Using cell deformation and motion to predict forces and collective behavior in morphogenesis

Choice of friction coefficient deeply affects tissue behaviour in stochastic epithelial vertex models

To understand the mechanisms that coordinate the formation of biological tissues, the use of numerical implementations is necessary. The complexity of such models involves many assumptions and parameter choices that result in unpredictable consequences, obstructing the comparison with experimental data. Here, we focus on vertex models, a family of spatial models used extensively to simulate the dynamics of epithelial tissues. Usually, in the literature, the choice of the friction coefficient is not addressed using quasi-static deformation arguments that generally do not apply to realistic scenarios. In this manuscript, we discuss the role that the choice of friction coefficient has on the relaxation times and consequently in the conditions of cell cycle progression and division. We explore the effects that these changes have on the morphology, growth rate and topological transitions of the tissue dynamics. These results provide a deeper understanding of the role that an accurate mechanical description plays in the use of vertex models as inference tools. This article is part of a discussion meeting issue 'Causes and consequences of stochastic processes in development and disease'.

Using a micro-device with a deformable ceiling to probe stiffness heterogeneities within 3D cell aggregates

Recent advances in the field of mechanobiology have led to the development of methods to characterise single-cell or monolayer mechanical properties and link them to their functional behaviour. However, there remains a strong need to establish this link for three-dimensional (3D) multicellular aggregates, which better mimic tissue function. Here we present a platform to actuate and observe many such aggregates within one deformable micro-device. The platform consists of a single polydimethylsiloxane piece cast on a 3D-printed mould and bonded to a glass slide or coverslip. It consists of a chamber containing cell spheroids, which is adjacent to air cavities that are fluidically independent. Controlling the air pressure in these air cavities leads to a vertical displacement of the chamber's ceiling. The device can be used in static or dynamic modes over time scales of seconds to hours, with displacement amplitudes from a fewµm to several tens of microns. Further, we show how the compression protocols can be used to obtain measurements of stiffness heterogeneities within individual co-culture spheroids, by comparing image correlations of spheroids at different levels of compression with finite element simulations. The labelling of the cells and their cytoskeleton is combined with image correlation methods to relate the structure of the co-culture spheroid with its mechanical properties at different locations. The device is compatible with various microscopy techniques, including confocal microscopy, which can be used to observe the displacements and rearrangements of single cells and neighbourhoods within the aggregate. The complete experimental and imaging platform can now be used to provide multi-scale measurements that link single-cell behaviour with the global mechanical response of the aggregates.

Differences in boundary behavior in the 3D vertex and Voronoi models

An important open question in the modeling of biological tissues is how to identify the right scale for coarse-graining, or equivalently, the right number of degrees of freedom. For confluent biological tissues, both vertex and Voronoi models, which differ only in their representation of the degrees of freedom, have effectively been used to predict behavior, including fluid-solid transitions and cell tissue compartmentalization, which are important for biological function. However, recent work in 2D has hinted that there may be differences between the two models in systems with heterotypic interfaces between two tissue types, and there is a burgeoning interest in 3D tissue models. Therefore, we compare the geometric structure and dynamic sorting behavior in mixtures of two cell types in both 3D vertex and Voronoi models. We find that while the cell shape indices exhibit similar trends in both models, the registration between cell centers and cell orientation at the boundary are significantly different between the two models. We demonstrate that these macroscopic differences are caused by changes to the cusp-like restoring forces introduced by the different representations of the degrees of freedom at the boundary, and that the Voronoi model is more strongly constrained by forces that are an artifact of the way the degrees of freedom are represented. This suggests that vertex models may be more appropriate for 3D simulations of tissues with heterotypic contacts.

