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

Bacterial Subcellular Architecture, Structural Epistasis, and Antibiotic Resistance

Epistasis refers to the way in which genetic interactions between some genetic loci affect phenotypes and fitness. In this study, we propose the concept of "structural epistasis" to emphasize the role of the variable physical interactions between molecules located in particular spaces inside the bacterial cell in the emergence of novel phenotypes. The architecture of the bacterial cell (typically Gram-negative), which consists of concentrical layers of membranes, particles, and molecules with differing configurations and densities (from the outer membrane to the nucleoid) determines and is in turn determined by the cell shape and size, depending on the growth phases, exposure to toxic conditions, stress responses, and the bacterial environment. Antibiotics change the bacterial cell's internal molecular topology, producing unexpected interactions among molecules. In contrast, changes in shape and size may alter antibiotic action. The mechanisms of antibiotic resistance (and their vectors, as mobile genetic elements) also influence molecular connectivity in the bacterial cell and can produce unexpected phenotypes, influencing the action of other antimicrobial agents.

Energetic convenience of cell division in biological tissues

A typical feature of living tissues is proliferation by division: it is a fundamental aspect of many biological processes, including embryonic development, morphogenesis, and cancer growth. Here, we study the energetics of cell division occurring in epithelia, highlighting the interplay of the key parameters ruling mitosis. We find the existence of a region, in the parameter space, which is independent of the cell elasticity and weakly dependent on the ratio between mother and daughter cells areas. In this region, cell division is energetically favorable. Our results may lead to an exact characterization of cells having anomalous proliferation.

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.

Topological traits of a cellular pattern versus growth rate anisotropy in radish roots

The topology of a cellular pattern, which means the spatial arrangement of cells, directly corresponds with cell packing, which is crucial for tissue and organ functioning. The topological features of cells that are typically analyzed are the number of their neighbors and the cell area. To date, the objects of most topological studies have been the growing cells of the surface tissues of plant and animal organs. Some of these researches also provide verification of Lewis's Law concerning the linear correlation between the number of neighboring cells and the cell area. Our aim was to analyze the cellular topology and applicability of Lewis's Law to an anisotropically growing plant organ. The object of our study was the root apex of radish. Based on the tensor description of plant organ growth, we specified the level of anisotropy in specific zones (the root proper, the columella of the cap and the lateral parts of the cap) and in specific types of both external (epidermis) and internal tissues (stele and ground tissue) of the apex. The strongest anisotropy occurred in the root proper, while both zones of the cap showed an intermediate level of anisotropy of growth. Some differences in the topology of the cellular pattern in the zones were also detected; in the root proper, six-sided cells predominated, while in the root cap columella and in the lateral parts of the cap, most cells had five neighbors. The correlation coefficient rL between the number of neighboring cells and the cell area was high in the apex as a whole as well as in all of the zones except the root proper and in all of the tissue types except the ground tissue. In general, Lewis's Law was fulfilled in the anisotropically growing radish root apex. However, the level of the applicability (rL value) of Lewis's Law was negatively correlated with the level of the anisotropy of growth, which may suggest that in plant organs in the regions of anisotropic growth, the number of neighboring cells is less dependent on the cell size.

E-cadherin expression pattern during zebrafish embryonic epidermis development

Background: E-cadherin is the major adhesion receptor in epithelial adherens junctions (AJs). On established epidermis, E-cadherin performs fine-tuned cell-cell contact remodeling to maintain tissue integrity, which is characterized by modulation of cell shape, size and packing density. In zebrafish, the organization and distribution of E-cadherin in AJs during embryonic epidermis development remain scarcely described.

Methods: Combining classical immunofluorescence, deconvolution microscopy and 3D-segmentation of AJs in epithelial cells, a quantitative approach was implemented to assess the spatial and temporal distribution of E-cadherin across zebrafish epidermis between 24 and 72 hpf.

Results: increasing levels of E-cadh protein parallel higher cell density and the appearance of hexagonal cells in the enveloping layer (EVL) as well as the establishments of new cell-cell contacts in the epidermal basal layer (EBL), being significantly between 31 and 48 hpf .

Conclusions: Increasing levels of E-cadherin in AJs correlates with extensive changes in cell morphology towards hexagonal packing during the epidermis morphogenesis.

Development of epithelial tissues: How are cleavage planes chosen?

The cross-section of a cell in a monolayer epithelial tissue can be modeled mathematically as a k-sided polygon. Empirically studied distributions of the proportions of k-sided cells in epithelia show remarkable similarities in a wide range of evolutionarily distant organisms. A variety of mathematical models have been proposed for explaining this phenomenon. The highly parsimonious simulation model of (Patel et al., PLoS Comput. Biol., 2009) that takes into account only the number of sides of a given cell and cell division already achieves a remarkably good fit with empirical distributions from Drosophila, Hydra, Xenopus, Cucumber, and Anagallis. Within the same modeling framework as in that paper, we introduce additional options for the choice of the endpoints of the cleavage plane that appear to be biologically more realistic. By taking the same data sets as our benchmarks, we found that combinations of some of our new options consistently gave better fits with each of these data sets than previously studied ones. Both our algorithm and simulation data are made available as research tools for future investigations.

