Cellular interfacial and surface tensions determined from aggregate compression tests using a finite element model

Assessing mechanical agency during apical apoptotic cell extrusion

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

Using Biosensors to Study Organoids, Spheroids and Organs-on-a-Chip: A Mechanobiology Perspective

The increasing popularity of 3D cell culture models is being driven by the demand for more in vivo-like conditions with which to study the biochemistry and biomechanics of numerous biological processes in health and disease. Spheroids and organoids are 3D culture platforms that self-assemble and regenerate from stem cells, tissue progenitor cells or cell lines, and that show great potential for studying tissue development and regeneration. Organ-on-a-chip approaches can be used to achieve spatiotemporal control over the biochemical and biomechanical signals that promote tissue growth and differentiation. These 3D model systems can be engineered to serve as disease models and used for drug screens. While culture methods have been developed to support these 3D structures, challenges remain to completely recapitulate the cell-cell and cell-matrix biomechanical interactions occurring in vivo. Understanding how forces influence the functions of cells in these 3D systems will require precise tools to measure such forces, as well as a better understanding of the mechanobiology of cell-cell and cell-matrix interactions. Biosensors will prove powerful for measuring forces in both of these contexts, thereby leading to a better understanding of how mechanical forces influence biological systems at the cellular and tissue levels. Here, we discussed how biosensors and mechanobiological research can be coupled to develop accurate, physiologically relevant 3D tissue models to study tissue development, function, malfunction in disease, and avenues for disease intervention.

Multi-scale nature of the tissue surface tension: Theoretical consideration on tissue model systems

Tissue surface tension is one of the key parameters that govern tissue rearrangement, shaping, and segregation within various compartments during organogenesis, wound healing, and cancer diseases. Deeper insight into the relationship between tissue surface tension and cell residual stress accumulation caused by collective cell migration can help us to understand the multi-scale nature of cell rearrangement with pronounced oscillatory trend. Oscillatory change of cell velocity that caused strain and generated cell residual stress were discussed in the context of mechanical waves. The tissue surface tension also showed oscillatory behaviour. The main goal of this theoretical consideration is to emphasize an inter-relation between various scenarios of cell rearrangement and tissue surface tension by distinguishing liquid-like and solid-like surfaces. This complex phenomenon is discussed in the context of an artificial tissue model system, namely cell aggregate rounding after uni-axial compression between parallel plates. Experimentally obtained oscillatory changes in the cell aggregate shape during the aggregate rounding, which is accompanied by oscillatory decrease in the aggregate surface area, points to oscillatory changes in the tissue surface tension. Besides long-time oscillations, cell surface tension can perform short time relaxation cycles. This behaviour of the tissue surface tension distinguishes living matter from other soft matter systems. This complex phenomenon is discussed based on dilatational viscoelasticity and thermodynamic approach.

Physical models of notochord cell packing reveal how tension ratios determine morphometry

The physical and geometric aspects of notochords are investigated using a model of finite-length notochords, with interior vacuolated cells arranged in two common packing configurations, and sheath modeled as homogeneous and thin. The key ratios governing packing patterns and eccentricity are number of cells per unit length λ and cell tension ratio Γ. By analyzing simulations that vary Γ and total number of cells N, we find that eccentricity, λ, and internal pressure approach consistent asymptotic values away from the tapering ends, as N increases. The length of the tapering ends is quantified as a function of Γ and pattern. Formulas are derived for geometric ratios, pressure, and energy as functions of Γ and pattern. These observations on the relationship between mechanics, geometry, and pattern provide a framework for further work which may provide insight into the roles of mechanosensing and pressure-volume regulation in the notochord.

