Cell Shape Distribution Research Articles

Spherical harmonics analysis reveals cell shape-fate relationships in zebrafish lateral line neuromasts.

Cell shape is a powerful readout of cell state, fate and function. We describe a custom workflow to perform semi-automated, 3D cell and nucleus segmentation, and spherical harmonics and principal components analysis to distill cell and nuclear shape variation into discrete biologically meaningful parameters. We apply these methods to analyze shape in the neuromast cells of the zebrafish lateral line system, finding that shapes vary with cell location and identity. The distinction between hair cells and support cells accounted for much of the variation, which allowed us to train classifiers to predict cell identity from shape features. Using transgenic markers for support cell subpopulations, we found that subtypes had different shapes from each other. To investigate how loss of a neuromast cell type altered cell shape distributions, we examined atoh1a mutants that lack hair cells. We found that mutant neuromasts lacked the cell shape phenotype associated with hair cells, but did not exhibit a mutant-specific cell shape. Our results demonstrate the utility of using 3D cell shape features to characterize, compare and classify cells in a living developing organism.

On the origin of universal cell shape variability in confluent epithelial monolayers.

Cell shape is fundamental in biology. The average cell shape can influence crucial biological functions, such as cell fate and division orientation. But cell-to-cell shape variability is often regarded as noise. In contrast, recent works reveal that shape variability in diverse epithelial monolayers follows a nearly universal distribution. However, the origin and implications of this universality remain unclear. Here, assuming contractility and adhesion are crucial for cell shape, characterized via aspect ratio (r), we develop a mean-field analytical theory for shape variability. We find that all the system-specific details combine into a single parameter α that governs the probability distribution function (PDF) of r; this leads to a universal relation between the standard deviation and the average of r. The PDF for the scaled r is not strictly but nearly universal. In addition, we obtain the scaled area distribution, described by the parameter μ. Information of α and μ together can distinguish the effects of changing physical conditions, such as maturation, on different system properties. We have verified the theory via simulations of two distinct models of epithelial monolayers and with existing experiments on diverse systems. We demonstrate that in a confluent monolayer, average shape determines both the shape variability and dynamics. Our results imply that cell shape distribution is inevitable, where a single parameter describes both statics and dynamics and provides a framework to analyze and compare diverse epithelial systems. In contrast to existing theories, our work shows that the universal properties are consequences of a mathematical property and should be valid in general, even in the fluid regime.

Effect of paclitaxel treatment on cellular mechanics and morphology of human oesophageal squamous cell carcinoma in 2D and 3D environments.

During chemotherapy, structural and mechanical changes in malignant cells have been observed in several cancers, including leukaemia and pancreatic and prostate cancer. Such cellular changes may act as physical biomarkers for chemoresistance and cancer recurrence. This study aimed to determine how exposure to paclitaxel affects the intracellular stiffness of human oesophageal cancer of South African origin in vitro. A human oesophageal squamous cell carcinoma cell line WHCO1 was cultured on glass substrates (2D) and in collagen gels (3D) and exposed to paclitaxel for up to 48 h. Cellular morphology and stiffness were assessed with confocal microscopy, visually aided morpho-phenotyping image recognition and mitochondrial particle tracking microrheology at 24 and 48 h. In the 2D environment, the intracellular stiffness was higher for the paclitaxel-treated than for untreated cells at 24 and 48 h. In the 3D environment, the paclitaxel-treated cells were stiffer than the untreated cells at 24 h, but no statistically significant differences in stiffness were observed at 48 h. In 2D, paclitaxel-treated cells were significantly larger at 24 and 48 h and more circular at 24 but not at 48 h than the untreated controls. In 3D, there were no significant morphological differences between treated and untreated cells. The distribution of cell shapes was not significantly different across the different treatment conditions in 2D and 3D environments. Future studies with patient-derived primary cancer cells and prolonged drug exposure will help identify physical cellular biomarkers to detect chemoresistance onset and assess therapy effectiveness in oesophageal cancer patients.

Quantification of Cell-Substrate Adhesion Area and Cell Shape Distributions in MCF7 Cell Monolayers.

The methods presented here quantify some parameters of confluent adherent cell monolayers from multiple appropriately stained confocal images: adhesion to the substrate as a function of the number and size of focal adhesions, and cell shape, characterized by the cell shape index and other shape descriptors. Focal adhesions were visualized by paxillin staining and cell-cell borders were marked by junction plakoglobin and actin. The methods for cell culture and staining were standard; images represent single focal planes; image analysis was performed using publicly available image processing software. The presented protocols are used to quantify the number and size of focal adhesions and the differences in cell shape distribution in the monolayers, but they can be repurposed for the quantification of the size and shape of any other distinct cellular structure that can be stained (e.g., mitochondria or nuclei). Assessing these parameters is important in the characterization of the dynamic forces in adherent cell layer, including cell adhesion and actomyosin contractility that affects cell shape.

