The emergence of geometric order in proliferating metazoan epithelia

Cell size and growth regulation in the Arabidopsis thaliana apical stem cell niche

Cell size and growth kinetics are fundamental cellular properties with important physiological implications. Classical studies on yeast, and recently on bacteria, have identified rules for cell size regulation in single cells, but in the more complex environment of multicellular tissues, data have been lacking. In this study, to characterize cell size and growth regulation in a multicellular context, we developed a 4D imaging pipeline and applied it to track and quantify epidermal cells over 3-4 d in Arabidopsis thaliana shoot apical meristems. We found that a cell size checkpoint is not the trigger for G2/M or cytokinesis, refuting the unexamined assumption that meristematic cells trigger cell cycle phases upon reaching a critical size. Our data also rule out models in which cells undergo G2/M at a fixed time after birth, or by adding a critical size increment between G2/M transitions. Rather, cell size regulation was intermediate between the critical size and critical increment paradigms, meaning that cell size fluctuations decay by ∼75% in one generation compared with 100% (critical size) and 50% (critical increment). Notably, this behavior was independent of local cell-cell contact topologies and of position within the tissue. Cells grew exponentially throughout the first >80% of the cell cycle, but following an asymmetrical division, the small daughter grew at a faster exponential rate than the large daughter, an observation that potentially challenges present models of growth regulation. These growth and division behaviors place strong constraints on quantitative mechanistic descriptions of the cell cycle and growth control.

Rac1/RhoA antagonism defines cell-to-cell heterogeneity during epidermal morphogenesis in nematodes

The antagonism between the GTPases Rac1 and RhoA controls cell-to-cell heterogeneity in isogenic populations of cells in vitro and epithelial morphogenesis in vivo. Its involvement in the regulation of cell-to-cell heterogeneity during epidermal morphogenesis has, however, never been addressed. We used a quantitative cell imaging approach to characterize epidermal morphogenesis at a single-cell level during early elongation of Caenorhabditis elegans embryos. This study reveals that a Rac1-like pathway, involving the Rac/Cdc42 guanine-exchange factor β-PIX/PIX-1 and effector PAK1/PAK-1, and a RhoA-like pathway, involving ROCK/LET-502, control the remodeling of apical junctions and the formation of basolateral protrusions in distinct subsets of hypodermal cells. In these contexts, protrusions adopt lamellipodia or an amoeboid morphology. We propose that lamella formation may reduce tension building at cell-cell junctions during morphogenesis. Cell-autonomous antagonism between these pathways enables cells to switch between Rac1- and RhoA-like morphogenetic programs. This study identifies the first case of cell-to-cell heterogeneity controlled by Rac1/RhoA antagonism during epidermal morphogenesis.

Robust cell tracking in epithelial tissues through identification of maximum common subgraphs

Tracking of cells in live-imaging microscopy videos of epithelial sheets is a powerful tool for investigating fundamental processes in embryonic development. Characterizing cell growth, proliferation, intercalation and apoptosis in epithelia helps us to understand how morphogenetic processes such as tissue invagination and extension are locally regulated and controlled. Accurate cell tracking requires correctly resolving cells entering or leaving the field of view between frames, cell neighbour exchanges, cell removals and cell divisions. However, current tracking methods for epithelial sheets are not robust to large morphogenetic deformations and require significant manual interventions. Here, we present a novel algorithm for epithelial cell tracking, exploiting the graph-theoretic concept of a 'maximum common subgraph' to track cells between frames of a video. Our algorithm does not require the adjustment of tissue-specific parameters, and scales in sub-quadratic time with tissue size. It does not rely on precise positional information, permitting large cell movements between frames and enabling tracking in datasets acquired at low temporal resolution due to experimental constraints such as phototoxicity. To demonstrate the method, we perform tracking on the Drosophila embryonic epidermis and compare cell-cell rearrangements to previous studies in other tissues. Our implementation is open source and generally applicable to epithelial tissues.

Long Term Ex Vivo Culture and Live Imaging of Drosophila Larval Imaginal Discs

Continuous imaging of live tissues provides clear temporal sequence of biological events. The Drosophila imaginal discs have been popular experimental subjects for the study of a wide variety of biological phenomena, but long term culture that allows normal development has not been satisfactory. Here we report a culture method that can sustain normal development for 18 hours and allows live imaging. The method is validated in multiple discs and for cell proliferation, differentiation and migration. However, it does not support disc growth and cannot support cell proliferation for more than 7 to 12 hr. We monitored the cellular behavior of retinal basal glia in the developing eye disc and found that distinct glia type has distinct properties of proliferation and migration. The live imaging provided direct proof that wrapping glia differentiated from existing glia after migrating to the anterior front, and unexpectedly found that they undergo endoreplication before wrapping axons, and their nuclei migrate up and down along the axons. UV-induced specific labeling of a single carpet glia also showed that the two carpet glia membrane do not overlap and suggests a tiling or repulsion mechanism between the two cells. These findings demonstrated the usefulness of an ex vivo culture method and live imaging.

Collective migration and cell jamming in asthma, cancer and development

Collective cellular migration within the epithelial layer impacts upon development, wound healing and cancer invasion, but remains poorly understood. Prevailing conceptual frameworks tend to focus on the isolated role of each particular underlying factor - taken one at a time or at most a few at a time - and thus might not be tailored to describe a cellular collective that embodies a wide palette of physical and molecular interactions that are both strong and complex. To bridge this gap, we shift the spotlight to the emerging concept of cell jamming, which points to only a small set of parameters that govern when a cellular collective might jam and rigidify like a solid, or instead unjam and flow like a fluid. As gateways to cellular migration, the unjamming transition (UJT) and the epithelial-to-mesenchymal transition (EMT) share certain superficial similarities, but their congruence - or lack thereof - remains unclear. In this Commentary, we discuss aspects of cell jamming, its established role in human epithelial cell layers derived from the airways of non-asthmatic and asthmatic donors, and its speculative but emerging roles in development and cancer cell invasion.

