The emergence of geometric order in proliferating metazoan epithelia

Structural effects of the insertion of large rings in two-dimensional networks

The structural effect of inserting large central rings into a two-dimensional network of three-coordinate nodes is investigated using a ring-growth Monte Carlo procedure. The size of the central ring is systematically varied, as is the inherent level of disorder in the surrounding network (as controlled by the Monte Carlo "temperature" and characterized by the fraction of six-membered rings). The effect of the central ring on the overall network topology is analyzed in terms of both topological and geometric distances. For larger central rings, the first topological shell becomes exclusively populated by four- and five-membered rings, which leads to an effective upper limit on the size of the central ring that can effectively be accommodated. The topological shells are found to show ordering at significant distances away from the central ring. The effective correlation lengths are determined as a function of both central ring size and level of network disorder, which allows for an understanding of the potential density of large rings that may be accommodated.

Interfacial energy constraints are sufficient to align cells over large distances

During development and wound healing, cells need to form long-range ordered structures to ensure precise formation of organs and repair damage. This requires cells to locate specific partner cells to which to adhere. How such cell matching reliably happens is an open problem, particularly in the presence of biological variability. Here, we use an equilibrium energy model to simulate how cell matching can occur with subcellular precision. A single parameter-encapsulating the competition between selective cell adhesion and cell compressibility-can reproduce experimental observations of cell alignment in the Drosophila embryonic heart. This demonstrates that adhesive differences between cells (in the case of the heart, mediated by filopodia interactions) are sufficient to drive cell matching without requiring cell rearrangements. The biophysical model can explain observed matching defects in mutant conditions and when there is significant biological variability. Using a dynamic vertex model, we demonstrate the existence of an optimal range of effective cell rigidities for efficient matching. Overall, this work shows that equilibrium energy considerations are consistent with observed cell matching in cardioblasts and has potential application to other systems, such as neuron connections and wound repair.

Planar polarized force propagation integrates cell behavior with tissue shaping during convergent extension

Convergent extension (CE) is an evolutionarily conserved developmental process that elongates tissues and organs via collective cell movements known as cell intercalation. Here, we sought to understand the mechanisms connecting cell behaviors and tissue shaping. We focus on an often-overlooked aspect of cell intercalation, the resolution of 4-cell vertices. Our data reveal that imbalanced cellular forces are involved in a timely vertex resolution, which, in turn, enables the propagation of such cellular forces, facilitating the propagation of tissue-scale CE. Conversely, delayed vertex resolution leads to a subtle but significant change in tissue-wide cell packing and exerts a profound impact by blocking force propagation, resulting in CE propagation defects. Our findings propose a collaborative nature of local cell intercalations in propagating tissue-wide CE. It unveils a multiscale biomechanical synergy underpinning the cellular mechanisms that orchestrate tissue morphogenesis during CE.

Topology and Nuclear Size Determine Cell Packing on Growing Lung Spheroids

Within multicellular living systems, cells coordinate their positions with spatiotemporal accuracy to form various tissue structures and control development. These arrangements can be regulated by tissue geometry, biochemical cues, as well as mechanical perturbations. However, how cells pack during dynamic three-dimensional multicellular architectures formation remains unclear. Here, examining a growing spherical multicellular system, human lung alveolospheres, we observe an emergence of hexagonal packing order and a structural transition of cells that comprise the spherical epithelium. Surprisingly, the cell packing behavior on the spherical surface of lung alveolospheres resembles hard-disks packing on spheres, where the less deformable cell nuclei act as effective "hard disks" and prevent cells from getting too close. Nucleus-to-cell size ratio increases during lung spheroids growth; as a result, we find more hexagon-concentrated cellular packing with increasing bond orientational order. Furthermore, by osmotically changing the compactness of cells on alveolospheres, we observe a more ordered packing when nucleus-to-cell size ratio increases, and vice versa. These more ordered cell packing characteristics are consistent with reduced cell dynamics, together suggesting that better cellular packing stabilizes local cell neighborhoods and may regulate more complex biological functions such as cellular maturation and tissue morphogenesis.

Actin-mediated avoidance of tricellular junction influences global topology at the Arabidopsis shoot apical meristem

Division plane orientation contributes to cell shape and topological organization, playing a key role in morphogenesis, but the precise physical and molecular mechanism influencing these processes remains largely obscure in plants. In particular, it is less clear how the placement of the new walls occurs in relation to the walls of neighboring cells. Here, we show that genetic perturbation of the actin cytoskeleton results in more rectangular cell shapes and higher incidences of four-way junctions, perturbing the global topology of cells in the shoot apical meristem of Arabidopsis thaliana. Actin mutants also exhibit changes in the expansion rate of the new versus the maternal cell wall after division, affecting the evolution of internal angles at tricellular junctions. Further, the increased width of the preprophase band in the actin mutant contributes to inaccuracy in the placement of the new cell wall. Computational simulation further substantiates this hypothesis and reproduces the observed cell shape defects.

Assessing mechanical agency during apical apoptotic cell extrusion

Homeostasis is necessary for epithelia to maintain barrier function and prevent the accumulation of defective cells. Unfit, excess, and dying cells in the larval zebrafish tail fin epidermis are removed via controlled cell death and extrusion. Extrusion coincides with oscillations of cell area, both in the extruding cell and its neighbors. Here, we develop a biophysical model of this process to explore the role of autonomous and non-autonomous mechanics. We vary biophysical properties and oscillatory behaviors of extruding cells and their neighbors along with tissue-wide cell density and viscosity. We find that cell autonomous processes are major contributors to the dynamics of extrusion, with the mechanical microenvironment providing a less pronounced contribution. We also find that some cells initially resist extrusion, influencing the duration of the expulsion process. Our model provides insights into the cellular dynamics and mechanics that promote elimination of unwanted cells from epithelia during homeostatic tissue maintenance.

Single-cell morphometrics reveals T-box gene-dependent patterns of epithelial tension in the Second Heart field

The vertebrate heart tube extends by progressive addition of epithelial second heart field (SHF) progenitor cells from the dorsal pericardial wall. The interplay between epithelial mechanics and genetic mechanisms during SHF deployment is unknown. Here, we present a quantitative single-cell morphometric analysis of SHF cells during heart tube extension, including force inference analysis of epithelial stress. Joint spatial Principal Component Analysis reveals that cell orientation and stress direction are the main parameters defining apical cell morphology and distinguishes cells adjacent to the arterial and venous poles. Cell shape and mechanical forces display a dynamic relationship during heart tube formation. Moreover, while the T-box transcription factor Tbx1 is necessary for cell orientation towards the arterial pole, activation of Tbx5 in the posterior SHF correlates with the establishment of epithelial stress and SHF deletion of Tbx5 relaxes the progenitor epithelium. Integrating findings from cell-scale feature patterning and mechanical stress provides new insights into cardiac morphogenesis.