The image-based ultrasonic cell shaking test

Mechanical signals play a vital role in cell biology and is a vast area of research. Thus, there is motivation to understand cell deformation and mechanobiological responses. However, the ability to controllably deform cells in the ultrasonic regime and test their response is a noted challenge throughout the literature. Quantifying and eliciting an appropriate stimulus has proven to be difficult, resulting in methods that are either too aggressive or oversimplified. Furthermore, the ability to gain a real-time insight into cell deformation and link this with the biological response is yet to be achieved. One application of this understanding is in ultrasonic surgical cutting, which is a promising alternative to traditional methods, but with little understanding of its effect on cells. Here we present the image based ultrasonic cell shaking test, a novel method that enables controllable loading of cells and quantification of their response to ultrasonic vibrations. Practically, this involves seeding cells on a substrate that resonates at ultrasonic frequencies and transfers the deformation to the cells. This is then incorporated into microscopic imaging techniques to obtain high-speed images of ultrasonic cell deformation that can be analysed using digital image correlation techniques. Cells can then be extracted after excitation to undergo analysis to understand the biological response to the deformation. This method could aid in understanding the effects of ultrasonic stimulation on cells and how activated mechanobiological pathways result in physical and biochemical responses.

The mechano-chemical circuit drives skin organoid self-organization

Stem cells in organoids self-organize into tissue patterns with unknown mechanisms. Here, we use skin organoids to analyze this process. Cell behavior videos show that the morphological transformation from multiple spheroidal units with morphogenesis competence (CMU) to planar skin is characterized by two abrupt cell motility-increasing events before calming down. The self-organizing processes are controlled by a morphogenetic module composed of molecular sensors, modulators, and executers. Increasing dermal stiffness provides the initial driving force (driver) which activates Yap1 (sensor) in epidermal cysts. Notch signaling (modulator 1) in epidermal cyst tunes the threshold of Yap1 activation. Activated Yap1 induces Wnts and MMPs (epidermal executers) in basal cells to facilitate cellular flows, allowing epidermal cells to protrude out from the CMU. Dermal cell-expressed Rock (dermal executer) generates a stiff force bridge between two CMU and accelerates tissue mixing via activating Laminin and β1-integrin. Thus, this self-organizing coalescence process is controlled by a mechano-chemical circuit. Beyond skin, self-organization in organoids may use similar mechano-chemical circuit structures.

Effective mechanical potential of cell-cell interaction explains three-dimensional morphologies during early embryogenesis

Mechanical forces are critical for the emergence of diverse three-dimensional morphologies of multicellular systems. However, it remains unclear what kind of mechanical parameters at cellular level substantially contribute to tissue morphologies. This is largely due to technical limitations of live measurements of cellular forces. Here we developed a framework for inferring and modeling mechanical forces of cell-cell interactions. First, by analogy to coarse-grained models in molecular and colloidal sciences, we approximated cells as particles, where mean forces (i.e. effective forces) of pairwise cell-cell interactions are considered. Then, the forces were statistically inferred by fitting the mathematical model to cell tracking data. This method was validated by using synthetic cell tracking data resembling various in vivo situations. Application of our method to the cells in the early embryos of mice and the nematode Caenorhabditis elegans revealed that cell-cell interaction forces can be written as a pairwise potential energy in a manner dependent on cell-cell distances. Importantly, the profiles of the pairwise potentials were quantitatively different among species and embryonic stages, and the quantitative differences correctly described the differences of their morphological features such as spherical vs. distorted cell aggregates, and tightly vs. non-tightly assembled aggregates. We conclude that the effective pairwise potential of cell-cell interactions is a live measurable parameter whose quantitative differences can be a parameter describing three-dimensional tissue morphologies.

A novel tool for the unbiased characterization of epithelial monolayer development in culture

The function of an epithelial tissue is intertwined with its architecture. Epithelial tissues are often described as pseudo-two-dimensional, but this view may be partly attributed to experimental bias: many model epithelia, including cultured cell lines, are easiest to image from the "top-down." We measured the three-dimensional architecture of epithelial cells in culture and found that it varies dramatically across cultured regions, presenting a challenge for reproducibility and cross-study comparisons. We therefore developed a novel tool (Automated Layer Analysis, "ALAn") to characterize architecture in an unbiased manner. Using ALAn, we find that cultured epithelial cells can organize into four distinct architectures and that architecture correlates with cell density. Cells exhibit distinct biological properties in each architecture. Organization in the apical-basal axis is determined early in monolayer development by substrate availability, while disorganization in the apical-basal axis arises from an inability to form substrate connections. Our work highlights the need to carefully control for three-dimensional architecture when using cell culture as a model system for epithelial cell biology and introduces a novel tool, built on a set of rules that can be widely applied to epithelial cell culture.