Modeling cell shape and dynamics on micropatterns

Adhesive micropatterns have become a standard tool to study cells under defined conditions. Applications range from controlling the differentiation and fate of single cells to guiding the collective migration of cell sheets. In long-term experiments, single cell normalization is challenged by cell division. For all of these setups, mathematical models predicting cell shape and dynamics can guide pattern design. Here we review recent advances in predicting and explaining cell shape, traction forces and dynamics on micropatterns. Starting with contour models as the simplest approach to explain concave cell shapes, we move on to network and continuum descriptions as examples for static models. To describe dynamic processes, cellular Potts, vertex and phase field models can be used. Different types of model are appropriate to address different biological questions and together, they provide a versatile tool box to predict cell behavior on micropatterns.

A node-based version of the cellular Potts model

The cellular Potts model (CPM) is a lattice-based Monte Carlo method that uses an energetic formalism to describe the phenomenological mechanisms underlying the biophysical problem of interest. We here propose a CPM-derived framework that relies on a node-based representation of cell-scale elements. This feature has relevant consequences on the overall simulation environment. First, our model can be implemented on any given domain, provided a proper discretization (which can be regular or irregular, fixed or time evolving). Then, it allowed an explicit representation of cell membranes, whose displacements realistically result in cell movement. Finally, our node-based approach can be easily interfaced with continuous mechanics or fluid dynamics models. The proposed computational environment is here applied to some simple biological phenomena, such as cell sorting and chemotactic migration, also in order to achieve an analysis of the performance of the underlying algorithm. This work is finally equipped with a critical comparison between the advantages and disadvantages of our model with respect to the traditional CPM and to some similar vertex-based approaches.

Cell Division Drives Epithelial Cell Rearrangements during Gastrulation in Chick

During early embryonic development, cells are organized as cohesive epithelial sheets that are continuously growing and remodeled without losing their integrity, giving rise to a wide array of tissue shapes. Here, using live imaging in chick embryo, we investigate how epithelial cells rearrange during gastrulation. We find that cell division is a major rearrangement driver that powers dramatic epithelial cell intercalation events. We show that these cell division-mediated intercalations, which represent the majority of epithelial rearrangements within the early embryo, are absolutely necessary for the spatial patterning of gastrulation movements. Furthermore, we demonstrate that these intercalation events result from overall low cortical actomyosin accumulation within the epithelial cells of the embryo, which enables dividing cells to remodel junctions in their vicinity. These findings uncover a role for cell division as coordinator of epithelial growth and remodeling that might underlie various developmental, homeostatic, or pathological processes in amniotes.

Maintenance of the Epithelial Barrier and Remodeling of Cell-Cell Junctions during Cytokinesis

Epithelial integrity and barrier function must be maintained during the complex cell shape changes that occur during cytokinesis in vertebrate epithelial tissue. Here, we investigate how adherens junctions and bicellular and tricellular tight junctions are maintained and remodeled during cell division in the Xenopus laevis embryo. We find that epithelial barrier function is not disrupted during cytokinesis and is mediated by sustained tight junctions. Using fluorescence recovery after photobleaching (FRAP), we demonstrate that adherens junction proteins are stabilized at the cleavage furrow by increased tension. We find that Vinculin is recruited to the adherens junction at the cleavage furrow, and that inhibiting recruitment of Vinculin by expressing a dominant-negative mutant increases the rate of furrow ingression. Furthermore, we show that cells neighboring the cleavage plane are pulled between the daughter cells, making a new interface between neighbors, and two new tricellular tight junctions flank the midbody following cytokinesis. Our data provide new insight into how epithelial integrity and barrier function are maintained throughout cytokinesis in vertebrate epithelial tissue.

Insights into Biological Complexity from Simple Foundations

We discuss an overtly "simple approach" to complex biological systems borrowing selectively from theoretical physics. The approach is framed by three maxims, and we show examples of its success in two different applications: investigating cellular robustness at the level of gene regulatory networks and quantifying rare events of DNA replication errors.

Viscoelastic lithography for fabricating self-organizing soft micro-honeycomb structures with ultra-high aspect ratios

High-aspect ratio micro- and nano-structures have been used for the production of a variety of applications. In this paper, we describe a simple and cost-effective approach to fabricate an arrayed microarchitecture with an ultra-high aspect ratio using soft materials. The shapes and sizes of the honeycomb structure can be easily modulated by changing the dimensions and position of the base mould pattern and the pressure. The honeycomb structure is used to prepare a drug delivery patch and a microwell array to form cell spheroids without cell loss. The honeycomb structures prepared using natural ECM (collagen-Matrigel) materials are successfully fabricated. The hepatocytes and endothelial cells are seeded and co-cultured in the ECM-based micro-honeycomb to prepare a 3D liver model successfully mimicking an ultrastructure of liver and providing enhanced liver function.

Looking Beyond the Genes: The Interplay Between Signaling Pathways and Mechanics in the Shaping and Diversification of Epithelial Tissues

The core of Evo-Devo lies in the intuition that the way tissues grow during embryonic development, the way they sustain their structure and function throughout lifetime, and the way they evolve are closely linked. Epithelial tissues are ubiquitous in metazoans, covering the gut and internal branched organs, as well as the skin and its derivatives (ie, teeth). Here, we discuss in vitro, in vivo, and in silico studies on epithelial tissues to illustrate the conserved, dynamical, and complex aspects of their development. We then explore the implications of the dynamical and nonlinear nature of development on the evolution of their size and shape at the phenotypic and genetic levels. In rare cases, when the interplay between signaling and mechanics is well understood at the cell level, it is becoming clear that the structure of development leads to covariation of characters, an integration which in turn provides some predictable structure to evolutionary changes. We suggest that such nonlinear systems are prone to genetic drift, cryptic genetic variation, and context-dependent mutational effects. We argue that experimental and theoretical studies at the cell level are critical to our understanding of the phenotypic and genetic evolution of epithelial tissues, including carcinomas.