Local and global changes in cell density induce reorganisation of 3D packing in a proliferating epithelium

Tissue morphogenesis is intimately linked to the changes in shape and organisation of individual cells. In curved epithelia, cells can intercalate along their own apicobasal axes, adopting a shape named 'scutoid' that allows energy minimization in the tissue. Although several geometric and biophysical factors have been associated with this 3D reorganisation, the dynamic changes underlying scutoid formation in 3D epithelial packing remain poorly understood. Here, we use live imaging of the sea star embryo coupled with deep learning-based segmentation to dissect the relative contributions of cell density, tissue compaction and cell proliferation on epithelial architecture. We find that tissue compaction, which naturally occurs in the embryo, is necessary for the appearance of scutoids. Physical compression experiments identify cell density as the factor promoting scutoid formation at a global level. Finally, the comparison of the developing embryo with computational models indicates that the increase in the proportion of scutoids is directly associated with cell divisions. Our results suggest that apico-basal intercalations appearing immediately after mitosis may help accommodate the new cells within the tissue. We propose that proliferation in a compact epithelium induces 3D cell rearrangements during development.

Evolving topological order in the postnatal visceral pleura

BACKGROUND

Changes in epithelial cell shape reflects optimal cell packing and the minimization of surface free energy, but also cell-cell interactions, cell proliferation, and cytoskeletal rearrangements.

RESULTS

Here, we studied the structure of the rat pleura in the first 15 days after birth. After pleural isolation and image segmentation, the analysis demonstrated a progression of epithelial order from postnatal day 1 (P1) to P15. The cells with the largest surface area and greatest shape variability were observed at P1. In contrast, the cells with the smallest surface area and most shape consistency were observed at P15. A comparison of polygonal cell geometries demonstrated progressive optimization with an increase in the number of hexagons (six-sided) as well as five-sided and seven-sided polygons. Analysis of the epithelial organization with Voronoi tessellations and graphlet motif frequencies demonstrated a developmental path strikingly distinct from mathematical and natural reference paths. Graph Theory analysis of cell connectivity demonstrated a progressive decrease in network heterogeneity and clustering coefficient from P1 to P15.

CONCLUSIONS

We conclude that the rat pleura undergoes a striking change in pleural structure from P1 to P15. Further, a geometric and network-based approach can provide a quantitative characterization of these developmental changes.

Mechanical state transitions in the regulation of tissue form and function

From embryonic development, postnatal growth and adult homeostasis to reparative and disease states, cells and tissues undergo constant changes in genome activity, cell fate, proliferation, movement, metabolism and growth. Importantly, these biological state transitions are coupled to changes in the mechanical and material properties of cells and tissues, termed mechanical state transitions. These mechanical states share features with physical states of matter, liquids and solids. Tissues can switch between mechanical states by changing behavioural dynamics or connectivity between cells. Conversely, these changes in tissue mechanical properties are known to control cell and tissue function, most importantly the ability of cells to move or tissues to deform. Thus, tissue mechanical state transitions are implicated in transmitting information across biological length and time scales, especially during processes of early development, wound healing and diseases such as cancer. This Review will focus on the biological basis of tissue-scale mechanical state transitions, how they emerge from molecular and cellular interactions, and their roles in organismal development, homeostasis, regeneration and disease.

Polynucleotides in Aesthetic Medicine: A Review of Current Practices and Perceived Effectiveness

Polynucleotides, complex molecules composed of nucleotides, have gained attention in aesthetic medicine for their potential to regulate gene expression and promote tissue regeneration. This review aims to provide an overview of the current practices and perceived effectiveness of polynucleotides in aesthetic medicine. A comprehensive search of the literature was conducted using keywords related to polynucleotides, cosmetic application, and aesthetic application. Studies were selected based on their relevance to aesthetic medicine and the inclusion of human subjects. The review found that polynucleotides have been used to improve skin texture, reduce wrinkle depth, and enhance facial appearance. The studies reported varying degrees of efficacy and safety, with some studies demonstrating significant improvements in skin elasticity and hydration. However, others reported limited or no benefits. The review also highlighted the need for further research to establish the optimal use and efficacy of polynucleotides in aesthetic medicine. While the existing literature suggests that polynucleotides may have potential benefits in aesthetic medicine, more research is needed to fully understand their mechanisms of action and optimal use. Clinicians should be aware of the current limitations and potential risks associated with the use of polynucleotides in aesthetic medicine.

Piezo regulates epithelial topology and promotes precision in organ size control

Mechanosensitive Piezo channels regulate cell division, cell extrusion, and cell death. However, systems-level functions of Piezo in regulating organogenesis remain poorly understood. Here, we demonstrate that Piezo controls epithelial cell topology to ensure precise organ growth by integrating live-imaging experiments with pharmacological and genetic perturbations and computational modeling. Notably, the knockout or knockdown of Piezo increases bilateral asymmetry in wing size. Piezo's multifaceted functions can be deconstructed as either autonomous or non-autonomous based on a comparison between tissue-compartment-level perturbations or between genetic perturbation populations at the whole-tissue level. A computational model that posits cell proliferation and apoptosis regulation through modulation of the cutoff tension required for Piezo channel activation explains key cell and tissue phenotypes arising from perturbations of Piezo expression levels. Our findings demonstrate that Piezo promotes robustness in regulating epithelial topology and is necessary for precise organ size control.

Clonal dynamics of surface-driven growing tissues

The self-organization of cells into complex tissues relies on a tight coordination of cell behavior. Identifying the cellular processes driving tissue growth is key to understanding the emergence of tissue forms and devising targeted therapies for aberrant growth, such as in cancer. Inferring the mode of tissue growth, whether it is driven by cells on the surface or by cells in the bulk, is possible in cell culture experiments but difficult in most tissues in living organisms (in vivo). Genetic tracing experiments, where a subset of cells is labeled with inheritable markers, have become important experimental tools to study cell fate in vivo. Here we show that the mode of tissue growth is reflected in the size distribution of the progeny of marked cells. To this end, we derive the clone size distributions using analytical calculations in the limit of negligible cell migration and cell death, and we test our predictions with an agent-based stochastic sampling technique. We show that for surface-driven growth the clone size distribution takes a characteristic power-law form with an exponent determined by fluctuations of the tissue surface. Our results propose a possible way of determining the mode of tissue growth from genetic tracing experiments.

Buckling forces and the wavy folds between pleural epithelial cells

Cell shapes in tissues are affected by the biophysical interaction between cells. Tissue forces can influence specific cell features such as cell geometry and cell surface area. Here, we examined the 2-dimensional shape, size, and perimeter of pleural epithelial cells at various lung volumes. We demonstrated a 1.53-fold increase in 2-dimensional cell surface area and a 1.43-fold increase in cell perimeter at total lung capacity compared to residual lung volume. Consistent with previous results, close inspection of the pleura demonstrated wavy folds between pleural epithelial cells at all lung volumes. To investigate a potential explanation for the wavy folds, we developed a physical simulacrum suggested by D'Arcy Thompson in On Growth and Form. The simulacrum suggested that the wavy folds were the result of redundant cell membranes unable to contract. To test this hypothesis, we developed a numerical simulation to evaluate the impact of an increase in 2-dimensional cell surface area and cell perimeter on the shape of the cell-cell interface. Our simulation demonstrated that an increase in cell perimeter, rather than an increase in 2-dimensional cell surface area, had the most direct impact on the presence of wavy folds. We conclude that wavy folds between pleural epithelial cells reflects buckling forces arising from the excess cell perimeter necessary to accommodate visceral organ expansion.