Small hand-designed convolutional neural networks outperform transfer learning in automated cell shape detection in confluent tissues

Mechanical cues such as stresses and strains are now recognized as essential regulators in many biological processes like cell division, gene expression or morphogenesis. Studying the interplay between these mechanical cues and biological responses requires experimental tools to measure these cues. In the context of large scale tissues, this can be achieved by segmenting individual cells to extract their shapes and deformations which in turn inform on their mechanical environment. Historically, this has been done by segmentation methods which are well known to be time consuming and error prone. In this context however, one doesn't necessarily require a cell-level description and a coarse-grained approach can be more efficient while using tools different from segmentation. The advent of machine learning and deep neural networks has revolutionized the field of image analysis in recent years, including in biomedical research. With the democratization of these techniques, more and more researchers are trying to apply them to their own biological systems. In this paper, we tackle a problem of cell shape measurement thanks to a large annotated dataset. We develop simple Convolutional Neural Networks (CNNs) which we thoroughly optimize in terms of architecture and complexity to question construction rules usually applied. We find that increasing the complexity of the networks rapidly no longer yields improvements in performance and that the number of kernels in each convolutional layer is the most important parameter to achieve good results. In addition, we compare our step-by-step approach with transfer learning and find that our simple, optimized CNNs give better predictions, are faster in training and analysis and don't require more technical knowledge to be implemented. Overall, we offer a roadmap to develop optimized models and argue that we should limit the complexity of such models. We conclude by illustrating this strategy on a similar problem and dataset.

Surface tension of model tissues during malignant transformation and epithelial–mesenchymal transition

Epithelial–mesenchymal transition is associated with migration, invasion, and metastasis. The translation at the tissue scale of these changes has not yet been enlightened while being essential in the understanding of tumor progression. Thus, biophysical tools dedicated to measurements on model tumor systems are needed to reveal the impact of epithelial–mesenchymal transition at the collective cell scale. Herein, using an original biophysical approach based on magnetic nanoparticle insertion inside cells, we formed and flattened multicellular aggregates to explore the consequences of the loss of the metastasis suppressor NME1 on the mechanical properties at the tissue scale. Multicellular spheroids behave as viscoelastic fluids, and their equilibrium shape is driven by surface tension as measured by their deformation upon magnetic field application. In a model of breast tumor cells genetically modified for NME1, we correlated tumor invasion, migration, and adhesion modifications with shape maintenance properties by measuring surface tension and exploring both invasive and migratory potential as well as adhesion characteristics.

Convergent extension requires adhesion-dependent biomechanical integration of cell crawling and junction contraction

Convergent extension (CE) is an evolutionarily conserved collective cell movement that elongates several organ systems during development. Studies have revealed two distinct cellular mechanisms, one based on cell crawling and the other on junction contraction. Whether these two behaviors collaborate is unclear. Here, using live-cell imaging, we show that crawling and contraction act both independently and jointly but that CE is more effective when they are integrated via mechano-reciprocity. We thus developed a computational model considering both crawling and contraction. This model recapitulates the biomechanical efficacy of integrating the two modes and further clarifies how the two modes and their integration are influenced by cell adhesion. Finally, we use these insights to understand the function of an understudied catenin, Arvcf, during CE. These data are significant for providing interesting biomechanical and cell biological insights into a fundamental morphogenetic process that is implicated in human neural tube defects and skeletal dysplasias.

Spatio-temporal analysis of collective migrationin vivoby particle image velocimetry

Collective cell migration drives the formation of complex organ systems as well as certain tumour invasions and wound healing processes. A characteristic feature of many migrating collectives is tissue-scale polarity, whereby 'leader' cells at the tissue edge guide 'followers' cells that become assembled into polarized epithelial tissues. In this study, we employed particle image velocimetry (PIV) as a tool to quantitate local dynamics underlying the migration of the posterior lateral line primordium (pLLP) in zebrafish at a short time scale. Epithelial cadherin-EGFP was the fluorescent tracer in time-lapse images for PIV analysis. At the tissue level, global speed and directionality of the primordium were extracted from spatially averaged velocity fields. Interestingly, fluctuating velocity patterns evolve at the mesoscale level, which distinguishes the pseudo-mesenchymal leading front from the epithelialized trailing edge, and superimpose to the global deceleration of the whole primordium during the separation of a protoneuromast. Local velocity fields obtained by PIV proved sensitive to estimate the migration speed and directionality of the pLLP in zebrafish, predicting protoneuromast separation at short time scales. Finally, the PIV approach may be suitable for analysing the dynamics of otherin vivomodels of collective migration.