Somatosensory organ topography across the star of the star-nosed mole (Condylura cristata)

Quantifying somatosensory receptor distribution in glabrous skin is usually difficult because of the diversity of skin receptor subtypes and their location within the dermis and epidermis. However, the glabrous noses of moles are an exception. In most species of moles, the skin on the nose is covered with domed mechanosensory units known as an Eimer's organs. Eimer's organs contain a stereotyped array of different mechanosensory neurons, meaning that the distribution of mechanosensitive nerve endings can be inferred by visual inspection of the skin surface. Here we detail the distribution of Eimer's organs on the highly derived somatosensory star on the rostrum of the star-nosed mole (Condylura cristata). The star consists of 22 fleshy appendages, or rays, that are covered in Eimer's organs. We find that the density of Eimer's organs increases from proximal to distal locations along the length of the star's rays with a ratio of 1:2.3:3.1 from the surface nearest to the nostril, to the middle part of ray, to the ray tip, respectively. This ratio is comparable to the increase in receptor unit density reported for the human hand, from the palm, to the middle of the digits, to the distal fingertips. We also note that the tactile fovea of the star-nosed mole, located on the medial ventral ray, does not have increased sensory organ density, and we describe these findings in comparison with other sensory fovea.

EpiTools: An Open-Source Image Analysis Toolkit for Quantifying Epithelial Growth Dynamics

Epithelia grow and undergo extensive rearrangements to achieve their final size and shape. Imaging the dynamics of tissue growth and morphogenesis is now possible with advances in time-lapse microscopy, but a true understanding of their complexities is limited by automated image analysis tools to extract quantitative data. To overcome such limitations, we have designed a new open-source image analysis toolkit called EpiTools. It provides user-friendly graphical user interfaces for accurately segmenting and tracking the contours of cell membrane signals obtained from 4D confocal imaging. It is designed for a broad audience, especially biologists with no computer-science background. Quantitative data extraction is integrated into a larger bioimaging platform, Icy, to increase the visibility and usability of our tools. We demonstrate the usefulness of EpiTools by analyzing Drosophila wing imaginal disc growth, revealing previously overlooked properties of this dynamic tissue, such as the patterns of cellular rearrangements.

Oriented cell division affects the global stress and cell packing geometry of a monolayer under stretch

Cell division plays a vital role in tissue morphogenesis and homeostasis, and the division plane is crucial for cell fate. For isolated cells, extensive studies show that the orientation of divisions is sensitive to cell shape and the direction of extrinsic mechanical forces. However, it is poorly understood that how the cell divides within a cell monolayer and how the local stress change, due to the division, affects the global stress of epithelial monolayers. Here, we use the vertex dynamics models to investigate the effects of division orientation on the configurations and mechanics of a cell monolayer under stretch. We examine three scenarios of the divisions: dividing along the stretch axis, dividing along the geometric long axis of cells, and dividing at a random angle. It is found that the division along the long cell axis can induce the minimal energy difference, and the global stress of the monolayer after stretch releases more rapidly in this case. Moreover, the long-axis division can result in more random cell orientations and more isotropic cell shapes within the monolayer, comparing with other two cases. This study helps understand the division orientation of cells within a monolayer under mechanical stimuli, and may shed light on linking individual cell's behaviors to the global mechanics and patterns of tissues.

Fundamental physical cellular constraints drive self-organization of tissues

Morphogenesis is driven by small cell shape changes that modulate tissue organization. Apical surfaces of proliferating epithelial sheets have been particularly well studied. Currently, it is accepted that a stereotyped distribution of cellular polygons is conserved in proliferating tissues among metazoans. In this work, we challenge these previous findings showing that diverse natural packed tissues have very different polygon distributions. We use Voronoi tessellations as a mathematical framework that predicts this diversity. We demonstrate that Voronoi tessellations and the very different tissues analysed share an overriding restriction: the frequency of polygon types correlates with the distribution of cell areas. By altering the balance of tensions and pressures within the packed tissues using disease, genetic or computer model perturbations, we show that as long as packed cells present a balance of forces within tissue, they will be under a physical constraint that limits its organization. Our discoveries establish a new framework to understand tissue architecture in development and disease.

Mitotic cells contract actomyosin cortex and generate pressure to round against or escape epithelial confinement

Little is known about how mitotic cells round against epithelial confinement. Here, we engineer micropillar arrays that subject cells to lateral mechanical confinement similar to that experienced in epithelia. If generating sufficient force to deform the pillars, rounding epithelial (MDCK) cells can create space to divide. However, if mitotic cells cannot create sufficient space, their rounding force, which is generated by actomyosin contraction and hydrostatic pressure, pushes the cell out of confinement. After conducting mitosis in an unperturbed manner, both daughter cells return to the confinement of the pillars. Cells that cannot round against nor escape confinement cannot orient their mitotic spindles and more likely undergo apoptosis. The results highlight how spatially constrained epithelial cells prepare for mitosis: either they are strong enough to round up or they must escape. The ability to escape from confinement and reintegrate after mitosis appears to be a basic property of epithelial cells.

