Models of morphogenesis: the mechanisms and mechanics of cell rearrangement

Engineering pattern formation and morphogenesis

The development of natural tissues, organs and bodies depends on mechanisms of patterning and of morphogenesis, typically (but not invariably) in that order, and often several times at different final scales. Using synthetic biology to engineer patterning and morphogenesis will both enhance our basic understanding of how development works, and provide important technologies for advanced tissue engineering. Focusing on mammalian systems built to date, this review describes patterning systems, both contact-mediated and reaction-diffusion, and morphogenetic effectors. It also describes early attempts to connect the two to create self-organizing physical form. The review goes on to consider how these self-organized systems might be modified to increase the complexity and scale of the order they produce, and outlines some possible directions for future research and development.

Cell rearrangement induced by filopodial tension accounts for the late phase of convergent extension in the sea urchin archenteron

George Oster was a pioneer in using mechanical models to interrogate morphogenesis in animal embryos. Convergent extension is a particularly important morphogenetic process to which George Oster gave significant attention. Late elongation of the sea urchin archenteron is a classic example of convergent extension in a monolayered tube, which has been proposed to be driven by extrinsic axial tension due to the activity of secondary mesenchyme cells. Using a vertex-based mechanical model, we show that key features of archenteron elongation can be accounted for by passive cell rearrangement due to applied tension. The model mimics the cell elongation and the Poisson effect (necking) that occur in actual archenterons. We also show that, as predicted by the model, ablation of secondary mesenchyme cells late in archenteron elongation does not result in extensive elastic recoil. Moreover, blocking the addition of cells to the base of the archenteron late in archenteron elongation leads to excessive cell rearrangement consistent with tension-induced rearrangement of a smaller cohort of cells. Our mechanical simulation suggests that responsive rearrangement can account for key features of archenteron elongation and provides a useful starting point for designing future experiments to examine the mechanical properties of the archenteron.

Physical defects in basement membrane-mimicking collagen-IV matrices trigger cellular EMT and invasion

In fibrosis and cancer, degradation of basement membrane (BM) and cell invasion are considered as key outcomes of a cellular transformation called epithelial-mesenchymal transition (EMT). Here, we pose a converse question - can preexisting physical defects in the BM matrix cause EMT in normal epithelial cells? On a BM-mimicking matrix of collagen-IV-coated polyacrylamide (PA) gel, we have discovered a reverse phenomenon in which preexisting defects trigger EMT in normal epithelial cells. Through spatiotemporal measurements and simulations in silico, we demonstrate that the EMT precedes cellular mechanoactivation on defective matrices, but they occur concurrently on stiff matrices. The defect-dependent EMT caused cell invasion though a stroma-mimicking collagen-I layer, which could be disabled through MMP9 inhibition. Our findings reveal that the known BM degradation caused by cellular EMT and invasion is not a one-way process. Instead, normal epithelial cells can exploit physical defects in the BM matrix to undergo disease-like cellular transformations.

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.

Hybrid cell-centred/vertex model for multicellular systems with equilibrium-preserving remodelling

We present a hybrid cell-centred/vertex model for mechanically simulating planar cellular monolayers undergoing cell reorganisation. Cell centres are represented by a triangular nodal network, while the cell boundaries are formed by an associated vertex network. The two networks are coupled through a kinematic constraint which we allow to relax progressively. Special attention is paid to the change of cell-cell connectivity due to cell reorganisation or remodelling events. We handle these situations by using a variable resting length and applying an Equilibrium-Preserving Mapping on the new connectivity, which computes a new set of resting lengths that preserve nodal and vertex equilibrium. We illustrate the properties of the model by simulating monolayers subjected to imposed extension and during a wound healing process. The evolution of forces and the Equilibrium-Preserving Mapping are analysed during the remodelling events. As a by-product, the proposed technique enables to recover fully vertex or fully cell-centred models in a seamless manner by modifying a numerical parameter of the model.