Attractive internuclear force drives the collective behavior of nuclear arrays in Drosophila embryos

The collective behavior of the nuclear array in Drosophila embryos during nuclear cycle (NC) 11 to NC14 is crucial in controlling cell size, establishing developmental patterns, and coordinating morphogenesis. After live imaging on Drosophila embryos with light sheet microscopy, we extract the nuclear trajectory, speed, and internuclear distance with an automatic nuclear tracing method. We find that the nuclear speed shows a period of standing waves along the anterior-posterior (AP) axis after each metaphase as the nuclei collectively migrate towards the embryo poles and partially move back. And the maximum nuclear speed dampens by 28-45% in the second half of the standing wave. Moreover, the nuclear density is 22-42% lower in the pole region than the middle of the embryo during the interphase of NC12-14. To find mechanical rules controlling the collective motion and packing patterns of the nuclear array, we use a deep neural network (DNN) to learn the underlying force field from data. We apply the learned spatiotemporal attractive force field in the simulations with a particle-based model. And the simulations recapitulate nearly all the observed characteristic collective behaviors of nuclear arrays in Drosophila embryos.

Revisiting tissue tensegrity: Biomaterial-based approaches to measure forces across length scales

Cell-generated forces play a foundational role in tissue dynamics and homeostasis and are critically important in several biological processes, including cell migration, wound healing, morphogenesis, and cancer metastasis. Quantifying such forces in vivo is technically challenging and requires novel strategies that capture mechanical information across molecular, cellular, and tissue length scales, while allowing these studies to be performed in physiologically realistic biological models. Advanced biomaterials can be designed to non-destructively measure these stresses in vitro, and here, we review mechanical characterizations and force-sensing biomaterial-based technologies to provide insight into the mechanical nature of tissue processes. We specifically and uniquely focus on the use of these techniques to identify characteristics of cell and tissue “tensegrity:” the hierarchical and modular interplay between tension and compression that provide biological tissues with remarkable mechanical properties and behaviors. Based on these observed patterns, we highlight and discuss the emerging role of tensegrity at multiple length scales in tissue dynamics from homeostasis, to morphogenesis, to pathological dysfunction.

A rapid segmentation method of cell boundary for developing embryos using machine learning with a personal computer

Cell segmentation is crucial in the study of morphogenesis in developing embryos, but it had been limited in its accuracy until machine learning methods for image segmentation like U-Net. However, these methods take too much time. In this study, we provide a rapid method for cell segmentation using machine learning with a personal computer, termed Cell Segmentator using Machine Learning (CSML). CSML took four seconds per image with a personal computer for segmentation on average, much less than time to obtain an image. We observed that F-value of segmentation by CSML was around 0.97, showing better performance than state-of-the-art methods like RACE and watershed in assessing the segmentation of Xenopus ectodermal cells. CSML also showed slightly better performance and faster than other machine learning-based methods such as U-Net. CSML required only one whole embryo image for training a Fully Convolutional Network classifier and only two parameters. To validate its accuracy, we compared CSML to other methods in assessing several indicators of cell shape. We also examined the generality of this approach by measuring its performance of segmentation of independent images. Our data demonstrate the superiority of CSML, and we expect this application to improve efficiency in cell shape studies.

Mechanical heterogeneity along single cell-cell junctions is driven by lateral clustering of cadherins during vertebrate axis elongation

Morphogenesis is governed by the interplay of molecular signals and mechanical forces across multiple length scales. The last decade has seen tremendous advances in our understanding of the dynamics of protein localization and turnover at subcellular length scales, and at the other end of the spectrum, of mechanics at tissue-level length scales. Integrating the two remains a challenge, however, because we lack a detailed understanding of the subcellular patterns of mechanical properties of cells within tissues. Here, in the context of the elongating body axis of Xenopus embryos, we combine tools from cell biology and physics to demonstrate that individual cell-cell junctions display finely-patterned local mechanical heterogeneity along their length. We show that such local mechanical patterning is essential for the cell movements of convergent extension and is imparted by locally patterned clustering of a classical cadherin. Finally, the patterning of cadherins and thus local mechanics along cell-cell junctions are controlled by Planar Cell Polarity signaling, a key genetic module for CE that is mutated in diverse human birth defects.

