threshold polydispersity, independent of the method of creation of the tiling. These size-topology relations can be described by a simple analytical theory, which quantifies the effects of positional disorder in the monodisperse case and those of size disorder in the polydisperse case and is applicable in two and three dimensions. The theory thus gives a unifying framework for a wide range of amorphous systems, ranging from biological tissues, foams, and bidisperse disks to compressed emulsions and granular matter.

Mechanical forces mediate localized topological change in epithelia

Regulation of cell growth and proliferation has a fundamental role in tissue development, organogenesis, and disease progression. Conserved distribution of the number of sides of cells with a mean value of six was found in a variety of proliferating epithelia. Previous studies have shown that clones of proliferating cells bounded by quiescent cells have fewer sides than normal epithelia. However, the mechanisms for mediating such localized topological change remain poorly understood. In this study, we use a two-dimensional vertex model with consideration of mechanical forces to investigate how differential proliferation and forces can influence cell shape and tissue morphogenesis, and how they may lead to distorted topological change. We find that differential proliferation alone is insufficient to affect the topology of boundary proliferating cells. Rather, increased surface tension on the boundary, in addition to differential proliferation, can significantly decrease the average number of cell sides. Our results are consistent with experimental observations. We conclude that mechanical forces in addition to localized differential proliferation are required to produce the distorted topological change which significantly impacts the overall cell shape and tissue morphogenesis.

ROCK1 and ROCK2 regulate epithelial polarisation and geometric cell shape

BACKGROUND INFORMATION

Cell-cell adhesion and contraction play an essential role in the maintenance of geometric shape and polarisation of epithelial cells. However, the molecular regulation of contraction during cell elongation leading to epithelial polarisation and acquisition of geometric cell shape is not clear.

RESULTS

Upon induction of cell-cell adhesion, we find that human keratinocytes acquire specific geometric shapes favouring hexagons, by re-modelling junction length/orientation and thus neighbour allocation. Acquisition of geometric shape correlates temporally with epithelial polarisation, as shown by an increase in lateral height. ROCK1 and ROCK2 are important regulators of myosin II contraction, but their specific role in epithelial cell shape has not been addressed. Depletion of ROCK proteins interferes with the correct proportion of hexagonal cell shapes and full elongation of lateral domain. Interestingly, ROCK proteins are not essential for maintenance of circumferential thin bundles, the main contractile epithelial F-actin pool. Instead, ROCK1 or ROCK2 regulates thin bundle contraction and positioning along the lateral domain, an important event for the stabilisation of the elongating lateral domain. Mechanistically, E-cadherin clustering specifically leads to ROCK1/ROCK2-dependent inactivation of myosin phosphatase and phosphorylation of myosin regulatory light chain. These events correlate temporally with the increase in lateral height and thin bundle compaction towards junctions.

CONCLUSION

We conclude that ROCK proteins are necessary for acquisition of elongated and geometric cell shape, two key events for epithelial differentiation.

Ka-me: a Voronoi image analyzer

Summary: Ka-me is a Voronoi image analyzer that allows users to analyze any image with a convex polygonal tessellation or any spatial point distribution by fitting Voronoi polygons and their dual, Delaunay triangulations, to the pattern. The analytical tools include a variety of graph theoretic and geometric tools that summarize the distribution of the numbers of edges per face, areas, perimeters, angles of Delaunay triangle edges (anglograms), Gabriel graphs, nearest neighbor graphs, minimal spanning trees, Ulam trees, Pitteway tests, circumcircles and convexhulls, as well as spatial statistics (Clark–Evans Nearest Neighborhood and Variance to Mean Ratio) and export functions for standard relationships (Lewis's Law, Desch's Law and Aboav–Weaire Law).

Availability: Ka-me: a Voronoi image analyzer is available as an executable with documentation and sample applications from the BioQUEST Library (http://bioquest.org/downloads/kame_1.0.rar).