Building a tissue: mesenchymal and epithelial cell spheroids' mechanical properties at micro- and nanoscale

Cell transitions between the epithelial and mesenchymal phenotypes provide the regulated morphogenesis and regeneration throughout the ontogenesis. The tissue mechanics and mechanotransduction play an essential role in these processes. Cell spheroids reproduce the cell density of native tissues and represent simple building blocks for the tissue engineering purposes. The mechanical properties of mesenchymal and epithelial cells have been extensively studied in 2D monolayer cultures, but have not been sufficiently compared in spheroids. Here, we have simultaneously applied several techniques to assess the mechanical parameters of such spheroids. The local surface mechanical properties were measured by AFM, and the bulk properties were analyzed with parallel-plate compression, as well as by observing cut opening after microdissection. The comparison of the collected data allowed us to apply the model of a solid body with surface tension, and estimate the parameters of this model. We found an expectedly higher surface tension in mesenchymal spheroids, as well as a higher bulk modulus and relaxation time. The two latter parameters agree with the bulk poroelastic behavior of spheroids, and with the higher cell density and extracellular matrix content in mesenchymal spheroids. The higher tension of the surface layer cells in mesenchymal cell spheroids was also confirmed by the viscoelastic AFM characterization. The cell phenotype affected the self-organization during the spheroid formation, as well as the structure, biomechanical properties, and spreading of spheroids. The obtained results will contribute to a more detailed description of spheroid and tissue biomechanics, and will help in controlling the tissue regeneration and morphogenesis. STATEMENT OF SIGNIFICANCE: Spheroids are widely used as building blocks for scaffold-based and scaffold-free strategies in tissue engineering. In the majority of the past studies, either the concept of a solid body or a liquid with surface tension was used to describe the biomechanical behavior of spheroids. Here, we have used a model which combines both aspects, a solid body with surface tension. The "solid" aspect was described as a visco-poroelastic material, affected by the liquid redistribution through the cells and ECM at the scale of the whole spheroid. A higher surface tension was found for mesenchymal spheroids than that for epithelial spheroids, observed as a higher stiffness of the spheroid surface, as well as a larger spontaneous opening of the cut edges after microdissection.

Characterization of convergent thickening, a major convergence force producing morphogenic movement in amphibians

The morphogenic process of convergent thickening (CT) was originally described as the mediolateral convergence and radial thickening of the explanted ventral involuting marginal zone (IMZ) of Xenopus gastrulae (Keller and Danilchik, 1988). Here, we show that CT is expressed in all sectors of the pre-involution IMZ, which transitions to expressing convergent extension (CE) after involution. CT occurs without CE and drives symmetric blastopore closure in ventralized embryos. Assays of tissue affinity and tissue surface tension measurements suggest CT is driven by increased interfacial tension between the deep IMZ and the overlying epithelium. The resulting minimization of deep IMZ surface area drives a tendency to shorten the mediolateral (circumblastoporal) aspect of the IMZ, thereby generating tensile force contributing to blastopore closure (Shook et al., 2018). These results establish CT as an independent force-generating process of evolutionary significance and provide the first clear example of an oriented, tensile force generated by an isotropic, Holtfreterian/Steinbergian tissue affinity change.

Numerical Modelling of Multicellular Spheroid Compression: Viscoelastic Fluid vs. Viscoelastic Solid

Parallel-plate compression of multicellular spheroids (MCSs) is a promising and popular technique to quantify the viscoelastic properties of living tissues. This work presents two different approaches to the simulation of the MCS compression based on viscoelastic solid and viscoelastic fluid models. The first one is the standard linear solid model implemented in ABAQUS/CAE. The second one is the new model for 3D viscoelastic free surface fluid flow, which combines the Oldroyd-B incompressible fluid model and the incompressible neo-Hookean solid model via incorporation of an additional elastic tensor and a dynamic equation for it. The simulation results indicate that either approach can be applied to model the MCS compression with reasonable accuracy. Future application of the viscoelastic free surface fluid model is the MCSs fusion highly-demanded in bioprinting.

Mechanics and self-organization in tissue development

Self-organization is an all-important feature of living systems that provides the means to achieve specialization and functionality at distinct spatio-temporal scales. Herein, we review this concept by addressing the packing organization of cells, the sorting/compartmentalization phenomenon of cell populations, and the propagation of organizing cues at the tissue level through traveling waves. We elaborate on how different theoretical models and tools from Topology, Physics, and Dynamical Systems have improved the understanding of self-organization by shedding light on the role played by mechanics as a driver of morphogenesis. Altogether, by providing a historical perspective, we show how ideas and hypotheses in the field have been revisited, developed, and/or rejected and what are the open questions that need to be tackled by future research.