Single-cell mechanical analysis and tension quantification via electrodeformation relaxation

The mechanical behavior and cortical tension of single cells are analyzed using electrodeformation relaxation. Four types of cells, namely, MCF-10A, MCF-7, MDA-MB-231, and GBM, are studied, with pulse durations ranging from 0.01 to 10 s. Mechanical response in the long-pulse regime is characterized by a power-law behavior, consistent with soft glassy rheology resulting from unbinding events within the cortex network. In the subsecond short-pulse regime, a single timescale well describes the process and indicates the naive tensioned (prestressed) state of the cortex with minimal force-induced alteration. A mathematical model is employed and the simple ellipsoidal geometry allows for use of an analytical solution to extract the cortical tension. At the shortest pulse of 0.01 s, tensions for all four cell types are on the order of 10^{-2} N/m.

Advancement of Sensor Integrated Organ-on-Chip Devices

Organ-on-chip devices have provided the pharmaceutical and tissue engineering worlds much hope since they arrived and began to grow in sophistication. However, limitations for their applicability were soon realized as they lacked real-time monitoring and sensing capabilities. The users of these devices relied solely on endpoint analysis for the results of their tests, which created a chasm in the understanding of life between the lab the natural world. However, this gap is being bridged with sensors that are integrated into organ-on-chip devices. This review goes in-depth on different sensing methods, giving examples for various research on mechanical, electrical resistance, and bead-based sensors, and the prospects of each. Furthermore, the review covers works conducted that use specific sensors for oxygen, and various metabolites to characterize cellular behavior and response in real-time. Together, the outline of these works gives a thorough analysis of the design methodology and sophistication of the current sensor integrated organ-on-chips.

Controllable Cell Deformation Using Acoustic Streaming for Membrane Permeability Modulation

Hydrodynamic force loading platforms for controllable cell mechanical deformation play an essential role in modern cell technologies. Current systems require assistance from specific microstructures thus limiting the controllability and flexibility in cell shape modulation, and studies on real-time 3D cell morphology analysis are still absent. This article presents a novel platform based on acoustic streaming generated from a gigahertz device for cell shape control and real-time cell deformation analysis. Details in cell deformation and the restoration process are thoroughly studied on the platform, and cell behavior control at the microscale is successfully achieved by tuning the treating time, intensity, and wave form of the streaming. The application of this platform in cell membrane permeability modulation and analysis is also exploited. Based on the membrane reorganization during cell deformation, the effects of deformation extent and deformation patterns on membrane permeability to micro- and macromolecules are revealed. This technology has shown its unique superiorities in cell mechanical manipulation such as high flexibility, high accuracy, and pure fluid force operation, indicating its promising prospect as a reliable tool for cell property study and drug therapy development.

In primary airway epithelial cells, the unjamming transition is distinct from the epithelial-to-mesenchymal transition

The epithelial-to-mesenchymal transition (EMT) and the unjamming transition (UJT) each comprises a gateway to cellular migration, plasticity and remodeling, but the extent to which these core programs are distinct, overlapping, or identical has remained undefined. Here, we triggered partial EMT (pEMT) or UJT in differentiated primary human bronchial epithelial cells. After triggering UJT, cell-cell junctions, apico-basal polarity, and barrier function remain intact, cells elongate and align into cooperative migratory packs, and mesenchymal markers of EMT remain unapparent. After triggering pEMT these and other metrics of UJT versus pEMT diverge. A computational model attributes effects of pEMT mainly to diminished junctional tension but attributes those of UJT mainly to augmented cellular propulsion. Through the actions of UJT and pEMT working independently, sequentially, or interactively, those tissues that are subject to development, injury, or disease become endowed with rich mechanisms for cellular migration, plasticity, self-repair, and regeneration.