Nuclear size-regulated emergence of topological packing order on growing human lung alveolospheres

Within multicellular living systems, cells coordinate their positions with spatiotemporal accuracy to form various structures, setting the clock to control developmental processes and trigger maturation. These arrangements can be regulated by tissue topology, biochemical cues, as well as mechanical perturbations. However, the fundamental rules of how local cell packing order is regulated in forming three-dimensional (3D) multicellular architectures remain unclear. Furthermore, how cellular coordination evolves during developmental processes, and whether this cell patterning behavior is indicative of more complex biological functions, is largely unknown. Here, using human lung alveolospheres as a model system, by combining experiments and numerical simulations, we find that, surprisingly, cell packing behavior on alveolospheres resembles hard-disk packing but with increased randomness; the stiffer cell nuclei act as the hard disks surrounded by deformable cell bodies. Interestingly, we observe the emergence of topological packing order during alveolosphere growth, as a result of increasing nucleus-to-cell size ratio. Specifically, we find more hexagon-concentrated cellular packing with increasing bond orientational order, indicating a topological gas-to-liquid transition. Additionally, by osmotically changing the compactness of cells on alveolospheres, we observe that the variations in packing order align with the change of nucleus-to-cell size ratio. Together, our findings reveal the underlying rules of cell coordination and topological phases during human lung alveolosphere growth. These static packing characteristics are consistent with cell dynamics, together suggesting that better cellular packing stabilizes local cell neighborhoods and may regulate more complex biological functions such as organ development and cellular maturation.

α-Spectrin regulates cell shape changes during disassembly of microtubule-driven protrusions in Drosophila wings

The dynamics of microtubule-mediated protrusions, termed Interplanar Amida Network (IPAN) in Drosophila pupal wing, involve cell shape changes. The molecular mechanisms underlying these processes are yet to be fully understood. This study delineates the stages of cell shape alterations during the disassembly of microtubule protrusions and underscores the pivotal role of α-Spectrin in driving these changes by regulating both the microtubule and actomyosin networks. Our findings also demonstrate that α-Spectrin is required for the apical relaxation of wing epithelia during protrusion disassembly, indicating its substantial contribution to the robustness of 3D tissue morphogenesis.

Topological balance of cell distributions in plane monolayers

Most of normal proliferative epithelia of plants and metazoans are topologically invariant and characterized by similar cell distributions according to the number of cell neighbors (DCNs). Here we study peculiarities of these distributions and explain why the DCN obtained from the location of intercellular boundaries and that based on the Voronoi tessellation with nodes located on cell nuclei may differ from each other. As we demonstrate, special microdomains where four or more intercellular boundaries converge are topologically charged. Using this fact, we deduce a new equation describing the topological balance of the DCNs. The developed theory is applied for a series of microphotographs of non-tumoral epithelial cells of the human cervix (HCerEpiC) to improve the image processing near the edges of microphotographs and reveal the topological invariance of the examined monolayers. Special contact microdomains may be present in epithelia of various natures, however, considering the well-known vertex model of epithelium, we show that such contacts are absent in the usual solid-like state of the model and appear only in the liquid-like cancer state. Also, we discuss a possible biological role of special contacts in context of proliferative epithelium dynamics and tissue morphogenesis.

The mechanical influence of densification on epithelial architecture

Epithelial tissues are the most abundant tissue type in animals, lining body cavities and generating compartment barriers. The function of a monolayered epithelial tissue-whether protective, secretory, absorptive, or filtrative-relies on the side-by-side arrangement of its component cells. The mechanical parameters that determine the shape of epithelial cells in the apical-basal plane are not well-understood. Epithelial tissue architecture in culture is intimately connected to cell density, and cultured layers transition between architectures as they proliferate. This prompted us to ask to what extent epithelial architecture emerges from two mechanical considerations: A) the constraints of densification and B) cell-cell adhesion, a hallmark feature of epithelial cells. To address these questions, we developed a novel polyline cell-based computational model and used it to make theoretical predictions about epithelial architecture upon changes to density and cell-cell adhesion. We tested these predictions using cultured cell experiments. Our results show that the appearance of extended lateral cell-cell borders in culture arises as a consequence of crowding-independent of cell-cell adhesion. However, cadherin-mediated cell-cell adhesion is associated with a novel architectural transition. Our results suggest that this transition represents the initial appearance of a distinctive epithelial architecture. Together our work reveals the distinct mechanical roles of densification and adhesion to epithelial layer formation and provides a novel theoretical framework to understand the less well-studied apical-basal plane of epithelial tissues.

High-resolution 3-D scanning electron microscopy (SEM) images of DOTTM polynucleotides (PN): Unique scaffold characteristics and potential applications in biomedicine

INTRODUCTION

Polynucleotides (PN) are becoming more prominent in aesthetic medicine. However, the structural characteristics of PN have not been published and PN from different companies may have different structural characteristics. This study aimed to elucidate the structural attributes of DOT™ PN and distinguish differences with polydeoxyribonucleotides (PDRN) using high-resolution scanning electron microscopy (SEM) imaging.

MATERIALS AND METHODS

DOT™ PN was examined using a Quanta 3-D field emission gun (FEG) Scanning Electron Microscope (SEM). Sample preparation involved cryogenic cooling, cleavage, etching, and metal coating to facilitate high-resolution imaging. Cryo-FIB/SEM techniques were employed for in-depth structural analysis.

RESULTS

PDRN exhibited an amorphous structure without distinct features. In contrast, DOT™ PN displayed well-defined polyhedral shapes with smooth, uniformly thick walls. These cells were empty, with diameters ranging from 3 to 8 micrometers, forming a seamless tessellation pattern.

DISCUSSION

DOT™ PN's distinct geometric tessellation design conforms to the principles of biotensegrity, providing both structural reinforcement and integrity. The presence of delicate partitions and vacant compartments hints at possible uses in the field of pharmaceutical delivery systems. Within the realms of beauty enhancement and regenerative medicine, DOT™ PN's capacity to bolster cell growth and tissue mending could potentially transform approaches to rejuvenation treatments. Its adaptability becomes apparent when considering its contributions to drug administration and surgical procedures.

CONCLUSION

This study unveils the intricate structural scaffold features of DOT™ PN for the first time, setting it apart from PDRN and inspiring innovation in biomedicine and materials science. DOT™ PN's unique attributes open doors to potential applications across healthcare and beyond.