Contact:noppadon.khiripet@nectec.or.th

Sculpting organs: mechanical regulation of tissue development

The ramified architectures of organs such as the mammary gland and lung are generated via branching morphogenesis, a developmental process through which individual cells bud and pinch off of pre-existing epithelial sheets. Although specified by signaling programs, organ development requires integration of all aspects of the microenvironment. We describe the essential role of endogenous cellular contractility in the formation of branching tubes. We also highlight the role of exogenous forces in normal and aberrant branching.

Tropomodulin 1 constrains fiber cell geometry during elongation and maturation in the lens cortex

Lens fiber cells exhibit a high degree of hexagonal packing geometry, determined partly by tropomodulin 1 (Tmod1), which stabilizes the spectrin-actin network on lens fiber cell membranes. To ascertain whether Tmod1 is required during epithelial cell differentiation to fiber cells or during fiber cell elongation and maturation, the authors quantified the extent of fiber cell disorder in the Tmod1-null lens and determined locations of disorder by confocal microscopy and computational image analysis. First, nearest neighbor analysis of fiber cell geometry in Tmod1-null lenses showed that disorder is confined to focal patches. Second, differentiating epithelial cells at the equator aligned into ordered meridional rows in Tmod1-null lenses, with disordered patches first observed in elongating fiber cells. Third, as fiber cells were displaced inward in Tmod1-null lenses, total disordered area increased due to increased sizes (but not numbers) of individual disordered patches. The authors conclude that Tmod1 is required first to coordinate fiber cell shapes and interactions during tip migration and elongation and second to stabilize ordered fiber cell geometry during maturation in the lens cortex. An unstable spectrin-actin network without Tmod1 may result in imbalanced forces along membranes, leading to fiber cell rearrangements during elongation, followed by propagation of disorder as fiber cells mature.

Multi-cellular rosettes in the mouse visceral endoderm facilitate the ordered migration of anterior visceral endoderm cells

The visceral endoderm (VE) is a simple epithelium that forms the outer layer of the egg-cylinder stage mouse embryo. The anterior visceral endoderm (AVE), a specialised subset of VE cells, is responsible for specifying anterior pattern. AVE cells show a stereotypic migratory behaviour within the VE, which is responsible for correctly orientating the anterior-posterior axis. The epithelial integrity of the VE is maintained during the course of AVE migration, which takes place by intercalation of AVE and other VE cells. Though a continuous epithelial sheet, the VE is characterised by two regions of dramatically different behaviour, one showing robust cell movement and intercalation (in which the AVE migrates) and one that is static, with relatively little cell movement and mixing. Little is known about the cellular rearrangements that accommodate and influence the sustained directional movement of subsets of cells (such as the AVE) within epithelia like the VE. This study uses an interdisciplinary approach to further our understanding of cell movement in epithelia. Using both wild-type embryos as well as mutants in which AVE migration is abnormal or arrested, we show that AVE migration is specifically linked to changes in cell packing in the VE and an increase in multi-cellular rosette arrangements (five or more cells meeting at a point). To probe the role of rosettes during AVE migration, we develop a mathematical model of cell movement in the VE. To do this, we use a vertex-based model, implemented on an ellipsoidal surface to represent a realistic geometry for the mouse egg-cylinder. The potential for rosette formation is included, along with various junctional rearrangements. Simulations suggest that while rosettes are not essential for AVE migration, they are crucial for the orderliness of this migration observed in embryos. Our simulations are similar to results from transgenic embryos in which Planar Cell Polarity (PCP) signalling is disrupted. Such embryos have significantly reduced rosette numbers, altered epithelial packing, and show abnormalities in AVE migration. Our results show that the formation of multi-cellular rosettes in the mouse VE is dependent on normal PCP signalling. Taken together, our model and experimental observations suggest that rosettes in the VE epithelium do not form passively in response to AVE migration. Instead, they are a PCP-dependent arrangement of cells that acts to buffer the disequilibrium in cell packing generated in the VE by AVE migration, enabling AVE cells to migrate in an orderly manner.