Isotropic expansion of external environment induces tissue elongation and collective cell alignment

Cell movement is crucial for morphogenesis in multicellular organisms. Growing embryos or tissues often expand isotropically, i.e., uniformly, in all dimensions. On the surfaces of these expanding environments, which we call "fields," cells are subjected to frictional forces and move passively in response. However, the potential roles of isotropically expanding fields in morphogenetic events have not been investigated well. Our previous mathematical simulations showed that a tissue was elongated on an isotropically expanding field (Imuta et al., 2014). However, the underlying mechanism remains unclarified, and how cells behave during tissue elongation was not investigated. In this study, we mathematically analyzed the effect of isotropically expanding fields using a vertex model, a standard type of multi-cellular model. We found that cells located on fields were elongated along a similar direction each other and exhibited a columnar configuration with nearly single-cell width. Simultaneously, it was confirmed that the cell clusters were also elongated, even though field expansion was absolutely isotropic. We then investigated the mechanism underlying these counterintuitive phenomena. In particular, we asked whether the dynamics of elongation was predominantly determined by the properties of the field, the cell cluster, or both. Theoretical analyses involving simplification of the model revealed that cell clusters have an intrinsic ability to asymmetrically deform, leading to their elongation. Importantly, this ability is effective only under the non-equilibrium conditions provided by field expansion. This may explain the elongation of the notochord, located on the surface of the growing mouse embryo. We established the mechanism underlying tissue elongation induced by isotropically expanding external environments, and its involvement in collective cell alignment with cell elongation, providing key insight into morphogenesis involving multiple adjacent tissues.

Employing Nanostructured Scaffolds to Investigate the Mechanical Properties of Adult Mammalian Retinae Under Tension

Numerous eye diseases are linked to biomechanical dysfunction of the retina. However, the underlying forces are almost impossible to quantify experimentally. Here, we show how biomechanical properties of adult neuronal tissues such as porcine retinae can be investigated under tension in a home-built tissue stretcher composed of nanostructured TiO₂ scaffolds coupled to a self-designed force sensor. The employed TiO₂ nanotube scaffolds allow for organotypic long-term preservation of adult tissues ex vivo and support strong tissue adhesion without the application of glues, a prerequisite for tissue investigations under tension. In combination with finite element calculations we found that the deformation behavior is highly dependent on the displacement rate which results in Young’s moduli of (760–1270) Pa. Image analysis revealed that the elastic regime is characterized by a reversible shear deformation of retinal layers. For larger deformations, tissue destruction and sliding of retinal layers occurred with an equilibration between slip and stick at the interface of ruptured layers, resulting in a constant force during stretching. Since our study demonstrates how porcine eyes collected from slaughterhouses can be employed for ex vivo experiments, our study also offers new perspectives to investigate tissue biomechanics without excessive animal experiments.

Linear and nonlinear mechanical responses can be quite different in models for biological tissues

The fluidity of biological tissues - whether cells can change neighbors and rearrange - is important for their function. In traditional materials, researchers have used linear response functions, such as the shear modulus, to accurately predict whether a material will behave as a fluid. Similarly, in disordered 2D vertex models for confluent biological tissues, the shear modulus becomes zero precisely when the cells can change neighbors and the tissue fluidizes, at a critical value of control parameter s0* = 3.81. However, the ordered ground states of 2D vertex models become linearly unstable at a lower value of control parameter (3.72), suggesting that there may be a decoupling between linear and nonlinear response. We demonstrate that the linear response does not correctly predict the nonlinear behavior in these systems: when the control parameter is between 3.72 and 3.81, cells cannot freely change neighbors even though the shear modulus is zero. These results highlight that the linear response of vertex models should not be expected to generically predict their rheology. We develop a simple geometric ansatz that correctly predicts the nonlinear response, which may serve as a framework for making nonlinear predictions in other vertex-like models.