Quantification of Cell-Substrate Adhesion Area and Cell Shape Distributions in MCF7 Cell Monolayers

Quantification of Cell-Substrate Adhesion Area and Cell Shape Distributions in MCF7 Cell Monolayers

Mechanical Testing of Metallic Foams for 3d Model and Simulation of Cell Distribution Effects

Cellular materials have a bulk matrix with a larger number of voids named also cells. Metallic foams made by powder technology represent stochastic closed cells. The related inhomogeneity leads to a scattering of results both in terms of stress–strain curves and maximum strength. Scattering is attributed to relative density variations and local cell discontinuities and it is confirmed also in case of dynamic loading. Finite element simulations through geometrical models that are able to capture the void morphology (named “mesoscale models”), confirm these results and some efforts have been already done to quantify the relationship between shape irregularities and mechanical behavior.The aim of this paper is to present the dynamic characterization of an AA7075 closed cell material and to calibrate its mesoscale finite element model according to the related cell shape distribution. Specimens have been derived from a small ingot (45x45x100 mm) divided along sections so that morphological analysis and experimental tests have been carried out. Specimens extracted from a half of the ingot have been used for dynamic compression tests by means of a split Hopkinson bar, meanwhile specimens extracted from the other half of the ingot have been dissected for porosity distribution analyses carried out by means of image analysis.Stress-strain curves obtained from the mechanical tests have been discussed in terms of strain rate and statistical descriptors of the porosity. Successively a 3D-model of the specimen has been generated starting from the Voronoi algorithm, assigning as input the above-mentioned statistical distribution of the porosity. Due to the peculiarity of the cell morphology (e.g. single larger cells), stress-strain localization has been demonstrated as one of the reasons of the scattering found during the experiments. A material model, to reproduce the investigated foam mechanical behavior, has been calibrated. Despite the difference among experiments the material model is able to reproduce all of them. Difference between the model coefficients quantifies roughly the difference due to the local geometry of the cells.

Mechanics of epithelial tissue formation

A key process in the life of any multicellular organism is its development from a single egg into a full grown adult. The first step in this process often consists of forming a tissue layer out of randomly placed cells on the surface of the egg. We present a model for generating such a tissue, based on mechanical interactions between the cells, and find that the resulting cellular pattern corresponds to the Voronoi tessellation of the nuclei of the cells. Experimentally, we obtain the same result in both fruit flies and flour beetles, with a distribution of cell shapes that matches that of the model, without any adjustable parameters. Finally, we show that this pattern is broken when the cells grow at different rates.

Flow morphometry to assess the red blood cell storage lesion.

We present a novel automated system for morphology analysis of red blood cells (RBC) under flow. RBC concentrates collected by blood banks for transfusions are stored for periods of up to several weeks, during which time a number of changes occur, collectively termed the storage lesion. Typically the extent of hemolysis is the defining criterion to determine the acceptability of the RBCs for transfusions. Morphological changes are related with biochemical alteration during the storage of RBCs. The typical blood smear procedure for determining such changes is a labor-intensive and potentially biased manual process. The advantage of the flow morphometry system presented here is that it provides fully automated morphological classification of RBCs with large sample numbers in a short time. Our system uses a commercially available flow cell and flow conditions that prevent adhesion of RBCs, thus eliminating the need for blocking agents such as albumin that affect the distribution of cell shapes. Our morphometry results are validated by comparison with standard biochemical assays (hemolysis, ATP) for blood from 17 donors stored under blood bank conditions for 13 weeks. We show that the percentage of spherocytes present can be used to estimate the status of RBC concentrates. © 2017 International Society for Advancement of Cytometry.

The effect of matrix stiffness on biomechanical properties of chondrocytes.

The behavior of chondrocytes is regulated by multiple mechanical microenvironmental cues. During development and degenerative disease of articular cartilage, as an external signal, the extracellular matrix stiffness of chondrocytes changes significantly, but whether and how this biophysical cue affects biomechanical properties of chondrocytes remain elusive. In the present study, we designed supporting-biomaterials as mimics of native pericellular matrix to study the effect of matrix stiffness on chondrocyte morphology and F-actin distribution. Furthermore, the active mechanical behavior of chondrocytes during sensing and responding to different matrix stiffness was quantitatively investigated using atom force microscope technique and theoretical model. Our results indicated that stiffer matrix tends to increase the cell spreading area, the percentage of irregular cell shape distribution and mechanical parameters including elastic modulus (Eelastic), instantaneous modulus (E0), relaxed modulus (ER) and apparent viscosity (μ) of chondrocytes. Knowledge of matrix stiffness-dependent biomechanical behaviors of chondrocytes has important implications for optimizing matrix material and advancing chondrocyte-based applications for functional tissue engineering.