Signatures of structural disorder in developing epithelial tissues

Epithelial cells generate functional tissues in developing embryos through collective movements and shape changes. In some morphogenetic events, a tissue dramatically reorganizes its internal structure - often generating high degrees of structural disorder - to accomplish changes in tissue shape. However, the origins of structural disorder in epithelia and what roles it might play in morphogenesis are poorly understood. We study this question in the Drosophila germband epithelium, which undergoes dramatic changes in internal structure as cell rearrangements drive elongation of the embryo body axis. Using two order parameters that quantify volumetric and shear disorder, we show that structural disorder increases during body axis elongation and is strongly linked with specific developmental processes. Both disorder metrics begin to increase around the onset of axis elongation, but then plateau at values that are maintained throughout the process. Notably, the disorder plateau values for volumetric disorder are similar to those for random cell packings, suggesting this may reflect a limit on tissue behavior. In mutant embryos with disrupted external stresses from the ventral furrow, both disorder metrics reach wild-type maximum disorder values with a delay, correlating with delays in cell rearrangements. In contrast, in mutants with disrupted internal stresses and cell rearrangements, volumetric disorder is reduced compared to wild type, whereas shear disorder depends on specific external stress patterns. Together, these findings demonstrate that internal and external stresses both contribute to epithelial tissue disorder and suggest that the maximum values of disorder in a developing tissue reflect physical or biological limits on morphogenesis.

Local and global changes in cell density induce reorganisation of 3D packing in a proliferating epithelium

Tissue morphogenesis is intimately linked to the changes in shape and organisation of individual cells. In curved epithelia, cells can intercalate along their own apicobasal axes adopting a shape named "scutoid" that allows energy minimization in the tissue. Although several geometric and biophysical factors have been associated with this 3D reorganisation, the dynamic changes underlying scutoid formation in 3D epithelial packing remain poorly understood. Here we use live-imaging of the sea star embryo coupled with deep learning-based segmentation, to dissect the relative contributions of cell density, tissue compaction, and cell proliferation on epithelial architecture. We find that tissue compaction, which naturally occurs in the embryo, is necessary for the appearance of scutoids. Physical compression experiments identify cell density as the factor promoting scutoid formation at a global level. Finally, the comparison of the developing embryo with computational models indicates that the increase in the proportion of scutoids is directly associated with cell divisions. Our results suggest that apico-basal intercalations appearing just after mitosis may help accommodate the new cells within the tissue. We propose that proliferation in a compact epithelium induces 3D cell rearrangements during development.

Programmed disassembly of a microtubule-based membrane protrusion network coordinates 3D epithelial morphogenesis in Drosophila

Comprehensive analysis of cellular dynamics during the process of morphogenesis is fundamental to understanding the principles of animal development. Despite recent advancements in light microscopy, how successive cell shape changes lead to complex three-dimensional tissue morphogenesis is still largely unresolved. Using in vivo live imaging of Drosophila wing development, we have studied unique cellular structures comprising a microtubule-based membrane protrusion network. This network, which we name here the Interplanar Amida Network (IPAN), links the two wing epithelium leaflets. Initially, the IPAN sustains cell-cell contacts between the two layers of the wing epithelium through basal protrusions. Subsequent disassembly of the IPAN involves loss of these contacts, with concomitant degeneration of aligned microtubules. These processes are both autonomously and non-autonomously required for mitosis, leading to coordinated tissue proliferation between two wing epithelia. Our findings further reveal that a microtubule organization switch from non-centrosomal to centrosomal microtubule-organizing centers (MTOCs) at the G2/M transition leads to disassembly of non-centrosomal microtubule-derived IPAN protrusions. These findings exemplify how cell shape change-mediated loss of inter-tissue contacts results in 3D tissue morphogenesis.

Patterned apoptosis has an instructive role for local growth and tissue shape regulation in a fast-growing epithelium

What regulates organ size and shape remains one fundamental mystery of modern biology. Research in this area has primarily focused on deciphering the regulation in time and space of growth and cell division, while the contribution of cell death has been overall neglected. This includes studies of the Drosophila wing, one of the best-characterized systems for the study of growth and patterning, undergoing massive growth during larval stage and important morphogenetic remodeling during pupal stage. So far, it has been assumed that cell death was relatively neglectable in this tissue both during larval stage and pupal stage, and as a result, the pattern of growth was usually attributed to the distribution of cell division. Here, using systematic mapping and registration combined with quantitative assessment of clone size and disappearance as well as live imaging, we outline a persistent pattern of cell death and clone elimination emerging in the larval wing disc and persisting during pupal wing morphogenesis. Local variation of cell death is associated with local variation of clone size, pointing to an impact of cell death on local growth that is not fully compensated by proliferation. Using morphometric analyses of adult wing shape and genetic perturbations, we provide evidence that patterned death locally and globally affects adult wing shape and size. This study describes a roadmap for precise assessment of the contribution of cell death to tissue shape and outlines an important instructive role of cell death in modulating quantitatively local growth and morphogenesis of a fast-growing tissue.

The dynamics and biophysics of shape formation: Common themes in plant and animal morphogenesis

The emergence of tissue form in multicellular organisms results from the complex interplay between genetics and physics. In both plants and animals, cells must act in concert to pattern their behaviors. Our understanding of the factors sculpting multicellular form has increased dramatically in the past few decades. From this work, common themes have emerged that connect plant and animal morphogenesis-an exciting connection that solidifies our understanding of the developmental basis of multicellular life. In this review, we will discuss the themes and the underlying principles that connect plant and animal morphogenesis, including the coordination of gene expression, signaling, growth, contraction, and mechanical and geometric feedback.

Adhesion and Polarity protein distribution-regulates hexagon dominated plasma membrane organization in Drosophila blastoderm embryos

Epithelial cells contain polarity complexes on the lateral membrane and are organized in a hexagon-dominated polygonal array. The mechanisms regulating the organization of polygonal architecture in metazoan embryogenesis are not completely understood. Drosophila embryogenesis enables mechanistic analysis of epithelial polarity formation and its impact on polygonal organization. The plasma membrane (PM) of syncytial Drosophila blastoderm embryos is organized as a polygonal array with pseudocleavage furrow formation during the almost synchronous cortical division cycles. We find that polygonal (PM) organization arises in the metaphase (MP) of division cycle 11, and hexagon dominance occurs with an increase in furrow length in the metaphase of cycle 12. There is a decrease in cell shape index in metaphase from cycles 11 to 13. This coincides with Drosophila E-cad (DE-cadherin) and Bazooka enrichment at the edges and the septin, Peanut at the vertices of the furrow. We further assess the role of polarity and adhesion proteins in pseudocleavage furrow formation and its organization as a polygonal array. We find that DE-cadherin depletion leads to decreased furrow length, loss of hexagon dominance, and increased cell shape index. Bazooka and Peanut depletion lead to decreased furrow length, delay in onset of hexagon dominance from cycle 12 to 13, and increased cell shape index. Hexagon dominance occurs with an increase in furrow length in cycle 13 and increased DE-cadherin, possibly due to the inhibition of endocytosis. We conclude that polarity protein recruitment and regulation of endocytic pathways enable pseudocleavage furrow stability and the formation of a hexagon-dominated polygon array.