Dynamic cellular finite-element method for modelling large-scale cell migration and proliferation under the control of mechanical and biochemical cues: a study of re-epithelialization

Computational modelling of cells can reveal insight into the mechanisms of the important processes of tissue development. However, current cell models have limitations and are challenged to model detailed changes in cellular shapes and physical mechanics when thousands of migrating and interacting cells need to be modelled. Here we describe a novel dynamic cellular finite-element model (DyCelFEM), which accounts for changes in cellular shapes and mechanics. It also models the full range of cell motion, from movements of individual cells to collective cell migrations. The transmission of mechanical forces regulated by intercellular adhesions and their ruptures are also accounted for. Intra-cellular protein signalling networks controlling cell behaviours are embedded in individual cells. We employ DyCelFEM to examine specific effects of biochemical and mechanical cues in regulating cell migration and proliferation, and in controlling tissue patterning using a simplified re-epithelialization model of wound tissue. Our results suggest that biochemical cues are better at guiding cell migration with improved directionality and persistence, while mechanical cues are better at coordinating collective cell migration. Overall, DyCelFEM can be used to study developmental processes when a large population of migrating cells under mechanical and biochemical controls experience complex changes in cell shapes and mechanics.

Pavement cells and the topology puzzle

D'Arcy Thompson emphasised the importance of surface tension as a potential driving force in establishing cell shape and topology within tissues. Leaf epidermal pavement cells grow into jigsaw-piece shapes, highly deviating from such classical forms. We investigate the topology of developing Arabidopsis leaves composed solely of pavement cells. Image analysis of around 50,000 cells reveals a clear and unique topological signature, deviating from previously studied epidermal tissues. This topological distribution is established early during leaf development, already before the typical pavement cell shapes emerge, with topological homeostasis maintained throughout growth and unaltered between division and maturation zones. Simulating graph models, we identify a heuristic cellular division rule that reproduces the observed topology. Our parsimonious model predicts how and when cells effectively place their division plane with respect to their neighbours. We verify the predicted dynamics through in vivo tracking of 800 mitotic events, and conclude that the distinct topology is not a direct consequence of the jigsaw piece-like shape of the cells, but rather owes itself to a strongly life history-driven process, with limited impact from cell-surface mechanics.

The E-cadherin/AmotL2 complex organizes actin filaments required for epithelial hexagonal packing and blastocyst hatching

Epithelial cells connect via cell-cell junctions to form sheets of cells with separate cellular compartments. These cellular connections are essential for the generation of cellular forms and shapes consistent with organ function. Tissue modulation is dependent on the fine-tuning of mechanical forces that are transmitted in part through the actin connection to E-cadherin as well as other components in the adherens junctions. In this report we show that p100 amotL2 forms a complex with E-cadherin that associates with radial actin filaments connecting cells over multiple layers. Genetic inactivation or depletion of amotL2 in epithelial cells in vitro or zebrafish and mouse in vivo, resulted in the loss of contractile actin filaments and perturbed epithelial packing geometry. We further showed that AMOTL2 mRNA and protein was expressed in the trophectoderm of human and mouse blastocysts. Genetic inactivation of amotL2 did not affect cellular differentiation but blocked hatching of the blastocysts from the zona pellucida. These results were mimicked by treatment with the myosin II inhibitor blebbistatin. We propose that the tension generated by the E-cadherin/AmotL2/actin filaments plays a crucial role in developmental processes such as epithelial geometrical packing as well as generation of forces required for blastocyst hatching.

Vertex models: from cell mechanics to tissue morphogenesis

Tissue morphogenesis requires the collective, coordinated motion and deformation of a large number of cells. Vertex model simulations for tissue mechanics have been developed to bridge the scales between force generation at the cellular level and tissue deformation and flows. We review here various formulations of vertex models that have been proposed for describing tissues in two and three dimensions. We discuss a generic formulation using a virtual work differential, and we review applications of vertex models to biological morphogenetic processes. We also highlight recent efforts to obtain continuum theories of tissue mechanics, which are effective, coarse-grained descriptions of vertex models.This article is part of the themed issue 'Systems morphodynamics: understanding the development of tissue hardware'.

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.