Mechanical properties of cell sheets and spheroids: the link between single cells and complex tissues

Cell aggregates, including sheets and spheroids, represent a simple yet powerful model system to study both biochemical and biophysical intercellular interactions. However, it is becoming evident that, although the mechanical properties and behavior of multicellular structures share some similarities with individual cells, yet distinct differences are observed in some principal aspects. The description of mechanical phenomena at the level of multicellular model systems is a necessary step for understanding tissue mechanics and its fundamental principles in health and disease. Both cell sheets and spheroids are used in tissue engineering, and the modulation of mechanical properties of cell constructs is a promising tool for regenerative medicine. Here, we review the data on mechanical characterization of cell sheets and spheroids, focusing both on advances in the measurement techniques and current understanding of the subject. The reviewed material suggest that interplay between the ECM, intercellular junctions, and cellular contractility determines the behavior and mechanical properties of the cell aggregates.

Cell Junction Mechanics beyond the Bounds of Adhesion and Tension

Cell-cell junctions, in particular adherens junctions, are major determinants of tissue mechanics during morphogenesis and homeostasis. In attempts to link junctional mechanics to tissue mechanics, many have utilized explicitly or implicitly equilibrium approaches based on adhesion energy, surface energy, and contractility to determine the mechanical equilibrium at junctions. However, it is increasingly clear that they have significant limitations, such as that it remains challenging to link the dynamics of the molecular components to the resulting physical properties of the junction, to its remodeling ability, and to its adhesion strength. In this perspective, we discuss recent attempts to consider the aspect of energy dissipation at junctions to draw contact points with soft matter physics where energy loss plays a critical role in adhesion theories. We set the grounds for a theoretical framework of the junction mechanics that bridges the dynamics at the molecular scale to the mechanics at the tissue scale.

A three dimensional model of multicellular aggregate compression

Multicellular aggregates are an excellent model system to explore the role of tissue biomechanics, which has been demonstrated to play a crucial role in many physiological and pathological processes. In this paper, we propose a three-dimensional mechanical model and apply it to the uniaxial compression of a multicellular aggregate in a realistic biological setting. In particular, we consider an aggregate of initially spherical shape and describe both its elastic deformations and the reorganisation of the cells forming the spheroid. The latter phenomenon, understood as remodelling, is accounted for by assuming that the aggregate undergoes plastic-like distortions. The study of the compression of the spheroid, achieved by means of two parallel, compressive plates, needs the formulation of a contact problem between the living spheroid itself and the plates, and is solved with the aid of the augmented Lagrangian method. The results of the performed numerical simulations are in qualitative agreement with the biological observations reported in the literature and can also be used to estimate quantitatively some fundamental aggregate mechanical parameters.

Engineering mesenchymal stem cell spheroids by incorporation of mechanoregulator microparticles

Mechanical forces throughout human mesenchymal stem cell (hMSC) spheroids (mesenspheres) play a predominant role in determining cellular functions of cell growth, proliferation, and differentiation through mechanotransductional mechanisms. Here, we introduce microparticle (MP) incorporation as a mechanical intervention method to alter tensional homeostasis of the mesensphere and explore MSC differentiation in response to MP stiffness. The microparticulate mechanoregulators with different elastic modulus (34 kPa, 0.6 MPa, and 2.2 MPa) were prepared by controlled crosslinking cell-sized microdroplets of polydimethylsiloxane (PDMS). Preparation of MP-MSC composite spheroids enabled us to study the possible effects of MPs through experimental and computational assays. Our results showed that MP incorporation selectively primed MSCs toward osteogenesis, yet hindered adipogenesis. Interestingly, this behavior depended on MP mechanics, as the spheroids that contained MPs with intermediate stiffness behaved similar to control MP-free mesenspheres with more tendencies toward chondrogenesis. However, by using the soft or stiff MPs, the MP-mesenspheres significantly showed signs of osteogenesis. This could be explained by the complex of forces which acted in the cell spheroid and, totally, provided a homeostasis situation. Incorporation of cell-sized polymer MPs as mechanoregulators of cell spheroids could be utilized as a new engineering toolkit for multicellular organoids in disease modeling and tissue engineering applications.