Non-neuronal cell outgrowth in C. elegans

Cell outgrowth is a hallmark of some non-migratory developing cells during morphogenesis. Understanding the mechanisms that control cell outgrowth not only increases our knowledge of tissue and organ development, but can also shed light on disease pathologies that exhibit outgrowth-like behavior. C. elegans is a highly useful model for the analysis of genes and the function of their respective proteins. In addition, C. elegans also has several cells and tissues that undergo outgrowth during development. Here we discuss the outgrowth mechanisms of nine different C. elegans cells and tissues. We specifically focus on how these cells and tissues grow outward and the interactions they make with their environment. Through our own identification, and a meta-analysis, we also identify gene families involved in multiple cell outgrowth processes, which defined potential C. elegans core components of cell outgrowth, as well as identify a potential stepwise cell behavioral cascade used by cells undergoing outgrowth.

Incorporation of aligned PCL-PEG nanofibers into porous chitosan scaffolds improved the orientation of collagen fibers in regenerated periodontium

The periodontal ligament (PDL) is a group of highly aligned and organized connective tissue fibers that intervenes between the root surface and the alveolar bone. The unique architecture is essential for the specific physiological functionalities of periodontium. The regeneration of periodontium has been extensively studied by researchers, but very few of them pay attention to the alignment of PDL fibers as well as its functionalities. In this study, we fabricated a three-dimensional multilayered scaffold by embedding highly aligned biodegradable poly (ε-caprolactone)-poly(ethylene glycol) (PCE) copolymer electrospun nanofibrous mats into porous chitosan (CHI) to provide topographic cues and guide the oriented regeneration of periodontal tissue. In vitro, compared with random group and porous control, aligned nanofibers embedded scaffold could guide oriented arrangement and elongation of cells with promoted infiltration, viability and increased periodontal ligament-related genes expression. In vivo, aligned nanofibers embedded scaffold showed more organized arrangement of regenerated PDL nearly perpendicular against the root surface with more extensive formation of mature collagen fibers than random group and porous control. Moreover, higher expression level of periostin and more significant formation of tooth-supporting mineralized tissue were presented in the regenerated periodontium of aligned scaffold group. Incorporation of aligned PCE nanofibers into porous CHI proved to be applicable for oriented regeneration of periodontium, which might be further utilized in regeneration of a wide variety of human tissues with a specialized direction.

STATEMENT OF SIGNIFICANCE

The regeneration of periodontium has been extensively studied by researchers, but very few of them give attention to the alignment of periodontal ligament (PDL) fibers as well as its functionalities. The key issue is to provide guidance to the orientation of cells with aligned arrangement of collagen fibers perpendicular against the root surface. This study aimed to promote oriented regeneration of periodontium by structural mimicking of scaffolds. The in vitro and in vivo performances of the scaffolds were further evaluated to test the topographic-guiding and periodontium healing potentials. We also think our research may provide ideas in regeneration of a wide variety of human tissues with a specialized direction.

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.

Persistent cellular motion control and trapping using mechanotactic signaling

Chemotactic signaling and the associated directed cell migration have been extensively studied owing to their importance in emergent processes of cellular aggregation. In contrast, mechanotactic signaling has been relatively overlooked despite its potential for unique ways to artificially signal cells with the aim to effectively gain control over their motile behavior. The possibility of mimicking cellular mechanotactic signals offers a fascinating novel strategy to achieve targeted cell delivery for in vitro tissue growth if proven to be effective with mammalian cells. Using (i) optimal level of extracellular calcium ([Ca²⁺ ]_ext mM) we found, (ii) controllable fluid shear stress of low magnitude (), and (iii) the ability to swiftly reverse flow direction (within one second), we are able to successfully signal Dictyostelium discoideum amoebae and trigger migratory responses with heretofore unreported control and precision. Specifically, we are able to systematically determine the mechanical input signal required to achieve any predetermined sequences of steps including straightforward motion, reversal and trapping. The mechanotactic cellular trapping is achieved for the first time and is associated with a stalling frequency of Hz for a reversing direction mechanostimulus, above which the cells are effectively trapped while maintaining a high level of directional sensing. The value of this frequency is very close to the stalling frequency recently reported for chemotactic cell trapping [Meier B, et al. (2011) Proc Natl Acad Sci USA 108:11417–11422], suggesting that the limiting factor may be the slowness of the internal chemically-based motility apparatus.