INTEGRATING MECHANICAL CONTROL THEORY INTO MODELS OF BIOLOGICAL DEVELOPMENT — ANALYTICAL REVIEW

This paper presents both a general review on developmental biomechanics and a concrete proposition for the computation of a symmetry breaking instability of a model of biological development in terms of self-organization theory. The necessary biological and physical facts taken from the literature are described and discussed in the context of a unified statement of the problems for mathematical modeling of pattern formation. This is then applied to planar cell polarization (PCP) of the Drosophila wing. In this way, the process is modeled by an elastopolarization equation. In terms of this statement, the mechanical specificity (interaction with basal plate) of wing PCP is characterized. Some aspects of modeling somite formation as well as other developmental processes are also concerned.

Analytical results for size-topology correlations in 2D disk and cellular packings

Random tilings or packings in the plane are characterized by a size distribution of individual elements (domains) and by the statistics of neighbor relations between the domains. Most systems occurring in nature or technology have a unimodal distribution of both areas and number of neighbors. Empirically, strong correlations between these distributions have been observed and formulated as universal laws. Using only the local, correlation-free granocentric model approach with no free parameters, we construct accurate analytical descriptions for disk crystallization, size-topology correlations, and Lemaître's law.

Normal morphogenesis of epithelial tissues and progression of epithelial tumors

Epithelial cells organize into various tissue architectures that largely maintain their structure throughout the life of an organism. For decades, the morphogenesis of epithelial tissues has fascinated scientists at the interface of cell, developmental, and molecular biology. Systems biology offers ways to combine knowledge from these disciplines by building integrative models that are quantitative and predictive. Can such models be useful for gaining a deeper understanding of epithelial morphogenesis? Here, we take inventory of some recurring themes in epithelial morphogenesis that systems approaches could strive to capture. Predictive understanding of morphogenesis at the systems level would prove especially valuable for diseases such as cancer, where epithelial tissue architecture is profoundly disrupted.

Epithelial organisation revealed by a network of cellular contacts

The emergence of differences in the arrangement of cells is the first step towards the establishment of many organs. Understanding this process is limited by the lack of systematic characterization of epithelial organisation. Here we apply network theory at the scale of individual cells to uncover patterns in cell-to-cell contacts that govern epithelial organisation. We provide an objective characterization of epithelia using network representation where cells are nodes and cell contacts are links. The features of individual cells, together with attributes of the cellular network produce a defining signature that distinguishes epithelia from different organs, species, developmental stages and genetic conditions. The approach permits characterization, quantification and classification of normal and perturbed epithelia and establishes a framework for understanding molecular mechanisms that underpin the architecture of complex tissues.

Dynamic ordering of nuclei in syncytial embryos: a quantitative analysis of the role of cytoskeletal networks

In syncytial embryos nuclei undergo cycles of division and rearrangement within a common cytoplasm. It is presently unclear to what degree and how the nuclear array maintains positional order in the face of rapid cell divisions. Here we establish a quantitative assay, based on image processing, for analysing the dynamics of the nuclear array. By tracking nuclear trajectories in Drosophila melanogaster embryos, we are able to define and evaluate local and time-dependent measures for the level of geometrical order in the array. We find that after division, order is re-established in a biphasic manner, indicating the competition of different ordering processes. Using mutants and drug injections, we show that the order of the nuclear array depends on cytoskeletal networks organised by centrosomes. While both f-actin and microtubules are required for re-establishing order after mitosis, only f-actin is required to maintain the stability of this arrangement. Furthermore, f-actin function relies on myosin-independent non-contractile filaments that suppress individual nuclear mobility, whereas microtubules promote mobility and attract adjacent nuclei. Actin caps are shown to act to prevent nuclear incorporation into adjacent microtubule baskets. Our data demonstrate that two principal ordering mechanisms thus simultaneously contribute: (1) a passive crowding mechanism in which nuclei and actin caps act as spacers and (2) an active self-organisation mechanism based on a microtubule network.