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

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

Bonded-cell model for particle fracture.

Particle degradation and fracture play an important role in natural granular flows and in many applications of granular materials. We analyze the fracture properties of two-dimensional disklike particles modeled as aggregates of rigid cells bonded along their sides by a cohesive Mohr-Coulomb law and simulated by the contact dynamics method. We show that the compressive strength scales with tensile strength between cells but depends also on the friction coefficient and a parameter describing cell shape distribution. The statistical scatter of compressive strength is well described by the Weibull distribution function with a shape parameter varying from 6 to 10 depending on cell shape distribution. We show that this distribution may be understood in terms of percolating critical intercellular contacts. We propose a random-walk model of critical contacts that leads to particle size dependence of the compressive strength in good agreement with our simulation data.

Forces Behind Cell Adhesion and Migration in Microgravity

Cells sense and respond to their environment according to many factors, including gravity. Changes in the gravitational field during space exploration may alter cellular interactions. Our understanding of the fundamental mechanisms by which gravitational forces ultimately affect cell function, however, is limited. Based on our prior observations, human mesenchymal stem cells (hMSCs) adopt a more rounded morphology during simulated microgravity (clinorotation). We hypothesize that microgravity affects the cell-substrate forces, which in turn affects cell adhesion and motility. Therefore, we investigated the correlation between traction forces, spreading and chemotaxis. As an extension to our previously reported “clinochip” device, we developed a lab-on-a-chip device suitable for implementing traction force microscopy during clinorotation. The device contains a channel coated with an array of fluorescent beads embedded in a polyacrylamide substrate that can be processed to calculate cell-substrate traction forces. For our studies, we investigated both hMSCs and osteosarcoma cancer cells (143-B), because they represent highly regulated and deregulated cell states in the osteogenic lineage, respectively. Clinorotation speeds of 0, 30, and 75 rpm were examined, and cell shape, adhesion area, traction forces, and chemotactic migration were measured. Interestingly, results indicate that hMSCs exhibit a dose-dependent response to clinorotation speed based on a shift in the population distribution of cell shape and adhesion area, while osteosarcoma cells do not. These results suggest that a deregulated cell phenotype may possess distinct mechanosensing characteristics, which may be related to our measures of cell adhesion, traction and chemotaxis. Our results are among the first efforts to directly measure the physical interplay between the cell and its substrate during simulated microgravity. This will allow us to gain a deeper understanding of the cellular mechanisms that lead to tissue-level changes, such as atrophy and reduced bone mineral density, observed in astronauts.

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

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

Synchrotron X-ray computed laminography of the three-dimensional anatomy of tomato leaves.

Synchrotron radiation computed laminography (SR-CL) is presented as an imaging method for analyzing the three-dimensional (3D) anatomy of leaves. The SR-CL method was used to provide 3D images of 1-mm² samples of intact leaves at a pixel resolution of 750nm. The method allowed visualization and quantitative analysis of palisade and spongy mesophyll cells, and showed local venation patterns, aspects of xylem vascular structure and stomata. The method failed to image subcellular organelles such as chloroplasts. We constructed 3D computer models of leaves that can provide a basis for calculating gas exchange, light penetration and water and solute transport. The leaf anatomy of two different tomato genotypes grown in saturating light conditions was compared by 3D analysis. Differences were found in calculated values of tissue porosity, cell number density, cell area to volume ratio and cell volume and cell shape distributions of palisade and spongy cell layers. In contrast, the exposed cell area to leaf area ratio in mesophyll, a descriptor that correlates to the maximum rate of photosynthesis in saturated light conditions, was no different between spongy and palisade cells or between genotypes. The use of 3D image processing avoids many of the limitations of anatomical analysis with two-dimensional sections.