Effects of mechanical properties on tumor invasion: insights from a cellular model

Understanding the regulating mechanism of tumor invasion is of crucial importance for both fundamental cancer research and clinical applications. Previous in vivo experiments have shown that invasive cancer cells dissociate from the primary tumor and invade into the stroma, forming an irregular invasive morphology. Although cell movements involved in tumor invasion are ultimately driven by mechanical forces of cell-cell interactions and tumor-host interactions, how these mechanical properties affect tumor invasion is still poorly understood. In this study, we use a recently developed two-dimensional cellular model to study the effects of mechanical properties on tumor invasion. We study the effects of cell-cell adhesions as well as the degree of degradation and stiffness of extracellular matrix (ECM). Our simulation results show that cell-cell adhesion relationship must be satisfied for tumor invasion. Increased adhesion to ECM and decreased adhesion among tumor cells result in invasive tumor behaviors. When this invasive behavior occurs, ECM plays an important role for both tumor morphology and the shape of invasive cancer cells. Increased stiffness and stronger degree of degradation of ECM promote tumor invasion, generating more aggressive tumor invasive morphologies. It can also generate irregular shape of invasive cancer cells, protruding towards ECM. The capability of our model suggests it a useful tool to study tumor invasion and might be used to propose optimal treatment in clinical applications.

Patterning of wound-induced intercellular Ca(2+) flashes in a developing epithelium

Differential mechanical force distributions are increasingly recognized to provide important feedback into the control of an organ's final size and shape. As a second messenger that integrates and relays mechanical information to the cell, calcium ions (Ca(2+)) are a prime candidate for providing important information on both the overall mechanical state of the tissue and resulting behavior at the individual-cell level during development. Still, how the spatiotemporal properties of Ca(2+) transients reflect the underlying mechanical characteristics of tissues is still poorly understood. Here we use an established model system of an epithelial tissue, the Drosophila wing imaginal disc, to investigate how tissue properties impact the propagation of Ca(2+) transients induced by laser ablation. The resulting intercellular Ca(2+) flash is found to be mediated by inositol 1,4,5-trisphosphate and depends on gap junction communication. Further, we find that intercellular Ca(2+) transients show spatially non-uniform characteristics across the proximal-distal axis of the larval wing imaginal disc, which exhibit a gradient in cell size and anisotropy. A computational model of Ca(2+) transients is employed to identify the principle factors explaining the spatiotemporal patterning dynamics of intercellular Ca(2+) flashes. The relative Ca(2+) flash anisotropy is principally explained by local cell shape anisotropy. Further, Ca(2+) velocities are relatively uniform throughout the wing disc, irrespective of cell size or anisotropy. This can be explained by the opposing effects of cell diameter and cell elongation on intercellular Ca(2+) propagation. Thus, intercellular Ca(2+) transients follow lines of mechanical tension at velocities that are largely independent of tissue heterogeneity and reflect the mechanical state of the underlying tissue.

Mechanical model of geometric cell and topological algorithm for cell dynamics from single-cell to formation of monolayered tissues with pattern

Geometric and mechanical properties of individual cells and interactions among neighboring cells are the basis of formation of tissue patterns. Understanding the complex interplay of cells is essential for gaining insight into embryogenesis, tissue development, and other emerging behavior. Here we describe a cell model and an efficient geometric algorithm for studying the dynamic process of tissue formation in 2D (e.g. epithelial tissues). Our approach improves upon previous methods by incorporating properties of individual cells as well as detailed description of the dynamic growth process, with all topological changes accounted for. Cell size, shape, and division plane orientation are modeled realistically. In addition, cell birth, cell growth, cell shrinkage, cell death, cell division, cell collision, and cell rearrangements are now fully accounted for. Different models of cell-cell interactions, such as lateral inhibition during the process of growth, can be studied in detail. Cellular pattern formation for monolayered tissues from arbitrary initial conditions, including that of a single cell, can also be studied in detail. Computational efficiency is achieved through the employment of a special data structure that ensures access to neighboring cells in constant time, without additional space requirement. We have successfully generated tissues consisting of more than 20,000 cells starting from 2 cells within 1 hour. We show that our model can be used to study embryogenesis, tissue fusion, and cell apoptosis. We give detailed study of the classical developmental process of bristle formation on the epidermis of D. melanogaster and the fundamental problem of homeostatic size control in epithelial tissues. Simulation results reveal significant roles of solubility of secreted factors in both the bristle formation and the homeostatic control of tissue size. Our method can be used to study broad problems in monolayered tissue formation. Our software is publicly available.

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.

Multiscale Modeling of Cellular Epigenetic States: Stochasticity in Molecular Networks, Chromatin Folding in Cell Nuclei, and Tissue Pattern Formation of Cells

Genome sequences provide the overall genetic blueprint of cells, but cells possessing the same genome can exhibit diverse phenotypes. There is a multitude of mechanisms controlling cellular epigenetic states and that dictate the behavior of cells. Among these, networks of interacting molecules, often under stochastic control, depending on the specific wirings of molecular components and the physiological conditions, can have a different landscape of cellular states. In addition, chromosome folding in three-dimensional space provides another important control mechanism for selective activation and repression of gene expression. Fully differentiated cells with different properties grow, divide, and interact through mechanical forces and communicate through signal transduction, resulting in the formation of complex tissue patterns. Developing quantitative models to study these multi-scale phenomena and to identify opportunities for improving human health requires development of theoretical models, algorithms, and computational tools. Here we review recent progress made in these important directions.

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.

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

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

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

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