Square Cell Packing in the Drosophila Embryo through Spatiotemporally Regulated EGF Receptor Signaling

Cells display dynamic and diverse morphologies during development, but the strategies by which differentiated tissues achieve precise shapes and patterns are not well understood. Here we identify a developmental program that generates a highly ordered square cell grid in the Drosophila embryo through sequential and spatially regulated cell alignment, oriented cell division, and apicobasal cell elongation. The basic leucine zipper transcriptional regulator Cnc is necessary and sufficient to produce a square cell grid in the presence of a midline signal provided by the EGF receptor ligand Spitz. Spitz orients cell divisions through a Pins/LGN-dependent spindle-positioning mechanism and controls cell shape and alignment through a transcriptional pathway that requires the Pointed ETS domain protein. These results identify a strategy for producing ordered square cell packing configurations in epithelia and reveal a molecular mechanism by which organized tissue structure is generated through spatiotemporally regulated responses to EGF receptor activation.

The orthologous Tbx transcription factors Omb and TBX2 induce epithelial cell migration and extrusion in vivo without involvement of matrix metalloproteinases

The transcription factors TBX2 and TBX3 are overexpressed in various human cancers. Here, we investigated the effect of overexpressing the orthologous Tbx genes Drosophila optomotor-blind (omb) and human TBX2 in the epithelium of the Drosophila wing imaginal disc and observed two types of cell motility. Omb/TBX2 overexpressing cells could move within the plane of the epithelium. Invasive cells migrated long-distance as single cells retaining or regaining normal cell shape and apico-basal polarity in spite of attenuated apical DE-cadherin concentration. Inappropriate levels of DE-cadherin were sufficient to drive cell migration in the wing disc epithelium. Omb/TBX2 overexpression and reduced DE-cadherin-dependent adhesion caused the formation of actin-rich lateral cell protrusions. Omb/TBX2 overexpressing cells could also delaminate basally, penetratingthe basal lamina, however, without degradation of extracellular matrix. Expression of Timp, an inhibitor of matrix metalloproteases, blocked neither intraepithelial motility nor basal extrusion. Our results reveal an MMP-independent mechanism of cell invasion and suggest a conserved role of Tbx2-related proteins in cell invasion and metastasis-related processes.

An absolute interval scale of order for point patterns

Human observers readily make judgements about the degree of order in planar arrangements of points (point patterns). Here, based on pairwise ranking of 20 point patterns by degree of order, we have been able to show that judgements of order are highly consistent across individuals and the dimension of order has an interval scale structure spanning roughly 10 just-notable-differences (jnd) between disorder and order. We describe a geometric algorithm that estimates order to an accuracy of half a jnd by quantifying the variability of the size and shape of spaces between points. The algorithm is 70% more accurate than the best available measures. By anchoring the output of the algorithm so that Poisson point processes score on average 0, perfect lattices score 10 and unit steps correspond closely to jnds, we construct an absolute interval scale of order. We demonstrate its utility in biology by using this scale to quantify order during the development of the pattern of bristles on the dorsal thorax of the fruit fly.

Cell shapes and patterns as quantitative indicators of tissue stress in the plant epidermis

In a confluent, single-cell tissue layer, we show that cell shapes and statistics correlate directly with the tissue's mechanical properties, described by an energy functional with generic interfacial terms only. Upon increasing the cohesive component of the model, we observe a clear transition from a tense state with isotropic cells to a relaxed state with anisotropic cells. Signatures of the transition are present in the interfacial mechanics, the domain geometry, and the domain statistics, thus linking all three fields of study. This transition persists for all cell size distributions, but its exact position is crucially dependent on fluctuations in the parameter values of the functional (quenched disorder). The magnitude of fluctuations can be matched to the observed shape distribution of cells, so that visual observation of cell shapes and statistics provides information about the mechanical state of the tissue. Comparing with experimental data from the Cucumis epidermis, we find that the system is located right at the transition, allowing the tissue to relieve most of the local stress while maintaining integrity.

Geometrical and topological analysis of in vivo confocal microscopy images reveals dynamic maturation of epidermal structures during the first years of life

Reflectance confocal microscopy is successfully used in infant skin research. Infant skin structure, function, and composition are undergoing a maturation process. We aimed to uncover how the epidermal architecture and cellular topology change with time. Images were collected from three age groups of healthy infants between one and four years of age and adults. Cell centers were manually identified on the images at the stratum granulosum (SG) and stratum spinosum (SS) levels. Voronoi diagrams were used to calculate geometrical and topological parameters. Infant cell density is higher than that of adults and decreases with age. Projected cell area, cell perimeter, and average distance to the nearest neighbors increase with age but do so distinctly between the two layers. Structural entropy is different between the two strata, but remains constant with time. For all ages and layers, the distribution of the number of nearest neighbors is typical of a cooperator network architecture. The topological analysis provides evidence of the maturation process in infant skin. The differences between infant and adult are more pronounced in the SG than SS, while cell cooperation is evident in all cases of healthy skin examined.

The non-proliferative nature of ascidian folliculogenesis as a model of highly ordered cellular topology distinct from proliferative epithelia

Previous studies have addressed why and how mono-stratified epithelia adopt a polygonal topology. One major additional, and yet unanswered question is how the frequency of different cell shapes is achieved and whether the same distribution applies between non-proliferative and proliferative epithelia. We compared different proliferative and non-proliferative epithelia from a range of organisms as well as Drosophila melanogaster mutants, deficient for apoptosis or hyperproliferative. We show that the distribution of cell shapes in non-proliferative epithelia (follicular cells of five species of tunicates) is distinctly, and more stringently organized than proliferative ones (cultured epithelial cells and Drosophila melanogaster imaginal discs). The discrepancy is not supported by geometrical constraints (spherical versus flat monolayers), number of cells, or apoptosis events. We have developed a theoretical model of epithelial morphogenesis, based on the physics of divided media, that takes into account biological parameters such as cell-cell contact adhesions and tensions, cell and tissue growth, and which reproduces the effects of proliferation by increasing the topological heterogeneity observed experimentally. We therefore present a model for the morphogenesis of epithelia where, in a proliferative context, an extended distribution of cell shapes (range of 4 to 10 neighbors per cell) contrasts with the narrower range of 5-7 neighbors per cell that characterizes non proliferative epithelia.