Towards 3D in silico modeling of the sea urchin embryonic development

Embryogenesis is a dynamic process with an intrinsic variability whose understanding requires the integration of molecular, genetic, and cellular dynamics. Biological circuits function over time at the level of single cells and require a precise analysis of the topology, temporality, and probability of events. Integrative developmental biology is currently looking for the appropriate strategies to capture the intrinsic properties of biological systems. The "-omic" approaches require disruption of the function of the biological circuit; they provide static information, with low temporal resolution and usually with population averaging that masks fast or variable features at the cellular scale and in a single individual. This data should be correlated with cell behavior as cells are the integrators of biological activity. Cellular dynamics are captured by the in vivo microscopy observation of live organisms. This can be used to reconstruct the 3D + time cell lineage tree to serve as the basis for modeling the organism's multiscale dynamics. We discuss here the progress that has been made in this direction, starting with the reconstruction over time of three-dimensional digital embryos from in toto time-lapse imaging. Digital specimens provide the means for a quantitative description of the development of model organisms that can be stored, shared, and compared. They open the way to in silico experimentation and to a more theoretical approach to biological processes. We show, with some unpublished results, how the proposed methodology can be applied to sea urchin species that have been model organisms in the field of classical embryology and modern developmental biology for over a century.

A linear programming approach to reconstructing subcellular structures from confocal images for automated generation of representative 3D cellular models

This paper presents a novel computer vision algorithm to analyze 3D stacks of confocal images of fluorescently stained single cells. The goal of the algorithm is to create representative in silico model structures that can be imported into finite element analysis software for mechanical characterization. Segmentation of cell and nucleus boundaries is accomplished via standard thresholding methods. Using novel linear programming methods, a representative actin stress fiber network is generated by computing a linear superposition of fibers having minimum discrepancy compared with an experimental 3D confocal image. Qualitative validation is performed through analysis of seven 3D confocal image stacks of adherent vascular smooth muscle cells (VSMCs) grown in 2D culture. The presented method is able to automatically generate 3D geometries of the cell's boundary, nucleus, and representative F-actin network based on standard cell microscopy data. These geometries can be used for direct importation and implementation in structural finite element models for analysis of the mechanics of a single cell to potentially speed discoveries in the fields of regenerative medicine, mechanobiology, and drug discovery.

Emergent complexity of the cytoskeleton: from single filaments to tissue

Despite their overwhelming complexity, living cells display a high degree of internal mechanical and functional organization which can largely be attributed to the intracellular biopolymer scaffold, the cytoskeleton. Being a very complex system far from thermodynamic equilibrium, the cytoskeleton's ability to organize is at the same time challenging and fascinating. The extensive amounts of frequently interacting cellular building blocks and their inherent multifunctionality permits highly adaptive behavior and obstructs a purely reductionist approach. Nevertheless (and despite the field's relative novelty), the physics approach has already proved to be extremely successful in revealing very fundamental concepts of cytoskeleton organization and behavior. This review aims at introducing the physics of the cytoskeleton ranging from single biopolymer filaments to multicellular organisms. Throughout this wide range of phenomena, the focus is set on the intertwined nature of the different physical scales (levels of complexity) that give rise to numerous emergent properties by means of self-organization or self-assembly.