Differential adhesion and actomyosin cable collaborate to drive Echinoid-mediated cell sorting

Cell sorting involves the segregation of two cell populations into `immiscible' adjacent tissues with smooth borders. Echinoid (Ed), a nectin ortholog, is an adherens junction protein in Drosophila, and cells mutant for ed sort out from the surrounding wild-type cells. However, it remains unknown which factors trigger cell sorting. Here, we dissect the sequence of this process and find that cell sorting occurs when differential expression of Ed triggers the assembly of actomyosin cable. Conversely, Ed-mediated cell sorting can be rescued by recruitment of Ed, via homophilic or heterophilic interactions, to the wild-type cell side of the clonal interface, even when differential Ed expression persists. We found, unexpectedly, that when actomyosin cable was largely absent, differential adhesion was sufficient to cause limited cell segregation but with a jagged tissue border (imperfect sorting). We propose that Ed-mediated cell sorting is driven both by differential Ed adhesion that induces cell segregation with a jagged border and by actomyosin cable assembly at the interface that smoothens this border.

Origins of cellular geometry

Cells are highly complex and orderly machines, with defined shapes and a startling variety of internal organizations. Complex geometry is a feature of both free-living unicellular organisms and cells inside multicellular animals. Where does the geometry of a cell come from? Many of the same questions that arise in developmental biology can also be asked of cells, but in most cases we do not know the answers. How much of cellular organization is dictated by global cell polarity cues as opposed to local interactions between cellular components? Does cellular structure persist across cell generations? What is the relationship between cell geometry and tissue organization? What ensures that intracellular structures are scaled to the overall size of the cell? Cell biology is only now beginning to come to grips with these questions.

Drosophila twin spot clones reveal cell division dynamics in regenerating imaginal discs

Cell proliferation is required for tissue regeneration, yet the dynamics of proliferation during regeneration are not well understood. Here we investigated the proliferation of eye and leg regeneration in fragments of Drosophila imaginal discs. Using twin spot clones, we followed the proliferation and fates of sister cells arising from the same mother cell in the regeneration blastema. We show that the mother cell gives rise to two sisters that participate equally in regeneration. However, when cells switch disc identity and transdetermine to another fate, they fail to turn off the cell cycle and continue dividing long after regeneration is complete. We further demonstrate that the regeneration blastema moves as a sweep of proliferation, in which cells are displaced. Our results suggest that regenerating cells stop dividing once the missing parts are formed, but if they undergo a switch in cell fate, the proliferation clock is reset.

Analysis of micro- and nano-structures of the corneal surface of Drosophila and its mutants by atomic force microscopy and optical diffraction

Drosophila melanogaster is a model organism instrumental for numerous biological studies. The compound eye of this insect consists of some eight hundred individual ommatidia or facets, ca. 15 µm in cross-section. Each ommatidium contains eighteen cells including four cone cells secreting the lens material (cornea). High-resolution imaging of the cornea of different insects has demonstrated that each lens is covered by the nipple arrays - small outgrowths of ca. 200 nm in diameter. Here we for the first time utilize atomic force microscopy (AFM) to investigate nipple arrays of the Drosophila lens, achieving an unprecedented visualization of the architecture of these nanostructures. We find by Fourier analysis that the nipple arrays of Drosophila are disordered, and that the seemingly ordered appearance is a consequence of dense packing of the nipples. In contrast, Fourier analysis confirms the visibly ordered nature of the eye microstructures - the individual lenses. This is different in the frizzled mutants of Drosophila, where both Fourier analysis and optical imaging detect disorder in lens packing. AFM reveals intercalations of the lens material between individual lenses in frizzled mutants, providing explanation for this disorder. In contrast, nanostructures of the mutant lens show the same organization as in wild-type flies. Thus, frizzled mutants display abnormal organization of the corneal micro-, but not nano-structures. At the same time, nipples of the mutant flies are shorter than those of the wild-type. We also analyze corneal surface of glossy-appearing eyes overexpressing Wingless - the lipoprotein ligand of Frizzled receptors, and find the catastrophic aberration in nipple arrays, providing experimental evidence in favor of the major anti-reflective function of these insect eye nanostructures. The combination of the easily tractable genetic model organism and robust AFM analysis represents a novel methodology to analyze development and architecture of these surface formations.