Neuronal differentiation influences progenitor arrangement in the vertebrate neuroepithelium

Cell division, movement and differentiation contribute to pattern formation in developing tissues. This is the case in the vertebrate neural tube, in which neurons differentiate in a characteristic pattern from a highly dynamic proliferating pseudostratified epithelium. To investigate how progenitor proliferation and differentiation affect cell arrangement and growth of the neural tube, we used experimental measurements to develop a mechanical model of the apical surface of the neuroepithelium that incorporates the effect of interkinetic nuclear movement and spatially varying rates of neuronal differentiation. Simulations predict that tissue growth and the shape of lineage-related clones of cells differ with the rate of differentiation. Growth is isotropic in regions of high differentiation, but dorsoventrally biased in regions of low differentiation. This is consistent with experimental observations. The absence of directional signalling in the simulations indicates that global mechanical constraints are sufficient to explain the observed differences in anisotropy. This provides insight into how the tissue growth rate affects cell dynamics and growth anisotropy and opens up possibilities to study the coupling between mechanics, pattern formation and growth in the neural tube.

Summary: A mechanical model of the vertebrate neuroepithelium, based on experimental observations, suggests that the rate of neuronal differentiation influences tissue growth and the shape of lineage-related clones.

Adapting a Plant Tissue Model to Animal Development: Introducing Cell Sliding into VirtualLeaf

Cell-based, mathematical modeling of collective cell behavior has become a prominent tool in developmental biology. Cell-based models represent individual cells as single particles or as sets of interconnected particles and predict the collective cell behavior that follows from a set of interaction rules. In particular, vertex-based models are a popular tool for studying the mechanics of confluent, epithelial cell layers. They represent the junctions between three (or sometimes more) cells in confluent tissues as point particles, connected using structural elements that represent the cell boundaries. A disadvantage of these models is that cell-cell interfaces are represented as straight lines. This is a suitable simplification for epithelial tissues, where the interfaces are typically under tension, but this simplification may not be appropriate for mesenchymal tissues or tissues that are under compression, such that the cell-cell boundaries can buckle. In this paper, we introduce a variant of VMs in which this and two other limitations of VMs have been resolved. The new model can also be seen as on off-the-lattice generalization of the Cellular Potts Model. It is an extension of the open-source package VirtualLeaf, which was initially developed to simulate plant tissue morphogenesis where cells do not move relative to one another. The present extension of VirtualLeaf introduces a new rule for cell-cell shear or sliding, from which cell rearrangement (T1) and cell extrusion (T2) transitions emerge naturally, allowing the application of VirtualLeaf to problems of animal development. We show that the updated VirtualLeaf yields different results than the traditional vertex-based models for differential adhesion-driven cell sorting and for the neighborhood topology of soft cellular networks.

Coherent Timescales and Mechanical Structure of Multicellular Aggregates

Multicellular aggregates are an excellent model system to explore the role of tissue biomechanics in specifying multicellular reorganization during embryonic developments and malignant invasion. Tissue-like spheroids, when subjected to a compressive force, are known to exhibit liquid-like behaviors at long timescales (hours), largely because of cell rearrangements that serve to effectively dissipate the applied stress. At short timescales (seconds to minutes), before cell rearrangement, the mechanical behavior is strikingly different. The current work uses shape relaxation to investigate the structural characteristics of aggregates and discovers two coherent timescales: one on the order of seconds, the other tens of seconds. These timescales are universal, conserved across a variety of tested species, and persist despite great differences in other properties such as tissue surface tension and adhesion. A precise mathematical theory is used to correlate the timescales with mechanical properties and reveals that aggregates have a relatively strong envelope and an unusually "soft" interior (weak bulk elastic modulus). This characteristic is peculiar, considering that both layers consist of identical units (cells), but is consistent with the fact that this structure can engender both structural integrity and the flexibility required for remodeling. In addition, tissue surface tension, elastic modulus, and viscosity are proportional to each other. Considering that these tissue-level properties intrinsically derive from cellular-level properties, the proportionalities imply precise coregulation of the latter and in particular of the tension on the cell-medium and cell-cell interfaces.