A life off the beaten track in biomechanics: Imperfect elasticity, cytoskeletal glassiness, and epithelial unjamming

Textbook descriptions of elasticity, viscosity, and viscoelasticity fail to account for certain mechanical behaviors that typify soft living matter. Here, we consider three examples. First, strong empirical evidence suggests that within lung parenchymal tissues, the frictional stresses expressed at the microscale are fundamentally not of viscous origin. Second, the cytoskeleton (CSK) of the airway smooth muscle cell, as well as that of all eukaryotic cells, is more solid-like than fluid-like, yet its elastic modulus is softer than the softest of soft rubbers by a factor of 104-105. Moreover, the eukaryotic CSK expresses power law rheology, innate malleability, and fluidization when sheared. For these reasons, taken together, the CSK of the living eukaryotic cell is reminiscent of the class of materials called soft glasses, thus likening it to inert materials such as clays, pastes slurries, emulsions, and foams. Third, the cellular collective comprising a confluent epithelial layer can become solid-like and jammed, fluid-like and unjammed, or something in between. Esoteric though each may seem, these discoveries are consequential insofar as they impact our understanding of bronchospasm and wound healing as well as cancer cell invasion and embryonic development. Moreover, there are reasons to suspect that certain of these phenomena first arose in the early protist as a result of evolutionary pressures exerted by the primordial microenvironment. We have hypothesized, further, that each then became passed down virtually unchanged to the present day as a conserved core process. These topics are addressed here not only because they are interesting but also because they track the journey of one laboratory along a path less traveled by.

Assessing mechanical agency during apical apoptotic cell extrusion

Epithelial tissues maintain homeostasis through the continual addition and removal of cells. Homeostasis is necessary for epithelia to maintain barrier function and prevent the accumulation of defective cells. Unfit, excess, and dying cells can be removed from epithelia by the process of extrusion. Controlled cell death and extrusion in the epithelium of the larval zebrafish tail fin coincides with oscillation of cell area, both in the extruding cell and its neighbors. Both cell-autonomous and non-autonomous factors have been proposed to contribute to extrusion but have been challenging to test by experimental approaches. Here we develop a dynamic cell-based biophysical model that recapitulates the process of oscillatory cell extrusion to test and compare the relative contributions of these factors. Our model incorporates the mechanical properties of individual epithelial cells in a two-dimensional simulation as repelling active particles. The area of cells destined to extrude oscillates with varying durations or amplitudes, decreasing their mechanical contribution to the epithelium and surrendering their space to surrounding cells. Quantitative variations in cell shape and size during extrusion are visualized by a hybrid weighted Voronoi tessellation technique that renders individual cell mechanical properties directly into an epithelial sheet. To explore the role of autonomous and non-autonomous mechanics, we vary the biophysical properties and behaviors of extruding cells and neighbors such as the period and amplitude of repulsive forces, cell density, and tissue viscosity. Our data suggest that cell autonomous processes are major contributors to the dynamics of extrusion, with the mechanical microenvironment providing a less pronounced contribution. Our computational model based on in vivo data serves as a tool to provide insights into the cellular dynamics and localized changes in mechanics that promote elimination of unwanted cells from epithelia during homeostatic tissue maintenance.

Tension Remodeling Regulates Topological Transitions in Epithelial Tissues

Cell neighbor exchanges play a critical role in regulating tissue fluidity during epithelial morphogenesis and repair. In vivo, these neighbor exchanges are often hindered by the formation of transiently stable fourfold vertices, which can develop into complex multicellular rosettes where five or more cell junctions meet. Despite their importance, the mechanical origins of multicellular rosettes have remained elusive, and current cellular models lack the ability to explain their formation and maintenance. Here we present a dynamic vertex model of epithelial tissues with strain-dependent tension remodeling and mechanical memory dissipation. We show that an increase in cell junction tension upon contraction and reduction in tension upon extension can stabilize higher-order vertices, temporarily stalling cell rearrangements. On the other hand, inducing mechanical memory dissipation via relaxation of junction strain and stress promotes the resolution of higher-order vertices, facilitating cell neighbor exchanges. We demonstrate that by tuning the rates of tension remodeling and mechanical memory dissipation, we can control topological transitions and tissue material properties, recapitulating complex cellular topologies seen in developing organisms.

Topological data analysis of spatial patterning in heterogeneous cell populations: clustering and sorting with varying cell-cell adhesion

Different cell types aggregate and sort into hierarchical architectures during the formation of animal tissues. The resulting spatial organization depends (in part) on the strength of adhesion of one cell type to itself relative to other cell types. However, automated and unsupervised classification of these multicellular spatial patterns remains challenging, particularly given their structural diversity and biological variability. Recent developments based on topological data analysis are intriguing to reveal similarities in tissue architecture, but these methods remain computationally expensive. In this article, we show that multicellular patterns organized from two interacting cell types can be efficiently represented through persistence images. Our optimized combination of dimensionality reduction via autoencoders, combined with hierarchical clustering, achieved high classification accuracy for simulations with constant cell numbers. We further demonstrate that persistence images can be normalized to improve classification for simulations with varying cell numbers due to proliferation. Finally, we systematically consider the importance of incorporating different topological features as well as information about each cell type to improve classification accuracy. We envision that topological machine learning based on persistence images will enable versatile and robust classification of complex tissue architectures that occur in development and disease.

Topological properties and shape of proliferative and nonproliferative cell monolayers

During embryonic development, structures with complex geometry can emerge from planar epithelial monolayers; studying these shape transitions is of key importance for revealing the biophysical laws involved in the morphogenesis of biological systems. Here, using the example of normal proliferative monkey kidney (COS) cell monolayers, we investigate global and local topological characteristics of this model system in dependence on its shape. The obtained distributions of cells by their valence demonstrate a difference between the spherical and planar monolayers. In addition, in both spherical and planar monolayers, the probability of observing a pair of neighboring cells with certain valences depends on the topological charge of the pair. The zero topological charge of the cell pair can increase the probability for the cells to be the nearest neighbors. We then test and confirm that analogous relationships take place in a more ordered spherical system with a larger fraction of 6-valent cells, namely, in the nonproliferative epithelium (follicular system) of ascidian species oocytes. However, unlike spherical COS cell monolayers, ascidian monolayers are prone to nonrandom agglomeration of 6-valent cells and have linear topological defects called scars and pleats. The reasons for this difference in morphology are discussed. The morphological peculiarities found are compared with predictions of the widely used vertex model of epithelium.

Tissues as networks of cells: towards generative rules of complex organ development

Network analysis is a well-known and powerful tool in molecular biology. More recently, it has been introduced in developmental biology. Tissues can be readily translated into spatial networks such that cells are represented by nodes and intercellular connections by edges. This discretization of cellular organization enables mathematical approaches rooted in network science to be applied towards the understanding of tissue structure and function. Here, we describe how such tissue abstractions can enable the principles that underpin tissue formation and function to be uncovered. We provide an introduction into biologically relevant network measures, then present an overview of different areas of developmental biology where these approaches have been applied. We then summarize the general developmental rules underpinning tissue topology generation. Finally, we discuss how generative models can help to link the developmental rule back to the tissue topologies. Our collection of results points at general mechanisms as to how local developmental rules can give rise to observed topological properties in multicellular systems.