Tension and epithelial morphogenesis in Drosophila early embryos

During morphogenesis, tissues are shaped by cell behaviors such as apical cell constriction and cell intercalation, which are the result of cell intrinsic forces, but are also shaped passively by forces acting on the cells. The latter extrinsic forces can be produced either within the deforming tissue by the tissue-scale integration of intrinsic forces, or outside the tissue by other tissue movements or by fluid flows. Here we review the intrinsic and extrinsic forces that sculpt the epithelium of early Drosophila embryos, focusing on three conserved morphogenetic processes: tissue internalization, axis extension, and segment boundary formation. Finally, we look at how the actomyosin cytoskeleton forms force-generating structures that power these three morphogenetic events at the cell and the tissue scales.

Hydrodynamics of cell-cell mechanical signaling in the initial stages of aggregation

Mechanotactic cell motility has recently been shown to be a key player in the initial aggregation of crawling cells such as leukocytes and amoebae. The effects of mechanotactic signaling in the early aggregation of amoeboid cells are here investigated using a general mathematical model based on known biological evidence. We elucidate the hydrodynamic fundamentals of the direct guiding of a cell through mechanotaxis in the case where one cell transmits a mechanotactic signal through the fluid flow by changing its shape. It is found that any mechanosensing cells placed in the stimulus field of mechanical stress are able to determine the signal transmission direction with a certain angular dispersion which does not preclude the aggregation from happening. The ubiquitous presence of noise is accounted for by the model. Finally, the mesoscopic pattern of aggregation is obtained which constitutes the bridge between, on one hand, the microscopic world where the changes in the cell shape occur and, on the other hand, the cooperative behavior of the cells at the mesoscopic scale.

Emergent morphogenesis: elastic mechanics of a self-deforming tissue

Multicellular organisms are generated by coordinated cell movements during morphogenesis. Convergent extension is a key tissue movement that organizes mesoderm, ectoderm, and endoderm in vertebrate embryos. The goals of researchers studying convergent extension, and morphogenesis in general, include understanding the molecular pathways that control cell identity, establish fields of cell types, and regulate cell behaviors. Cell identity, the size and boundaries of tissues, and the behaviors exhibited by those cells shape the developing embryo; however, there is a fundamental gap between understanding the molecular pathways that control processes within single cells and understanding how cells work together to assemble multicellular structures. Theoretical and experimental biomechanics of embryonic tissues are increasingly being used to bridge that gap. The efforts to map molecular pathways and the mechanical processes underlying morphogenesis are crucial to understanding: (1) the source of birth defects, (2) the formation of tumors and progression of cancer, and (3) basic principles of tissue engineering. In this paper, we first review the process of tissue convergent extension of the vertebrate axis and then review models used to study the self-organizing movements from a mechanical perspective. We conclude by presenting a relatively simple "wedge-model" that exhibits key emergent properties of convergent extension such as the coupling between tissue stiffness, cell intercalation forces, and tissue elongation forces.

Mechanotransduction in development: a growing role for contractility

Mechanotransduction research has focused historically on how externally applied forces can affect cell signalling and function. A growing body of evidence suggests that contractile forces that are generated internally by the actomyosin cytoskeleton are also important in regulating cell behaviour, and suggest a broader role for mechanotransduction in biology. Although the molecular basis for these cellular forces in mechanotransduction is being pursued in cell culture, researchers are also beginning to appreciate their contribution to in vivo developmental processes. Here, we examine the role for mechanical forces and contractility in regulating cell and tissue structure and function during development.

Epithelial histogenesis during tooth development

This paper reviews the current understanding of the progressive changes mediating dental epithelial histogenesis as a basis for future collaborative studies. Tooth development involves morphogenesis, epithelial histogenesis and cell differentiation. The consecutive morphological stages of lamina, bud, cap and bell are also characterized by changes in epithelial histogenesis. Differential cell proliferation rates, apoptosis, and alterations in adhesion and shape lead to the positioning of groups of cells with different functions. During tooth histo-morphogenesis changes occur in basement membrane composition, expression of signalling molecules and the localization of cell surface components. Cell positional identity may be related to cell history. Another important parameter is cell plasticity. Independently of signalling molecules, which play a major role in inducing or modulating specific steps, cell-cell and cell-matrix interactions regulate the plasticity/rigidity of particular domains of the enamel organ. This involves specifying in space the differential growth and influences the progressive tooth morphogenesis by shaping the epithelial-mesenchymal junction. Deposition of a mineralized matrix determines the final shape of the crown. All data reviewed in this paper were investigated in the mouse.