Actin behavior in bulk cytoplasm is cell cycle regulated in early vertebrate embryos

The mechanical properties of cells change as they proceed through the cell cycle, primarily owing to regulation of actin and myosin II. Most models for cell mechanics focus on actomyosin in the cortex and ignore possible roles in bulk cytoplasm. We explored cell cycle regulation of bulk cytoplasmic actomyosin in Xenopus egg extracts, which is almost undiluted cytoplasm from unfertilized eggs. We observed dramatic gelation-contraction of actomyosin in mitotic (M phase) extract where Cdk1 activity is high, but not in interphase (I-phase) extract. In spread droplets, M-phase extract exhibited regular, periodic pulses of gelation-contraction a few minutes apart that continued for many minutes. Comparing actin nucleation, disassembly and myosin II activity between M-phase and I-phase extracts, we conclude that regulation of nucleation is likely to be the most important for cell cycle regulation. We then imaged F-actin in early zebrafish blastomeres using a GFP-Utrophin probe. Polymerization in bulk cytoplasm around vesicles increased dramatically during mitosis, consistent with enhanced nucleation. We conclude that F-actin polymerization in bulk cytoplasm is cell cycle regulated in early vertebrate embryos and discuss possible biological functions of this regulation.

Cell pattern in adult human corneal endothelium

A review of the current data on the cell density of normal adult human endothelial cells was carried out in order to establish some common parameters appearing in the different considered populations. From the analysis of cell growth patterns, it is inferred that the cell aging rate is similar for each of the different considered populations. Also, the morphology, the cell distribution and the tendency to hexagonallity are studied. The results are consistent with the hypothesis that this phenomenon is analogous with cell behavior in other structures such as dry foams and grains in polycrystalline materials. Therefore, its driving force may be controlled by the surface tension and the mobility of the boundaries.

Epithelial tissue statistics: eliminating bias reveals morphological and morphogenetic features

Geometric order in quasi-two-dimensional epithelia has been extensively researched in order to identify and classify different tissues to help our understanding of how tissues form (morphogenesis) and how their formation may be influenced (tissue regeneration). However, the significance of published data -such as the distribution of numbers of cell neighbors- has been debatable because of measurement bias. We shown that such bias can be detected and corrected without detailed knowledge of the original samples, using only the biased (measured) distributions. This is true for both of the most important sources of bias: the measurement of apparent four-fold vertices and the selective preference for measuring smaller cells introduced by selecting a finite sampling window. The resulting unbiased data allows for a meaningful comparison of all available data, from different sources, taken with different experimental resolution and methodology. Conclusive evidence is found that the apparent four-fold vertices are neither distributed randomly nor oriented randomly, revealing profound differences in topological correlation between proliferating and remodeling tissues. The method is applied to measurements of Drosophila wing tissue, where it successfully disentangles distributional moments, allowing for an assessment of their relative importance, independence, and significance in tissue identification and classification.

Correlating cell behavior with tissue topology in embryonic epithelia

Measurements on embryonic epithelial tissues in a diverse range of organisms have shown that the statistics of cell neighbor numbers are universal in tissues where cell proliferation is the primary cell activity. Highly simplified non-spatial models of proliferation are claimed to accurately reproduce these statistics. Using a systematic critical analysis, we show that non-spatial models are not capable of robustly describing the universal statistics observed in proliferating epithelia, indicating strong spatial correlations between cells. Furthermore we show that spatial simulations using the Subcellular Element Model are able to robustly reproduce the universal histogram. In addition these simulations are able to unify ostensibly divergent experimental data in the literature. We also analyze cell neighbor statistics in early stages of chick embryo development in which cell behaviors other than proliferation are important. We find from experimental observation that cell neighbor statistics in the primitive streak region, where cell motility and ingression are also important, show a much broader distribution. A non-spatial Markov process model provides excellent agreement with this broader histogram indicating that cells in the primitive streak may have significantly weaker spatial correlations. These findings show that cell neighbor statistics provide a potentially useful signature of collective cell behavior.