Integrated elastomer-based device for measuring the mechanics of adherent cell monolayers

Cells in the body collectively sustain mechanical deformations in almost all physiological functions. From the morphogenesis stage, cells' ability to sustain stress is essential for the body's well-being. Several pathologies have been associated with abnormal mechanical properties, thus suggesting the Young's modulus as a biomarker to diagnose diseases and determine their progression. Advancements in the field are quite slow because current techniques for measuring cell and tissue mechanics rely on complex and bulky measurement platforms that have low repeatability rates and limited measurement time-scales. We present the first miniaturized system that allows accurate quantification of the Young's modulus of adherent cell monolayers over a longer time (1-2 days). Our approach is based on tensile testing and optical read-out. Thanks to a thoughtful design and material choice, we are able to miniaturize tensile testing platforms into a 1 cm × 2 cm device. We provide highly repeatable Young's modulus measurements in the relevant range between 3 kPa and 300 kPa, over time and under physiological conditions, thus representing an interesting alternative to existing measurement platforms. Furthermore, the compatibility with standard biological equipment, continuous optical imaging and measurements on all types of adherent cells make this device highly versatile. Measurements on human sarcoma osteogenic (SaOS2) and Madin-Darby canine kidney cells (MDCK) are reported. The demonstrated capability to measure real-time changes in mechanical properties, such as after chemical treatment, opens the door for investigating the effects of drugs on cell mechanics.

Predicting Collective Migration of Cell Populations Defined by Varying Repolarization Dynamics

Collective migration of heterogeneous cell populations is an essential aspect of fundamental biological processes, including morphogenesis, wound healing, and tumor invasion. Through experiments and modeling, it has been shown that cells attain front-rear polarity, generate forces, and form adhesions to migrate. However, it remains unclear how the ability of individual cells in a population to dynamically repolarize themselves into new directions could regulate the collective response. We present a vertex-based model in which each deformable cell randomly chooses a new polarization direction after every defined time interval, elongates, proportionally generates forces, and causes collective migration. Our simulations predict that cell types that repolarize at longer time intervals attain more elongated shapes, migrate faster, deform the cell sheet, and roughen the leading edge. By imaging collectively migrating epithelial cell monolayers at high temporal resolution, we found longer repolarization intervals and elongated shapes of cells at the leading edge compared to those within the monolayer. Based on these experimental measurements and simulations, we defined aggressive mutant leader cells by long repolarization interval and minimal intercellular contact. The cells with frequent and random repolarization were defined as normal cells. In simulations with uniformly dispersed leader cells in a normal cell population at a 1:10 ratio, the resulting migration and deformation of the heterogeneous cell sheet remained low. However, when the 10% mutant leaders were placed only at the leading edge, we predicted a rise in the migration of an otherwise normal cell sheet. Our model predicts that a repolarization-based definition of leader cells and their placement within a healthy population can generate myriad modes of collective cell migration, which can enhance our understanding of collective cell migration in disease and development.

Adhesion forces and cortical tension couple cell proliferation and differentiation to drive epidermal stratification

To establish and maintain organ structure and function, tissues need to balance stem cell proliferation and differentiation rates and coordinate cell fate with position. By quantifying and modelling tissue stress and deformation in the mammalian epidermis, we find that this balance is coordinated through local mechanical forces generated by cell division and delamination. Proliferation within the basal stem/progenitor layer, which displays features of a jammed, solid-like state, leads to crowding, thereby locally distorting cell shape and stress distribution. The resulting decrease in cortical tension and increased cell-cell adhesion trigger differentiation and subsequent delamination, reinstating basal cell layer density. After delamination, cells establish a high-tension state as they increase myosin II activity and convert to E-cadherin-dominated adhesion, thereby reinforcing the boundary between basal and suprabasal layers. Our results uncover how biomechanical signalling integrates single-cell behaviours to couple proliferation, cell fate and positioning to generate a multilayered tissue.

Why we need mechanics to understand animal regeneration

Mechanical forces are an important contributor to cell fate specification and cell migration during embryonic development in animals. Similarities between embryogenesis and regeneration, particularly with regards to pattern formation and large-scale tissue movements, suggest similarly important roles for physical forces during regeneration. While the influence of the mechanical environment on stem cell differentiation in vitro is being actively exploited in the fields of tissue engineering and regenerative medicine, comparatively little is known about the role of stresses and strains acting during animal regeneration. In this review, we summarize published work on the role of physical principles and mechanical forces in animal regeneration. Novel experimental techniques aimed at addressing the role of mechanics in embryogenesis have greatly enhanced our understanding at scales from the subcellular to the macroscopic - we believe the time is ripe for the field of regeneration to similarly leverage the tools of the mechanobiological research community.