Geometric and network organization of visceral organ epithelium

Mammalian epithelia form a continuous sheet of cells that line the surface of visceral organs. To analyze the epithelial organization of the heart, lung, liver and bowel, epithelial cells were labeled in situ, isolated as a single layer and imaged as large epithelial digitally combine montages. The stitched epithelial images were analyzed for geometric and network organization. Geometric analysis demonstrated a similar polygon distribution in all organs with the greatest variability in the heart epithelia. Notably, the normal liver and inflated lung demonstrated the largest average cell surface area (p < 0.01). In lung epithelia, characteristic wavy or interdigitated cell boundaries were observed. The prevalence of interdigitations increased with lung inflation. To complement the geometric analyses, the epithelia were converted into a network of cell-to-cell contacts. Using the open-source software EpiGraph, subgraph (graphlet) frequencies were used to characterize epithelial organization and compare to mathematical (Epi-Hexagon), random (Epi-Random) and natural (Epi-Voronoi5) patterns. As expected, the patterns of the lung epithelia were independent of lung volume. In contrast, liver epithelia demonstrated a pattern distinct from lung, heart and bowel epithelia (p < 0.05). We conclude that geometric and network analyses can be useful tools in characterizing fundamental differences in mammalian tissue topology and epithelial organization.

The Mechanical Influence of Densification on Initial Epithelial Architecture

Epithelial tissues are the most abundant tissue type in animals, lining body cavities and generating compartment barriers. The function of a monolayer epithelium - whether protective, secretory, absorptive, or filtrative -relies on regular tissue architecture with respect to the apical-basal axis. Using an unbiased 3D analysis pipeline developed in our lab, we previously showed that epithelial tissue architectures in culture can be divided into distinct developmental categories, and that these are intimately connected to cell density: at sparse densities, cultured epithelial cell layers have a squamous morphology (Immature); at intermediate densities, these layers develop lateral cell-cell borders and rounded cell apices (Intermediate); cells at the highest densities reach their full height and demonstrate flattened apices (Mature). These observations prompted us to ask whether epithelial architecture emerges from the mechanical constraints of densification, and to what extent a hallmark feature of epithelial cells, namely cell-cell adhesion, contributes. In other words, to what extent is the shape of cells in an epithelial layer a simple matter of sticky, deformable objects squeezing together? We addressed this problem using a combination of computational modeling and experimental manipulations. Our results show that the first morphological transition, from Immature to Intermediate, can be explained simply by cell crowding. Additionally, we identify a new division (and thus transition) within the Intermediate category, and find that this second morphology relies on cell-cell adhesion.

Mechanobiological implications of age-related remodelling in the outer retina

The outer retina consists of the light-sensitive photoreceptors, the pigmented epithelium, and the choroid, which interact in a complex manner to sustain homeostasis. The organisation and function of these cellular layers are mediated by the extracellular matrix compartment named Bruch's membrane, situated between the retinal epithelium and the choroid. Like many tissues, the retina experiences age-related structural and metabolic changes, which are relevant for understanding major blinding diseases of the elderly, such as age-related macular degeneration. Compared with other tissues, the retina mainly comprises postmitotic cells, making it less able to maintain its mechanical homeostasis over the years functionally. Aspects of retinal ageing, like the structural and morphometric changes of the pigment epithelium and the heterogenous remodelling of the Bruch's membrane, imply changes in tissue mechanics and may affect functional integrity. In recent years, findings in the field of mechanobiology and bioengineering highlighted the importance of mechanical changes in tissues for understanding physiological and pathological processes. Here, we review the current knowledge of age-related changes in the outer retina from a mechanobiological perspective, aiming to generate food for thought for future mechanobiology studies in the outer retina.

Systematic analysis of RhoGEF/GAP localizations uncovers regulators of mechanosensing and junction formation during epithelial cell division

Cell proliferation is central to epithelial tissue development, repair, and homeostasis. During cell division, small RhoGTPases control both actomyosin dynamics and cell-cell junction remodeling to faithfully segregate the genome while maintaining tissue polarity and integrity. To decipher the mechanisms of RhoGTPase spatiotemporal regulation during epithelial cell division, we generated a transgenic fluorescently tagged library for the 48 Drosophila Rho guanine exchange factors (RhoGEFs) and GTPase-activating proteins (GAPs), and we systematically characterized their endogenous distributions by time-lapse microscopy. Therefore, we unveiled candidate regulators of the interplay between actomyosin and junctional dynamics during epithelial cell division. Building on these findings, we established that the conserved RhoGEF Cysts and RhoGEF4 play sequential and distinct roles to couple cytokinesis with de novo junction formation. During ring contraction, Cysts via Rho1 participates in the neighbor mechanosensing response, promoting daughter-daughter cell membrane juxtaposition in preparation to de novo junction formation. Subsequently and upon midbody formation, RhoGEF4 via Rac acts in the dividing cell to ensure the withdrawal of the neighboring cell membranes, thus controlling de novo junction length and cell-cell arrangements upon cytokinesis. Altogether, our findings delineate how the RhoGTPases Rho and Rac are locally and temporally activated during epithelial cytokinesis, highlighting the RhoGEF/GAP library as a key resource to understand the broad range of biological processes regulated by RhoGTPases.

Curvature-Induced Cell Rearrangements in Biological Tissues

On a curved surface, epithelial cells can adapt to geometric constraints by tilting and by exchanging their neighbors from apical to basal sides, known as an apico-basal topological transition 1 (AB-T1). The relationship between cell tilt, AB-T1s, and tissue curvature still lacks a unified understanding. Here, we propose a general framework for cell packing in curved environments and explain the formation of AB-T1s from the perspective of strain anisotropy. We find that steep curvature gradients can lead to cell tilting and induce AB-T1s. Alternatively, pressure differences across the epithelial tissue can drive AB-T1s in regions of large curvature anisotropy. The two mechanisms compete to determine the impact of tissue geometry and mechanics on optimized cell rearrangements in three dimensions.

The network structure of the corneal endothelium

A generic network model is applied to study the structure of the mammalian corneal endothelium. The model has been shown to reproduce the network properties of a wide range of systems, from low-dimensional inorganic glasses to colloidal nanoparticles deposited on a surface. Available extensive experimental microscopy results are analyzed and combined to highlight the behavior of two key metrics, the fraction of hexagonal rings (p₆) and the coefficient of variation of the area. Their behavior is analyzed as a function of patient age, the onset of diabetes, and contact lens wearing status. Wearing contact lenses for ∼10 years is shown to change the endothelium structure by the equivalent of ∼30 years contact lens-free. Model network configurations are obtained using a Monte Carlo bond-switching algorithm, with the resulting topologies controlled by two potential model parameters (the bond and angular force constants) and the Monte Carlo temperature. The effect of systematically varying these parameters is investigated. In addition, the effect of constraining the ring size distribution is investigated. The networks generated with relatively weak bond force constants are shown to correlate best with the experimental information. The importance of extracting the full ring size distribution (rather than simply the fraction of hexagons) is discussed.