Emergence of homeostatic epithelial packing and stress dissipation through divisions oriented along the long cell axis

Cell division plays an important role in animal tissue morphogenesis, which depends, critically, on the orientation of divisions. In isolated adherent cells, the orientation of mitotic spindles is sensitive to interphase cell shape and the direction of extrinsic mechanical forces. In epithelia, the relative importance of these two factors is challenging to assess. To do this, we used suspended monolayers devoid of ECM, where divisions become oriented following a stretch, allowing the regulation and function of epithelial division orientation in stress relaxation to be characterized. Using this system, we found that divisions align better with the long, interphase cell axis than with the monolayer stress axis. Nevertheless, because the application of stretch induces a global realignment of interphase long axes along the direction of extension, this is sufficient to bias the orientation of divisions in the direction of stretch. Each division redistributes the mother cell mass along the axis of division. Thus, the global bias in division orientation enables cells to act collectively to redistribute mass along the axis of stretch, helping to return the monolayer to its resting state. Further, this behavior could be quantitatively reproduced using a model designed to assess the impact of autonomous changes in mitotic cell mechanics within a stretched monolayer. In summary, the propensity of cells to divide along their long axis preserves epithelial homeostasis by facilitating both stress relaxation and isotropic growth without the need for cells to read or transduce mechanical signals.

Anisotropic stress orients remodelling of mammalian limb bud ectoderm

The physical forces that drive morphogenesis are not well characterized in vivo, especially among vertebrates. In the early limb bud, dorsal and ventral ectoderm converge to form the apical ectodermal ridge (AER), although the underlying mechanisms are unclear. By live imaging mouse embryos, we show that prospective AER progenitors intercalate at the dorsoventral boundary and that ectoderm remodels by concomitant cell division and neighbour exchange. Mesodermal expansion and ectodermal tension together generate a dorsoventrally biased stress pattern that orients ectodermal remodelling. Polarized distribution of cortical actin reflects this stress pattern in a β-catenin- and Fgfr2-dependent manner. Intercalation of AER progenitors generates a tensile gradient that reorients resolution of multicellular rosettes on adjacent surfaces, a process facilitated by β-catenin-dependent attachment of cortex to membrane. Therefore, feedback between tissue stress pattern and cell intercalations remodels mammalian ectoderm.

Mechanical force sensing in tissues

Tissue size, shape, and organization reflect individual cell behaviors such as proliferation, shape change, and movement. Evidence suggests that mechanical signals operate in tandem with biochemical cues to properly coordinate cell behavior and pattern tissues. The objective of this chapter is to present recent evidence demonstrating that forces transmitted between cells act as signals that coordinate cell behavior across tissues. We first briefly summarize molecular and cellular mechanisms by which forces are sensed by cells with an emphasis on forces generated and transmitted by cytoskeletal networks. We then discuss evidence for these mechanisms operating in multicellular contexts to coordinate complex cell and tissue behaviors that occur during embryonic development: specifically growth and morphogenesis.

Cell size versus body size in geophilomorph centipedes

Variation in animal body size is the result of a complex interplay between variation in cell number and cell size, but the latter has seldom been considered in wide-ranging comparative studies, although distinct patterns of variation have been described in the evolution of different lineages. We investigated the correlation between epidermal cell size and body size in a sample of 29 geophilomorph centipede species, representative of a wide range of body sizes, from 6 mm dwarf species to gigantic species more than 200 mm long, exploiting the marks of epidermal cells on the overlying cuticle in the form of micro-sculptures called scutes. We found conspicuous and significant variation in average scute area, both between suprageneric taxa and between genera, while the within-species range of variation is comparatively small. This supports the view that the average epidermal cell size is to some extent taxon specific. However, regression analyses show that neither body size nor the number of leg-bearing segments explain this variation, which suggests that cell size is not an usual target of change for body size evolution in this group of arthropods, although there is evidence of its correlation with other morphological variables, like cuticle thickness. Scute sizes of miniaturized geophilomorph species are well within the range of the lineage to which the species belong, suggesting recent evolutionary transitions to smaller body size.

Mechanics of blastopore closure during amphibian gastrulation

Blastopore closure in the amphibian embryo involves large scale tissue reorganization driven by physical forces. These forces are tuned to generate sustained blastopore closure throughout the course of gastrulation. We describe the mechanics of blastopore closure at multiple scales and in different regions around the blastopore by characterizing large scale tissue deformations, cell level shape change and subcellular F-actin organization and by measuring tissue force production and structural stiffness of the blastopore during gastrulation. We find that the embryo generates a ramping magnitude of force until it reaches a peak force on the order of 0.5μN. During this time course, the embryo also stiffens 1.5 fold. Strain rate mapping of the dorsal, ventral and lateral epithelial cells proximal to the blastopore reveals changing patterns of strain rate throughout closure. Cells dorsal to the blastopore, which are fated to become neural plate ectoderm, are polarized and have straight boundaries. In contrast, cells lateral and ventral to the blastopore are less polarized and have tortuous cell boundaries. The F-actin network is organized differently in each region with the highest percentage of alignment occurring in the lateral region. Interestingly F-actin was consistently oriented toward the blastopore lip in dorsal and lateral cells, but oriented parallel to the lip in ventral regions. Cell shape and F-actin alignment analyses reveal different local mechanical environments in regions around the blastopore, which was reflected by the strain rate maps.