Reversal of cell polarity and actin-myosin cytoskeleton reorganization under mechanical and chemical stimulation

To study reorganization of the actin system in cells that invert their polarity, we stimulated Dictyostelium cells by mechanical forces from alternating directions. The cells oriented in a fluid flow by establishing a protruding front directed against the flow and a retracting tail. Labels for polymerized actin and filamentous myosin-II marked front and tail. At 2.1 Pa, actin first disassembled at the previous front before it began to polymerize at the newly induced front. In contrast, myosin-II slowly disappeared from the previous tail and continuously redistributed to the new tail. Front specification was myosin-II independent and accumulation of polymerized actin was even more focused in mutants lacking myosin-II heavy chains. We conclude that under mechanical stimulation, the inversion of cell polarity is initiated by a global internal signal that turns down actin polymerization in the entire cell. It is thought to be elicited at the most strongly stimulated site of the cell, the incipient front region, and to be counterbalanced by a slowly generated, short-range signal that locally activates actin polymerization at the front. Similar pattern of front and tail interconversion were observed in cells reorienting in strong gradients of the chemoattractant cyclic AMP.

Early onset of regionalization in EMS lineage of C. elegans embryo: a quantitative study

Early localization of C. elegans founder cell descendents in certain regions of embryo has been documented. The purpose of this investigation is to evaluate the onset of ABp and EMS descendent cell regionalization in the embryo using the random motility coefficient as a quantitative parameter. The forward migration index (FMI) was also calculated in order to evaluate the chemotatic biases of ABp-dc and EMS-dc during regionalization. The results showed that the random motility coefficient declined as the cells tended to regionalize. The mean squared displacement (MSD) versus time plot showed a non-linear model which indicated non-random cell movement. FMI showed progressive increase as the cells tended to regionalized, and it was significantly higher in EMS-dc than ABp-dc, moreover the chemotatic biases were higher in EMS-dc than ABp-dc. The circular plots showed that the statistical differences between the two lineages were significant, while ABp-dc showed significant differences in xy, xz and yz planes; EMS derived cells showed no significant differences except in yz planes. The conclusion of this study is that the onset of early regionalization occurs in EMS-dc sooner than in ABp-dc.

Upregulation of forces and morphogenic asymmetries in dorsal closure during Drosophila development

Tissue dynamics during dorsal closure, a stage of Drosophila development, provide a model system for cell sheet morphogenesis and wound healing. Dorsal closure is characterized by complex cell sheet movements, driven by multiple tissue specific forces, which are coordinated in space, synchronized in time, and resilient to UV-laser perturbations. The mechanisms responsible for these attributes are not fully understood. We measured spatial, kinematic, and dynamic antero-posterior asymmetries to biophysically characterize both resiliency to laser perturbations and failure of closure in mutant embryos and compared them to natural asymmetries in unperturbed, wild-type closure. We quantified and mathematically modeled two processes that are upregulated to provide resiliency--contractility of the amnioserosa and formation of a seam between advancing epidermal sheets, i.e., zipping. Both processes are spatially removed from the laser-targeted site, indicating they are not a local response to laser-induced wounding and suggesting mechanosensitive and/or chemosensitive mechanisms for upregulation. In mutant embryos, tissue junctions initially fail at the anterior end indicating inhomogeneous mechanical stresses attributable to head involution, another developmental process that occurs concomitant with the end stages of closure. Asymmetries in these mutants are reversed compared to wild-type, and inhomogeneous stresses may cause asymmetries in wild-type closure.