Interplay of Cell Shape and Division Orientation Promotes Robust Morphogenesis of Developing Epithelia

Epithelial cells acquire functionally important shapes (e.g., squamous, cuboidal, columnar) during development. Here, we combine theory, quantitative imaging, and perturbations to analyze how tissue geometry, cell divisions, and mechanics interact to shape the presumptive enveloping layer (pre-EVL) on the zebrafish embryonic surface. We find that, under geometrical constraints, pre-EVL flattening is regulated by surface cell number changes following differentially oriented cell divisions. The division pattern is, in turn, determined by the cell shape distribution, which forms under geometrical constraints by cell-cell mechanical coupling. An integrated mathematical model of this shape-division feedback loop recapitulates empirical observations. Surprisingly, the model predicts that cell shape is robust to changes of tissue surface area, cell volume, and cell number, which we confirm in vivo. Further simulations and perturbations suggest the parameter linking cell shape and division orientation contributes to epithelial diversity. Together, our work identifies an evolvable design logic that enables robust cell-level regulation of tissue-level development.

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

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

PLoS Computational Biology Issue Image | Vol. 5(6) June 2009

Cell division is a key mechanism in morphogenesis, yet the relationship between local cell division and global tissue architecture (e.g., the distribution of cell shapes) remains poorly understood. In this study (Nagpal et al., doi:10.1371/journal.pcbi.1000412), the authors present a computational framework for studying the topological networks that are created by proliferative cell division (image). This framework reveals how different cell division mechanisms create strikingly different "signature" tissue statistics, which can be used to infer necessary division properties. The model also suggests that while nearly identical cell shape distributions have been observed in proliferating plant and fruitfly epithelia, they achieve this by distinct cell division mechanisms. Image Credit: Ankit Patel, Radhika Nagpal (Harvard University).

Modeling and inferring cleavage patterns in proliferating epithelia.

The regulation of cleavage plane orientation is one of the key mechanisms driving epithelial morphogenesis. Still, many aspects of the relationship between local cleavage patterns and tissue-level properties remain poorly understood. Here we develop a topological model that simulates the dynamics of a 2D proliferating epithelium from generation to generation, enabling the exploration of a wide variety of biologically plausible cleavage patterns. We investigate a spectrum of models that incorporate the spatial impact of neighboring cells and the temporal influence of parent cells on the choice of cleavage plane. Our findings show that cleavage patterns generate “signature” equilibrium distributions of polygonal cell shapes. These signatures enable the inference of local cleavage parameters such as neighbor impact, maternal influence, and division symmetry from global observations of the distribution of cell shape. Applying these insights to the proliferating epithelia of five diverse organisms, we find that strong division symmetry and moderate neighbor/maternal influence are required to reproduce the predominance of hexagonal cells and low variability in cell shape seen empirically. Furthermore, we present two distinct cleavage pattern models, one stochastic and one deterministic, that can reproduce the empirical distribution of cell shapes. Although the proliferating epithelia of the five diverse organisms show a highly conserved cell shape distribution, there are multiple plausible cleavage patterns that can generate this distribution, and experimental evidence suggests that indeed plants and fruitflies use distinct division mechanisms.

Epithelial topology

It is universally accepted that genetic control over basic aspects of cell and molecular biology is the primary organizing principle in development and homeostasis of living systems. However, instances do exist where important aspects of biological order arise without explicit genetic instruction, emerging instead from simple physical principles, stochastic processes, or the complex self-organizing interaction between random and seemingly unrelated parts. Being mostly resistant to direct genetic dissection, the analysis of such emergent processes falls into a grey area between mathematics, physics and molecular cell biology and therefore remains very poorly understood. We recently proposed a mathematical model predicting the emergence of a specific non-Gaussian distribution of polygonal cell shapes from the stochastic cell division process in epithelial cell sheets; this cell shape distribution appears to be conserved across a diverse set of animals and plants.1 The use of such topological models to study the process of cellular morphogenesis has a long history, starting almost a century ago, and many insights from those original works influence current experimental studies. Here we review current and past literature on this topic while exploring some new ideas on the origins and implications of topological order in proliferating epithelia.

Laminate model expressing mechanical properties of polypropylene foams having non-uniform cell-shape distributions

The tensile and bending deformations of polypropylene (PP) foam manufactured by using an extruding process were investigated using a laminate model based on the measured distribution of cell sizes. Anisotropic cell shapes and cell-size distribution were found to depend on the extrusion direction based on cross sectional observations of PP foam. The laminate model with anisotropic cell shapes and a non-uniform cell-size distribution can account for the measured deformation in PP foam. Each layer in the laminate model was composed of the same-sized anisotropic cells. A comparison of theoretical and experimental results showed that the laminate model was good for evaluating the actual elastic moduli and strengths of tensile and bending deformations. Therefore, the cell-size distribution depending on the manufacturing process was found to be an important consideration when mathematically evaluating deformation of foam.