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.

Cell division and the maintenance of epithelial order

Epithelia are polarized layers of adherent cells that are the building blocks for organ and appendage structures throughout animals. To preserve tissue architecture and barrier function during both homeostasis and rapid growth, individual epithelial cells divide in a highly constrained manner. Building on decades of research focused on single cells, recent work is probing the mechanisms by which the dynamic process of mitosis is reconciled with the global maintenance of epithelial order during development. These studies reveal how symmetrically dividing cells both exploit and conform to tissue organization to orient their mitotic spindles during division and establish new adhesive junctions during cytokinesis.

Multi-scale modelling of the dynamics of cell colonies: insights into cell-adhesion forces and cancer invasion from in silico simulations

Studying the biophysical interactions between cells is crucial to understanding how normal tissue develops, how it is structured and also when malfunctions occur. Traditional experiments try to infer events at the tissue level after observing the behaviour of and interactions between individual cells. This approach assumes that cells behave in the same biophysical manner in isolated experiments as they do within colonies and tissues. In this paper, we develop a multi-scale multi-compartment mathematical model that accounts for the principal biophysical interactions and adhesion pathways not only at a cell-cell level but also at the level of cell colonies (in contrast to the traditional approach). Our results suggest that adhesion/separation forces between cells may be lower in cell colonies than traditional isolated single-cell experiments infer. As a consequence, isolated single-cell experiments may be insufficient to deduce important biological processes such as single-cell invasion after detachment from a solid tumour. The simulations further show that kinetic rates and cell biophysical characteristics such as pressure-related cell-cycle arrest have a major influence on cell colony patterns and can allow for the development of protrusive cellular structures as seen in invasive cancer cell lines independent of expression levels of pro-invasion molecules.

Bubbly vertex dynamics: A dynamical and geometrical model for epithelial tissues with curved cell shapes

In order to describe two-dimensionally packed cells in epithelial tissues both mathematically and physically, there have been developed several sorts of geometrical models, such as the vertex model, the finite element model, the cell-centered model, and the cellular Potts model. So far, in any case, pressures have not neatly been dealt with and the curvatures of the cell boundaries have been even omitted through their approximations. We focus on these quantities and formulate them in the vertex model. Thus, a model with the curvatures is constructed, and its algorithm for simulation is provided. The possible extensions and applications of this model are also discussed.

Impairement of HT29 Cancer Cells Cohesion by the Soluble Form of Neurotensin Receptor-3

The neurotensin (NT) receptor-3 (NTSR3), also called sortilin is a multifunctional protein localized at the intracellular and plasma membrane level. The extracellular domain of NTSR3 (sNTSR3) is released by shedding from several cell lines including colonic cancer cells. This soluble protein acts as an active ligand through its ability to bind, to be internalized in the human adenocarcinoma epithelial HT29 cells and to stimulate the PI3 kinase pathway. The aim of this study was to investigate cellular responses induced by sNTSR3 in HT29 cells. The cellular functions of sNTSR3 were monitored by immunofluocytochemistry, electron microscopy and quantitative PCR in order to characterize the cell shape and the expression of adhesion proteins. We evidenced that sNTSR3 significantly regulates the cellular morphology as well as the cell-cell and the cell-matrix adherens properties by decreasing the expession of several integrins and by modifying the structure of desmosomes. Altogether, these properties lead to an increase of cell detachment upon sNTSR3 treatment on HT29, HCT116 and SW620 cancer cells. Our results indicate that sNTSR3 may induce the first phase of a process which weaken HT29 epithelial properties including desmosome architecture, cell spreading, and initiation of cell separation, all events which could be responsible for cancer metastasis.

How cells explore shape space: a quantitative statistical perspective of cellular morphogenesis

Through statistical analysis of datasets describing single cell shape following systematic gene depletion, we have found that the morphological landscapes explored by cells are composed of a small number of attractor states. We propose that the topology of these landscapes is in large part determined by cell-intrinsic factors, such as biophysical constraints on cytoskeletal organization, and reflects different stable signaling and/or transcriptional states. Cell-extrinsic factors act to determine how cells explore these landscapes, and the topology of the landscapes themselves. Informational stimuli primarily drive transitions between stable states by engaging signaling networks, while mechanical stimuli tune, or even radically alter, the topology of these landscapes. As environments fluctuate, the topology of morphological landscapes explored by cells dynamically adapts to these fluctuations. Finally we hypothesize how complex cellular and tissue morphologies can be generated from a limited number of simple cell shapes.

Towards long term cultivation of Drosophila wing imaginal discs in vitro

The wing imaginal disc of Drosophila melanogaster is a prominent experimental system for research on control of cell growth, proliferation and death, as well as on pattern formation and morphogenesis during organogenesis. The precise genetic methodology applicable in this system has facilitated conceptual advances of fundamental importance for developmental biology. Experimental accessibility and versatility would gain further if long term development of wing imaginal discs could be studied also in vitro. For example, culture systems would allow live imaging with maximal temporal and spatial resolution. However, as clearly demonstrated here, standard culture methods result in a rapid cell proliferation arrest within hours of cultivation of dissected wing imaginal discs. Analysis with established markers for cells in S- and M phase, as well as with RGB cell cycle tracker, a novel reporter transgene, revealed that in vitro cultivation interferes with cell cycle progression throughout interphase and not just exclusively during G1. Moreover, quantification of EGFP expression from an inducible transgene revealed rapid adverse effects of disc culture on basic cellular functions beyond cell cycle progression. Disc transplantation experiments confirmed that these detrimental consequences do not reflect fatal damage of imaginal discs during isolation, arguing clearly for a medium insufficiency. Alternative culture media were evaluated, including hemolymph, which surrounds imaginal discs during growth in situ. But isolated larval hemolymph was found to be even less adequate than current culture media, presumably as a result of conversion processes during hemolymph isolation or disc culture. The significance of prominent growth-regulating pathways during disc culture was analyzed, as well as effects of insulin and disc co-culture with larval tissues as potential sources of endocrine factors. Based on our analyses, we developed a culture protocol that prolongs cell proliferation in cultured discs.