Mechanics of Fluid-Filled Interstitial Gaps. I. Modeling Gaps in a Compact Tissue

Fluid-filled interstitial gaps are a common feature of compact tissues held together by cell-cell adhesion. Although such gaps can in principle be the result of weak, incomplete cell attachment, adhesion is usually too strong for this to occur. Using a mechanical model of tissue cohesion, we show that, instead, a combination of local prevention of cell adhesion at three-cell junctions by fluidlike extracellular material and a reduction of cortical tension at the gap surface are sufficient to generate stable gaps. The size and shape of these interstitial gaps depends on the mechanical tensions between cells and at gap surfaces, and on the difference between intracellular and interstitial pressures that is related to the volume of the interstitial fluid. As a consequence of the dependence on tension/tension ratios, the presence of gaps does not depend on the absolute strength of cell adhesion, and similar gaps are predicted to occur in tissues of widely differing cohesion. Tissue mechanical parameters can also vary within and between cells of a given tissue, generating asymmetrical gaps. Within limits, these can be approximated by symmetrical gaps.

Mechanics of Fluid-Filled Interstitial Gaps. II. Gap Characteristics in Xenopus Embryonic Ectoderm

The ectoderm of the Xenopus embryo is permeated by a network of channels that appear in histological sections as interstitial gaps. We characterized this interstitial space by measuring gap sizes, angles formed between adjacent cells, and curvatures of cell surfaces at gaps. From these parameters, and from surface-tension values measured previously, we estimated the values of critical mechanical variables that determine gap sizes and shapes in the ectoderm, using a general model of interstitial gap mechanics. We concluded that gaps of 1-4 μm side length can be formed by the insertion of extracellular matrix fluid at three-cell junctions such that cell adhesion is locally disrupted and a tension difference between cell-cell contacts and the free cell surface at gaps of 0.003 mJ/m² is generated. Furthermore, a cell hydrostatic pressure of 16.8 ± 1.7 Pa and an interstitial pressure of 3.9 ± 3.6 Pa, relative to the central blastocoel cavity of the embryo, was found to be consistent with the observed gap size and shape distribution. Reduction of cell adhesion by the knockdown of C-cadherin increased gap volume while leaving intracellular and interstitial pressures essentially unchanged. In both normal and adhesion-reduced ectoderm, cortical tension of the free cell surfaces at gaps does not return to the high values characteristic of the free surface of the whole tissue.

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.

Three-dimensional vertex model for simulating multicellular morphogenesis

During morphogenesis, various cellular activities are spatiotemporally coordinated on the protein regulatory background to construct the complicated, three-dimensional (3D) structures of organs. Computational simulations using 3D vertex models have been the focus of efforts to approach the mechanisms underlying 3D multicellular constructions, such as dynamics of the 3D monolayer or multilayer cell sheet like epithelia as well as the 3D compacted cell aggregate, including dynamic changes in layer structures. 3D vertex models enable the quantitative simulation of multicellular morphogenesis on the basis of single-cell mechanics, with complete control of various cellular activities such as cell contraction, growth, rearrangement, division, and death. This review describes the general use of the 3D vertex model, along with its applications to several simplified problems of developmental phenomena.

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.