Integrin alpha5beta1 and fibronectin regulate polarized cell protrusions required for Xenopus convergence and extension

BACKGROUND

Integrin recognition of fibronectin is required for normal gastrulation including the mediolateral cell intercalation behaviors that drive convergent extension and the elongation of the frog dorsal axis; however, the cellular and molecular mechanisms involved are unclear.

RESULTS

We report that depletion of fibronectin with antisense morpholinos blocks both convergent extension and mediolateral protrusive behaviors in explant preparations. Both chronic depletion of fibronectin and acute disruptions of integrin alpha5beta1 binding to fibronectin increases the frequency and randomizes the orientation of polarized cellular protrusions, suggesting that integrin-fibronectin interactions normally repress frequent random protrusions in favor of fewer mediolaterally oriented ones. In the absence of integrin alpha5beta1 binding to fibronectin, convergence movements still occur but result in convergent thickening instead of convergent extension.

CONCLUSIONS

These findings support a role for integrin signaling in regulating the protrusive activity that drives axial extension. We hypothesize that the planar spatial arrangement of the fibrillar fibronectin matrix, which delineates tissue compartments within the embryo, is critical for promoting productive oriented protrusions in intercalating cells.

Developmental functions of the P120-catenin sub-family

For more than a decade, cell, developmental and cancer investigators have brought about a wide interest in the biology of catenin proteins, an attraction being their varied functions within differing cellular compartments. While the diversity of catenin localizations and roles has been intriguing, it has also posed a challenge to the clear interpretation of loss- or gain-of-function developmental phenotypes. The most deeply studied member of the larger catenin family is beta-catenin, whose contributions span areas including cell adhesion and intracellular signaling/ transcriptional control. More recently, attention has been directed towards p120-catenin, which in conjunction with the p120-catenin sub-family members ARVCF- and delta-catenins, are the subjects of this review. Although the requirement for vertebrate versus invertebrate p120-catenin are at variance, vertebrate p120-catenin sub-family members may each inter-link cadherin, cytoskeletal and gene regulatory functions in embryogenesis and disease.

Three-dimensional modeling of mechanical forces in the extracellular matrix during epithelial lumen formation

Mechanical interactions between cells and extracellular matrix (ECM) mediate epithelial cyst formation. This work relies on the combination of numerical modeling with live cell imaging, to piece together a novel nonintrusive method for determining three-dimensional (3D) mechanical forces caused by shape changes of a multicellular aggregate at the early stages of epithelial cyst formation. We analyzed the evolution of Madin-Darby canine kidney cells in 3D cultures using time-lapse microscopy, with type I collagen gel forming the ECM. The evolving 3D interface between the ECM and the cell aggregate was obtained from microscopy images, and the stress on the surface of a proliferating aggregate and in the surrounding ECM was calculated using the finite element method. The viscoelastic properties of the ECM (a needed input for the finite element method solver) were obtained through oscillatory shear flow experiments on a rheometer. For validation purpose, the forces exerted by an aggregate on a force-sensor array were measured and compared against the computational results.

Lamellipodium-driven tissue reshaping: A parametric study

We recently showed that lamellipodia are able to generate forces of the right type to drive convergent extension (CE), an important class of tissue reshaping, in early stage embryos. The purpose of the present work is to quantify the mechanics of this process using parametric analyses. We use finite elements to implement a gamma-mu model in which a net interfacial tension gamma acts along each cell boundary and the cytoplasm exhibits an effective viscosity mu. The stress-strain characteristics of a rectangular patch of model tissue are investigated in terms of the rate r at which lamellipodia form and the relative strength q of their contractions. In tissues that are not constrained in-plane by adjacent tissues, the rate of tissue reshaping is proportional to r the rate of lamellipodium formation and its dependence on q is nonlinear and, near its expected value of 2 highly sensitive to q. Cell elongation, a central characteristic of CE, and stress is found to vary linearly with e the degree of kinematic restraint. Relevant "mechanical pathways" are also identified.