Magnetically shaped cell aggregates: from granular to contractile materials

In recent decades, significant advances have been made in the description and modelling of tissue morphogenesis. By contrast, the initial steps leading to the formation of a tissue structure, through cell-cell adhesion, have so far been described only for small numbers of interacting cells. Here, through the use of remote magnetic forces, we succeeded at creating cell aggregates of half million cells, instantaneously and for several cell types, not only those known to form spheroids. This magnetic compaction gives access to the cell elasticity, found in the range of 800 Pa. The magnetic force can be removed at any time, allowing the cell mass to evolve spontaneously thereafter. The dynamics of contraction of these cell aggregates just after their formation (or, in contrast, their spreading for non-interacting monocyte cells) provides direct information on cell-cell interactions and allows retrieving the adhesion energy, in between 0.05 and 2 mJ m(-2), depending on the cell type tested, and in the case of cohesive aggregates. Thus, we show, by probing a large number of cell types, that cell aggregates behave like complex materials, undergoing a transition from a wet granular to contractile network, and that this transition is controlled by cell-cell interactions.

Dynamic clonal analysis based on chronic in vivo imaging allows multiscale quantification of growth in the Drosophila wing disc

In the course of morphogenesis, tissues change shape and grow. How this is orchestrated is largely unknown, partly owing to the lack of experimental methods to visualize and quantify growth. Here, we describe a novel experimental approach to investigate the growth of tissues in vivo on a time-scale of days, as employed to study the Drosophila larval imaginal wing disc, the precursor of the adult wing. We developed a protocol to image wing discs at regular intervals in living anesthetized larvae so as to follow the growth of the tissue over extended periods of time. This approach can be used to image cells at high resolution in vivo. At intermediate scale, we tracked the increase in cell number within clones as well as the changes in clone area and shape. At scales extending to the tissue level, clones can be used as landmarks for measuring strain, as a proxy for growth. We developed general computational tools to extract strain maps from clonal shapes and landmark displacements in individual tissues, and to combine multiple datasets into a mean strain. In the disc, we use these to compare properties of growth at the scale of clones (a few cells) and at larger regional scales.

A new model for cell division and migration with spontaneous topology changes

Tissue topology, in particular proliferating epithelium topology, is remarkably similar between various species. Understanding the mechanisms that result in the observed topologies is needed for better insight into the processes governing tissue formation. We present a two-dimensional single-cell based model for cell divisions and tissue growth. The model accounts for cell mechanics and allows cell migration. Cells do not have pre-existing shapes or topologies. Shape changes and local rearrangements occur naturally as a response to the evolving cellular environment and cell-cell interactions. We show that the commonly observed tissue topologies arise spontaneously from this model. We consider different cellular rearrangements that accompany tissue growth and study their effects on tissue topology.

On the origins of the mitotic shift in proliferating cell layers

Background

During plant and animal development, monolayer cell sheets display a stereotyped distribution of polygonal cell shapes. In interphase cells these shapes range from quadrilaterals to decagons, with a robust average of six sides per cell. In contrast, the subset of cells in mitosis exhibits a distinct distribution with an average of seven sides. It remains unclear whether this ‘mitotic shift’ reflects a causal relationship between increased polygonal sidedness and increased division likelihood, or alternatively, a passive effect of local proliferation on cell shape.

Methods

We use a combination of probabilistic analysis and mathematical modeling to predict the geometry of mitotic polygonal cells in a proliferating cell layer. To test these predictions experimentally, we use Flp-Out stochastic labeling in the Drosophila wing disc to induce single cell clones, and confocal imaging to quantify the polygonal topologies of these clones as a function of cellular age. For a more generic test in an idealized cell layer, we model epithelial sheet proliferation in a finite element framework, which yields a computationally robust, emergent prediction of the mitotic cell shape distribution.

Results

Using both mathematical and experimental approaches, we show that the mitotic shift derives primarily from passive, non-autonomous effects of mitoses in neighboring cells on each cell’s geometry over the course of the cell cycle. Computationally, we predict that interphase cells should passively gain sides over time, such that cells at more advanced stages of the cell cycle will tend to have a larger number of neighbors than those at earlier stages. Validating this prediction, experimental analysis of randomly labeled epithelial cells in the Drosophila wing disc demonstrates that labeled cells exhibit an age-dependent increase in polygonal sidedness. Reinforcing these data, finite element simulations of epithelial sheet proliferation demonstrate in a generic framework that passive side-gaining is sufficient to generate a mitotic shift.

Conclusions

Taken together, our results strongly suggest that the mitotic shift reflects a time-dependent accumulation of shared cellular interfaces over the course of the cell cycle. These results uncover fundamental constraints on the relationship between cell shape and cell division that should be general in adherent, polarized cell layers.

Does osteoderm growth follow energy minimization principles?

Although the growth and development of tissues and organs of extinct species cannot be directly observed, their fossils can record and preserve evidence of these mechanisms. It is generally accepted that bone architecture is the result of genetically based biomechanical constraints, but what about osteoderms? In this article, the influence of physical constraints on cranial osteoderms growth is assessed. Comparisons among lepidosaurs, synapsids, and archosaurs are performed; according to these analyses, lepidosaur osteoderms growth is predicted to be less energy demanding than that of synapsids and archosaurs. Obtained results also show that, from an energetic viewpoint, ankylosaurid osteoderms growth resembles more that of mammals than the one of reptilians, adding evidence to debate whether dinosaurs were hot or cold blooded.