Tissue cohesion and the mechanics of cell rearrangement

Morphogenetic processes often involve the rapid rearrangement of cells held together by mutual adhesion. The dynamic nature of this adhesion endows tissues with liquid-like properties, such that large-scale shape changes appear as tissue flows. Generally, the resistance to flow (tissue viscosity) is expected to depend on the cohesion of a tissue (how strongly its cells adhere to each other), but the exact relationship between these parameters is not known. Here, we analyse the link between cohesion and viscosity to uncover basic mechanical principles of cell rearrangement. We show that for vertebrate and invertebrate tissues, viscosity varies in proportion to cohesion over a 200-fold range of values. We demonstrate that this proportionality is predicted by a cell-based model of tissue viscosity. To do so, we analyse cell adhesion in Xenopus embryonic tissues and determine a number of parameters, including tissue surface tension (as a measure of cohesion), cell contact fluctuation and cortical tension. In the tissues studied, the ratio of surface tension to viscosity, which has the dimension of a velocity, is 1.8 µm/min. This characteristic velocity reflects the rate of cell-cell boundary contraction during rearrangement, and sets a limit to rearrangement rates. Moreover, we propose that, in these tissues, cell movement is maximally efficient. Our approach to cell rearrangement mechanics links adhesion to the resistance of a tissue to plastic deformation, identifies the characteristic velocity of the process, and provides a basis for the comparison of tissues with mechanical properties that may vary by orders of magnitude.

Three functions of cadherins in cell adhesion

Cadherins are transmembrane proteins that mediate cell-cell adhesion in animals. By regulating contact formation and stability, cadherins play a crucial role in tissue morphogenesis and homeostasis. Here, we review the three major functions of cadherins in cell-cell contact formation and stability. Two of those functions lead to a decrease in interfacial tension at the forming cell-cell contact, thereby promoting contact expansion--first, by providing adhesion tension that lowers interfacial tension at the cell-cell contact, and second, by signaling to the actomyosin cytoskeleton in order to reduce cortex tension and thus interfacial tension at the contact. The third function of cadherins in cell-cell contact formation is to stabilize the contact by resisting mechanical forces that pull on the contact.

Ephrin-Eph signaling in embryonic tissue separation

The physical separation of the embryonic regions that give rise to the tissues and organs of multicellular organisms is a fundamental aspect of morphogenesis. Pioneer experiments by Holtfreter had shown that embryonic cells can sort based on "tissue affinities," which have long been considered to rely on differences in cell-cell adhesion. However, vertebrate embryonic tissues also express a variety of cell surface cues, in particular ephrins and Eph receptors, and there is now firm evidence that these molecules are systematically used to induce local repulsion at contacts between different cell types, efficiently preventing mixing of adjacent cell populations.

Glassy dynamics in three-dimensional embryonic tissues

Many biological tissues are viscoelastic, behaving as elastic solids on short timescales and fluids on long timescales. This collective mechanical behaviour enables and helps to guide pattern formation and tissue layering. Here, we investigate the mechanical properties of three-dimensional tissue explants from zebrafish embryos by analysing individual cell tracks and macroscopic mechanical response. We find that the cell dynamics inside the tissue exhibit features of supercooled fluids, including subdiffusive trajectories and signatures of caging behaviour. We develop a minimal, three-parameter mechanical model for these dynamics, which we calibrate using only information about cell tracks. This model generates predictions about the macroscopic bulk response of the tissue (with no fit parameters) that are verified experimentally, providing a strong validation of the model. The best-fit model parameters indicate that although the tissue is fluid-like, it is close to a glass transition, suggesting that small changes to single-cell parameters could generate a significant change in the viscoelastic properties of the tissue. These results provide a robust framework for quantifying and modelling mechanically driven pattern formation in tissues.

The mechanics of metastasis: insights from a computational model

Although it may seem obvious that mechanical forces are required to drive metastatic cell movements, understanding of the mechanical aspects of metastasis has lagged far behind genetic and biochemical knowledge. The goal of this study is to learn about the mechanics of metastasis using a cell-based finite element model that proved useful for advancing knowledge about the forces that drive embryonic cell and tissue movements. Metastasis, the predominant cause of cancer-related deaths, involves a series of mechanical events in which one or more cells dissociate from a primary tumour, migrate through normal tissue, traverse in and out of a multi-layer circulatory system vessel and resettle. The present work focuses on the dissemination steps, from dissociation to circulation. The model shows that certain surface tension relationships must be satisfied for cancerous cells to dissociate from a primary tumour and that these equations are analogous to those that govern dissociation of embryonic cells. For a dissociated cell to then migrate by invadopodium extension and contraction and exhibit the shapes seen in experiments, the invadopodium must generate a contraction equal to approximately twice that produced by the interfacial tension associated with surrounding cells. Intravasation through the wall of a vessel is governed by relationships akin to those in the previous two steps, while release from the vessel wall is governed by equations that involve surface and interfacial tensions. The model raises a number of potential research questions. It also identifies how specific mechanical properties and the sub-cellular structural components that give rise to them might be changed so as to thwart particular metastatic steps and thereby block the spread of cancer.