Scribble and E-cadherin cooperate to control symmetric daughter cell positioning by multiple mechanisms

The fate of the two daughter cells is intimately connected to their positioning, which is in turn regulated by cell junction remodelling and orientation of the mitotic spindle. How multiple cues are integrated to dictate the ultimate positioning of daughters is not clear. Here, we identify novel mechanisms of regulation of daughter positioning in single MCF10A cells. The polarity protein, Scribble cooperates with E-cadherin for sequential roles in daughter positioning. First Scribble stabilises E-cadherin at the mitotic cortex as well as the retraction fibres, to mediate spindle orientation. Second, Scribble re-locates to the junction between the two daughters to allow a new E-cadherin-based-interface to form between them, influencing the width of the nascent daughter-daughter junction and subsequent cell positioning. Thus, E-cadherin and Scribble dynamically relocate to different intracellular sites during cell division to orient the mitotic spindle and control placement of the daughter cells after cell division. This article has an associated First Person interview with the first author of the paper.

Large-scale analysis and computer modeling reveal hidden regularities behind variability of cell division patterns in Arabidopsis thaliana embryogenesis

Noise plays a major role in cellular processes and in the development of tissues and organs. Several studies have examined the origin, the integration or the accommodation of noise in gene expression, cell growth and elaboration of organ shape. By contrast, much less is known about variability in cell division plane positioning, its origin and links with cell geometry, and its impact on tissue organization. Taking advantage of the first-stereotyped-then-variable division patterns in the embryo of the model plant Arabidopsis thaliana, we combined 3D imaging and quantitative cell shape and cell lineage analysis together with mathematical and computer modeling to perform a large-scale, systematic analysis of variability in division plane orientation. Our results reveal that, paradoxically, variability in cell division patterns of Arabidopsis embryos is accompanied by a progressive reduction of heterogeneity in cell shape topology. The paradox is solved by showing that variability operates within a reduced repertoire of possible division plane orientations that is related to cell geometry. We show that in several domains of the embryo, a recently proposed geometrical division rule recapitulates observed variable patterns, suggesting that variable patterns emerge from deterministic principles operating in a variable geometrical context. Our work highlights the importance of emerging patterns in the plant embryo under iterated division principles, but also reveal domains where deviations between rule predictions and experimental observations point to additional regulatory mechanisms.

Entropy as a Geometrical Source of Information in Biological Organizations

Considering both biological and non-biological polygonal shape organizations, in this paper we introduce a quantitative method which is able to determine informational entropy as spatial differences between heterogeneity of internal areas from simulation and experimental samples. According to these data (i.e., heterogeneity), we are able to establish levels of informational entropy using statistical insights of spatial orders using discrete and continuous values. Given a particular state of entropy, we establish levels of information as a novel approach which can unveil general principles of biological organization. Thirty-five geometric aggregates are tested (biological, non-biological, and polygonal simulations) in order to obtain the theoretical and experimental results of their spatial heterogeneity. Geometrical aggregates (meshes) include a spectrum of organizations ranging from cell meshes to ecological patterns. Experimental results for discrete entropy using a bin width of 0.5 show that a particular range of informational entropy (0.08 to 0.27 bits) is intrinsically associated with low rates of heterogeneity, which indicates a high degree of uncertainty in finding non-homogeneous configurations. In contrast, differential entropy (continuous) results reflect negative entropy within a particular range (−0.4 to −0.9) for all bin widths. We conclude that the differential entropy of geometrical organizations is an important source of neglected information in biological systems.

A quantitative biophysical principle to explain the 3D cellular connectivity in curved epithelia

Epithelial cell organization and the mechanical stability of tissues are closely related. In this context, it has been recently shown that packing optimization in bended or folded epithelia is achieved by an energy minimization mechanism that leads to a complex cellular shape: the "scutoid". Here, we focus on the relationship between this shape and the connectivity between cells. We use a combination of computational, experimental, and biophysical approaches to examine how energy drivers affect the three-dimensional (3D) packing of tubular epithelia. We propose an energy-based stochastic model that explains the 3D cellular connectivity. Then, we challenge it by experimentally reducing the cell adhesion. As a result, we observed an increment in the appearance of scutoids that correlated with a decrease in the energy barrier necessary to connect with new cells. We conclude that tubular epithelia satisfy a quantitative biophysical principle that links tissue geometry and energetics with the average cellular connectivity.

The role of evolutionary game theory in spatial and non-spatial models of the survival of cooperation in cancer: a review

Evolutionary game theory (EGT) is a branch of mathematics which considers populations of individuals interacting with each other to receive pay-offs. An individual’s pay-off is dependent on the strategy of its opponent(s) as well as on its own, and the higher its pay-off, the higher its reproductive fitness. Its offspring generally inherit its interaction strategy, subject to random mutation. Over time, the composition of the population shifts as different strategies spread or are driven extinct. In the last 25 years there has been a flood of interest in applying EGT to cancer modelling, with the aim of explaining how cancerous mutations spread through healthy tissue and how intercellular cooperation persists in tumour-cell populations. This review traces this body of work from theoretical analyses of well-mixed infinite populations through to more realistic spatial models of the development of cooperation between epithelial cells. We also consider work in which EGT has been used to make experimental predictions about the evolution of cancer, and discuss work that remains to be done before EGT can make large-scale contributions to clinical treatment and patient outcomes.

Hexagonal Voronoi pattern detected in the microstructural design of the echinoid skeleton

Repeated polygonal patterns are pervasive in natural forms and structures. These patterns provide inherent structural stability while optimizing strength-per-weight and minimizing construction costs. In echinoids (sea urchins), a visible regularity can be found in the endoskeleton, consisting of a lightweight and resistant micro-trabecular meshwork (stereom). This foam-like structure follows an intrinsic geometrical pattern that has never been investigated. This study aims to analyse and describe it by focusing on the boss of tubercles-spine attachment sites subject to strong mechanical stresses-in the common sea urchin Paracentrotus lividus. The boss microstructure was identified as a Voronoi construction characterized by 82% concordance to the computed Voronoi models, a prevalence of hexagonal polygons, and a regularly organized seed distribution. This pattern is interpreted as an evolutionary solution for the construction of the echinoid skeleton using a lightweight microstructural design that optimizes the trabecular arrangement, maximizes the structural strength and minimizes the metabolic costs of secreting calcitic stereom. Hence, this identification is particularly valuable to improve the understanding of the mechanical function of the stereom as well as to effectively model and reconstruct similar structures in view of future applications in biomimetic technologies and designs.