Mechanisms of regulating tissue elongation in Drosophila wing: impact of oriented cell divisions, oriented mechanical forces, and reduced cell size

Regulation of cell growth and cell division plays fundamental roles in tissue morphogenesis. However, the mechanisms of regulating tissue elongation through cell growth and cell division are still not well understood. The wing imaginal disc of Drosophila provides a model system that has been widely used to study tissue morphogenesis. Here we use a recently developed two-dimensional cellular model to study the mechanisms of regulating tissue elongation in Drosophila wing. We simulate the effects of directional cues on tissue elongation. We also computationally analyze the role of reduced cell size. Our simulation results indicate that oriented cell divisions, oriented mechanical forces, and reduced cell size can all mediate tissue elongation, but they function differently. We show that oriented cell divisions and oriented mechanical forces act as directional cues during tissue elongation. Between these two directional cues, oriented mechanical forces have a stronger influence than oriented cell divisions. In addition, we raise the novel hypothesis that reduced cell size may significantly promote tissue elongation. We find that reduced cell size alone cannot drive tissue elongation. However, when combined with directional cues, such as oriented cell divisions or oriented mechanical forces, reduced cell size can significantly enhance tissue elongation in Drosophila wing. Furthermore, our simulation results suggest that reduced cell size has a short-term effect on cell topology by decreasing the frequency of hexagonal cells, which is consistent with experimental observations. Our simulation results suggest that cell divisions without cell growth play essential roles in tissue elongation.

Epithelial repair is a two-stage process driven first by dying cells and then by their neighbours

Epithelial cells maintain an essential barrier despite continuously undergoing mitosis and apoptosis. Biological and biophysical mechanisms have evolved to remove dying cells while maintaining that barrier. Cell extrusion is thought to be driven by a multicellular filamentous actin ring formed by neighbouring cells, the contraction of which provides the mechanical force for extrusion, with little or no contribution from the dying cell. Here, we use live confocal imaging, providing time-resolved three-dimensional observations of actomyosin dynamics, to reveal new mechanical roles for dying cells in their own extrusion from monolayers. Based on our observations, the clearance of dying cells can be subdivided into two stages. The first, previously unidentified, stage is driven by the dying cell, which exerts tension on its neighbours through the action of a cortical contractile F-actin and myosin ring at the cell apex. The second stage, consistent with previous studies, is driven by a multicellular F-actin ring in the neighbouring cells that moves from the apical to the basal plane to extrude the dying cell. Crucially, these data reinstate the dying cell as an active physical participant in cell extrusion.

Lewis' law revisited: the role of anisotropy in size-topology correlations

Since F T Lewis' pioneering work in the 1920s, a linear correlation between the average in-plane area of domains in a two-dimensional (2D) cellular structure and the number of neighbors of the domains has been empirically proposed, with many supporting and dissenting findings in the ensuing decades. Revisiting Lewis' original experiment, we take a larger set of more detailed data on the cells in the epidermal layer of Cucumis, and analyze the data in the light of recent results on size-topology correlations. We find that the correlation between the number-of-neighbor distribution (topology) and the area distribution is altered over that of many other 2D cellular systems (such as foams or disc packings), and that the systematic deviation can be explained by the anisotropic shape of the Cucumis cells. We develop a novel theory of size-topology correlation taking into account the characteristic aspect ratio of the cells within the framework of a granocentric model, and show that both Lewis' and our experimental data is consistent with the theory. In contrast to the granocentric model for isotropic domains, the new theory results in an approximately linear correlation consistent with Lewis' law. These statistical effects can be understood from the increased number of configurations available to a plane-filling domain system with non-isotropic elements, for the first time providing a firm explanation of why Lewis' law is valid in some systems and fails in others.

A multicellular view of cytokinesis in epithelial tissue

The study of cytokinesis in single-cell systems provided a wealth of knowledge on the molecular and biophysical mechanisms controlling daughter cell separation. In this review, we outline recent advances in the understanding of cytokinesis in epithelial tissues. These findings provide evidence for how the cytokinetic machinery adapts to a multicellular context and how the cytokinetic machinery is itself exploited by the tissue for the preservation of tissue function and architecture during proliferation. We propose that cytokinesis in epithelia should be viewed as a multicellular process, whereby the biochemical and mechanical interactions between the dividing cell and its neighbors are essential for successful daughter cell separation while defining epithelial tissue organization and preserving tissue integrity.

Theory of epithelial sheet morphology in three dimensions

Morphogenesis during embryo development requires the coordination of mechanical forces to generate the macroscopic shapes of organs. We propose a minimal theoretical model, based on cell adhesion and actomyosin contractility, which describes the various shapes of epithelial cells and the bending and buckling of epithelial sheets, as well as the relative stability of cellular tubes and spheres. We show that, to understand these processes, a full 3D description of the cells is needed, but that simple scaling laws can still be derived. The morphologies observed in vivo can be understood as stable points of mechanical equations and the transitions between them are either continuous or discontinuous. We then focus on epithelial sheet bending, a ubiquitous morphogenetic process. We calculate the curvature of an epithelium as a function of actin belt tension as well as of cell-cell and and cell-substrate tension. The model allows for a comparison of the relative stabilities of spherical or cylindrical cellular structures (acini or tubes). Finally, we propose a unique type of buckling instability of epithelia, driven by a flattening of individual cell shapes, and discuss experimental tests to verify our predictions.