The role of adhesion energy in controlling cell-cell contacts

Recent advances in microscopy techniques and biophysical measurements have provided novel insight into the molecular, cellular and biophysical basis of cell adhesion. However, comparably little is known about a core element of cell–cell adhesion—the energy of adhesion at the cell–cell contact. In this review, we discuss approaches to understand the nature and regulation of adhesion energy, and propose strategies to determine adhesion energy between cells in vitro and in vivo.

Cell sorting in development

During the development of multicellular organisms, cell fate specification is followed by the sorting of different cell types into distinct domains from where the different tissues and organs are formed. Cell sorting involves both the segregation of a mixed population of cells with different fates and properties into distinct domains, and the active maintenance of their segregated state. Because of its biological importance and apparent resemblance to fluid segregation in physics, cell sorting was extensively studied by both biologists and physicists over the last decades. Different theories were developed that try to explain cell sorting on the basis of the physical properties of the constituent cells. However, only recently the molecular and cellular mechanisms that control the physical properties driving cell sorting, have begun to be unraveled. In this review, we will provide an overview of different cell-sorting processes in development and discuss how these processes can be explained by the different sorting theories, and how these theories in turn can be connected to the molecular and cellular mechanisms driving these processes.

Identifying same-cell contours in image stacks: a key step in making 3D reconstructions

Identification of contours belonging to the same cell is a crucial step in the analysis of confocal stacks and other image sets in which cell outlines are visible, and it is central to the making of 3D cell reconstructions. When the cells are close packed, the contour grouping problem is more complex than that found in medical imaging, for example, because there are multiple regions of interest, the regions are not separable from each other by an identifiable background and regions cannot be distinguished by intensity differences. Here, we present an algorithm that uses three primary metrics-overlap of contour areas in adjacent images, co-linearity of the centroids of these areas across three images in a stack, and cell taper-to assign cells to groups. Decreasing thresholds are used to successively assign contours whose membership is less obvious. In a final step, remaining contours are assigned to existing groups by setting all thresholds to zero and groups having strong hour-glass shapes are partitioned. When applied to synthetic data from isotropic model aggregates, a curved model epithelium in which the long axes of the cells lie at all possible angles to the transection plane, and a confocal image stack, algorithm assignments were between 97 and 100% accurate in sets having at least four contours per cell. The algorithm is not particularly sensitive to the thresholds used, and a single set of parameters was used for all of the tests. The algorithm, which could be extended to time-lapse data, solves a key problem in the translation of image data into cell information.

Cinemechanometry (CMM): A method to determine the forces that drive morphogenetic movements from time-lapse images

Although cell-level mechanical forces are crucial to tissue self-organization in contexts ranging from embryo development to cancer metastases to regenerative engineering, the absence of methods to map them over time has been a major obstacle to new understanding. Here, we present a technique for constructing detailed, dynamic maps of the forces driving morphogenetic events from time-lapse images. Forces in the cell are considered to be separable into unknown active driving forces and known passive forces, where actomyosin systems and microtubules contribute primarily to the first group and intermediate filaments and cytoplasm to the latter. A finite-element procedure is used to estimate the field of forces that must be applied to the passive components to produce their observed incremental deformations. This field is assumed to be generated by active forces resolved along user-defined line segments whose location, often along cell edges, is informed by the underlying biology. The magnitudes and signs of these forces are determined by a mathematical inverse method. The efficacy of the approach is demonstrated using noisy synthetic data from a cross section of a generic invagination and from a planar aggregate that involves two cell types, edge forces that vary with time and a neighbor change.