Emergence of Resistance to MTI-101 Selects for a MET Genotype and Phenotype in EGFR Driven PC-9 and PTEN Deleted H446 Lung Cancer Cell Lines

MTI-101 is a first-in-class cyclic peptide that kills cells via calcium overload in a caspase-independent manner. Understanding biomarkers of response is critical for positioning a novel therapeutic toward clinical development. Isogenic MTI-101-acquired drug-resistant lung cancer cell line systems (PC-9 and H446) coupled with differential RNA-SEQ analysis indicated that downregulated genes were enriched in the hallmark gene set for epithelial-to-mesenchymal transition (EMT) in both MTI-101-acquired resistant cell lines. The RNA-SEQ results were consistent with changes in the phenotype, including a decreased invasion in Matrigel and expression changes in EMT markers (E-cadherin, vimentin and Twist) at the protein level. Furthermore, in the EGFR-driven PC-9 cell line, selection for resistance towards MTI-101 resulted in collateral sensitivity toward EGFR inhibitors. MTI-101 treatment showed synergistic activity with the standard of care agents erlotinib, osimertinib and cisplatin when used in combination in PC-9 and H446 cells, respectively. Finally, in vivo data indicate that MTI-101 treatment selects for increased E-cadherin and decreased vimentin in H446, along with a decreased incident of bone metastasis in the PC-9 in vivo model. Together, these data indicate that chronic MTI-101 treatment can lead to a change in cell state that could potentially be leveraged therapeutically to reduce metastatic disease.

Two types of critical cell density for mechanical elimination of abnormal cell clusters from epithelial tissue

Recent technological advances in high-resolution imaging and artificial modulation of genetic functions at different times and regions have enabled direct observations of the formation and elimination of abnormal cell populations. A recent trend in cell competition research is the incorporation of cell mechanics. In different tissues and species, abnormal cells developing in epithelial tissues are mechanically eliminated by cell contraction via actomyosin accumulation at the interface between normal and abnormal cells. This mechanical cell elimination process has attracted attention as a potential universal defense mechanism. Here, we theoretically examined the conditions for mechanical elimination of growing abnormal cell populations. Simulations and mathematical analyses using a vertex dynamics model revealed two types of critical cell density associated with mechanical elimination of abnormal cell clusters. One is a subtype of homeostatic density, in which the frequencies of spontaneous mechanical cell elimination and proliferation are balanced, even if no explicit dependence of proliferation or apoptosis on the cell density is assumed. This density is related to the mechanical stability of a single cell. The other is density related to mechanical stability as a cell population under external pressure. Both density types are determined by tissue mechanical properties. In solid tissues, the former type is reached first as the intensity of interfacial contraction increases, and it functions as a critical density. On the other hand, the latter type becomes critical when tissues are highly fluid. The derived analytical solution explicitly reveals the dependence of critical contractile force and density on different parameters. We also found a negative correlation between the proliferation rate of abnormal cells and the likelihood of the abnormal cell population expanding by escaping elimination. This is counterintuitive because in the context of cell competition, fast-growing cell populations generally win. These findings provide new insight into, and interpretation of, the results from experimental studies.

High-resolution imaging techniques have revealed that abnormal cells developing in epithelial tissues are mechanically eliminated via contraction at the interface between the abnormal cells and normal surrounding cells. This phenomenon is seen in various species and tissues and thus is regarded as a primitive defense system against precancerous cells common to all animals. For comprehensive understanding of this potential defense system, we derived mathematical conditions to achieve mechanical elimination of growing abnormal cell populations. We identified two characteristic cell density types associated with successful mechanical elimination of abnormal cell clusters. Both are determined by tissue physical properties, and the smaller of the two functions as a critical density above which abnormal cell populations cannot exist. We also found a counterintuitive phenomenon in which slower proliferation of abnormal cells promotes their growth as a population. Our results will help elucidate the mechanisms of intrinsic tissue defenses against cancer from the perspective of cell mechanics.

Random nature of epithelial cancer cell monolayers

Although the polygonal shape of epithelial cells has been drawing the attention of scientists for several centuries, only a decade and a half ago it was demonstrated that distributions of polygon types (DOPTs) are similar in proliferative epithelia of many different plant and animal species. In this study, we show that hyper-proliferation of cancer cells disrupts this universal paradigm and results in randomly organized epithelial structures. Examining non-synchronized and synchronized HeLa cervix cells, we suppose that the spread of cell sizes is the main parameter controlling the DOPT in the cancer cell monolayers. To test this hypothesis, we develop a theory of morphologically similar random polygonal packings. By analysing differences between tumoural and normal epithelial cell monolayers, we conclude that the latter have more ordered structures because of their lower proliferation rates and, consequently, more effective relaxation of mechanical stress associated with cell division and growth. To explain the structural features of normal proliferative epithelium, we take into account the spread of cell sizes in the monolayer. The proposed theory also rationalizes some highly ordered unconventional post-mitotic epithelia.

Linear viscoelastic properties of the vertex model for epithelial tissues

Epithelial tissues act as barriers and, therefore, must repair themselves, respond to environmental changes and grow without compromising their integrity. Consequently, they exhibit complex viscoelastic rheological behavior where constituent cells actively tune their mechanical properties to change the overall response of the tissue, e.g., from solid-like to fluid-like. Mesoscopic mechanical properties of epithelia are commonly modeled with the vertex model. While previous studies have predominantly focused on the rheological properties of the vertex model at long time scales, we systematically studied the full dynamic range by applying small oscillatory shear and bulk deformations in both solid-like and fluid-like phases for regular hexagonal and disordered cell configurations. We found that the shear and bulk responses in the fluid and solid phases can be described by standard spring-dashpot viscoelastic models. Furthermore, the solid-fluid transition can be tuned by applying pre-deformation to the system. Our study provides insights into the mechanisms by which epithelia can regulate their rich rheological behavior.

Modelling the Collective Mechanical Regulation of the Structure and Morphology of Epithelial Cell Layers

The morphology and function of epithelial sheets play an important role in healthy tissue development and cancer progression. The maintenance of structure of closely packed epithelial layers requires the coordination of various mechanical forces due to intracellular activities and interactions with other cells and tissues. However, a general model for the combination of mechanical properties which determine the cell shape and the overall structure of epithelial layers remains elusive. Here, we propose a computational model, based on the Cellular Potts Model, to analyse the interplay between mechanical properties of cells and dynamical transitions in epithelial cell shapes and structures. We map out phase diagrams as functions of cellular properties and the orientation of cell division. Results show that monolayers of squamous, cuboidal, and columnar cells are formed when the axis of cell proliferation is perpendicular to the substrate or along the major axis of the cells. Monolayer-to-multilayer transition is promoted via cell extrusion, depending on the mechanical properties of cells and the orientation of cell division. The results and model predictions are discussed in the context of experimental observations.

Impact of contact inhibition on collective cell migration and proliferation

Contact inhibition limits migration and proliferation of cells in cell colonies. We consider a multiphase field model to investigate the growth dynamics of a cell colony, composed of proliferating cells. The model takes into account the mechanism of contact inhibition of proliferation by local mechanical interactions. We compare nonmigrating and migrating cells, in order to provide a quantitative characterization of the dynamics and analyze the velocity of the colony boundary for both cases. Additionally, we measure single cell velocities, number of neighbor distributions, as well as the influence of stress and age on positions of the cells and with respect to each other.