Mechanical characterization of disordered and anisotropic cellular monolayers

The mechanical mechanism of angiotensin II induced activation of hepatic stellate cells promoting portal hypertension

In the development of chronic liver disease, the hepatic stellate cell (HSC) plays a pivotal role in increasing intrahepatic vascular resistance (IHVR) and inducing portal hypertension (PH) in cirrhosis. Our research demonstrated that HSC contraction, prompted by angiotensin II (Ang II), significantly contributed to the elevation of type I collagen (COL1A1) expression. This increase was intimately associated with enhanced cell tension and YAP nuclear translocation, mediated through α-smooth muscle actin (α-SMA) expression, microfilaments (MF) polymerization, and stress fibers (SF) assembly. Further investigation revealed that the Rho/ROCK signaling pathway regulated MF polymerization and SF assembly by facilitating the phosphorylation of cofilin and MLC, while Ca2+ chiefly governed SF assembly via MLC. Inhibiting α-SMA-MF-SF assembly changed Ang II-induced cell contraction, YAP nuclear translocation, and COL1A1 expression, findings corroborated in cirrhotic mice models. Overall, our study offers insights into mitigating IHVR and PH through cell mechanics, heralding potential breakthroughs.

Discrete network models of endothelial cells and their interactions with the substrate

Endothelial cell monolayers line the inner surfaces of blood and lymphatic vessels. They are continuously exposed to different mechanical loads, which may trigger mechanobiological signals and hence play a role in both physiological and pathological processes. Computer-based mechanical models of cells contribute to a better understanding of the relation between cell-scale loads and cues and the mechanical state of the hosting tissue. However, the confluency of the endothelial monolayer complicates these approaches since the intercellular cross-talk needs to be accounted for in addition to the cytoskeletal mechanics of the individual cells themselves. As a consequence, the computational approach must be able to efficiently model a large number of cells and their interaction. Here, we simulate cytoskeletal mechanics by means of molecular dynamics software, generally suitable to deal with large, locally interacting systems. Methods were developed to generate models of single cells and large monolayers with hundreds of cells. The single-cell model was considered for a comparison with experimental data. To this end, we simulated cell interactions with a continuous, deformable substrate, and computationally replicated multistep traction force microscopy experiments on endothelial cells. The results indicate that cell discrete network models are able to capture relevant features of the mechanical behaviour and are thus well-suited to investigate the mechanics of the large cytoskeletal network of individual cells and cell monolayers.

Mechanical stress combines with planar polarised patterning during metaphase to orient embryonic epithelial cell divisions

The planar orientation of cell division (OCD) is important for epithelial morphogenesis and homeostasis. Here, we ask how mechanics and antero-posterior (AP) patterning combine to influence the first divisions after gastrulation in the Drosophila embryonic epithelium. We analyse hundreds of cell divisions and show that stress anisotropy, notably from compressive forces, can reorient division directly in metaphase. Stress anisotropy influences the OCD by imposing metaphase cell elongation, despite mitotic rounding, and overrides interphase cell elongation. In strongly elongated cells, the mitotic spindle adapts its length to, and hence its orientation is constrained by, the cell long axis. Alongside mechanical cues, we find a tissue-wide bias of the mitotic spindle orientation towards AP-patterned planar polarised Myosin-II. This spindle bias is lost in an AP-patterning mutant. Thus, a patterning-induced mitotic spindle orientation bias overrides mechanical cues in mildly elongated cells, whereas in strongly elongated cells the spindle is constrained close to the high stress axis.

Mechanical control of neural plate folding by apical domain alteration

Vertebrate neural tube closure is associated with complex changes in cell shape and behavior, however, the relative contribution of these processes to tissue folding is not well understood. At the onset of Xenopus neural tube folding, we observed alternation of apically constricted and apically expanded cells. This apical domain heterogeneity was accompanied by biased cell orientation along the anteroposterior axis, especially at neural plate hinges, and required planar cell polarity signaling. Vertex models suggested that dispersed isotropically constricting cells can cause the elongation of adjacent cells. Consistently, in ectoderm, cell-autonomous apical constriction was accompanied by neighbor expansion. Thus, a subset of isotropically constricting cells may initiate neural plate bending, whereas a 'tug-of-war' contest between the force-generating and responding cells reduces its shrinking along the body axis. This mechanism is an alternative to anisotropic shrinking of cell junctions that are perpendicular to the body axis. We propose that apical domain changes reflect planar polarity-dependent mechanical forces operating during neural folding.

Couple stresses and discrete potentials in the vertex model of cellular monolayers

The vertex model is widely used to simulate the mechanical properties of confluent epithelia and other multicellular tissues. This inherently discrete framework allows a Cauchy stress to be attributed to each cell, and its symmetric component has been widely reported, at least for planar monolayers. Here, we consider the stress attributed to the neighbourhood of each tricellular junction, evaluating in particular its leading-order antisymmetric component and the associated couple stresses, which characterise the degree to which individual cells experience (and resist) in-plane bending deformations. We develop discrete potential theory for localised monolayers having disordered internal structure and use this to derive the analogues of Airy and Mindlin stress functions. These scalar potentials typically have broad-banded spectra, highlighting the contributions of small-scale defects and boundary layers to global stress patterns. An affine approximation attributes couple stresses to pressure differences between cells sharing a trijunction, but simulations indicate an additional role for non-affine deformations.

Micro and Macroscopic Stress-Strain Relations in Disordered Tessellated Networks

We demonstrate that for a rigid and incompressible network in mechanical equilibrium, the microscopic stress and strain follows a simple relation, σ=pE, where σ is the deviatoric stress, E is a mean-field strain tensor, and p is the hydrostatic pressure. This relationship arises as the natural consequence of energy minimization or equivalently, mechanical equilibration. The result suggests not only that the microscopic stress and strain are aligned in the principal directions, but also microscopic deformations are predominantly affine. The relationship holds true regardless of the different (foam or tissue) energy model considered, and directly leads to a simple prediction for the shear modulus, μ=⟨p⟩/2, where ⟨p⟩ is the mean pressure of the tessellation, for general randomized lattices.

Mechanical control of neural plate folding by apical domain alteration

Vertebrate neural tube closure is associated with complex changes in cell shape and behavior, however, the relative contribution of these processes to tissue folding is not well understood. In this study, we evaluated morphology of the superficial cell layer in the Xenopus neural plate. At the stages corresponding to the onset of tissue folding, we observed the alternation of cells with apically constricting and apically expanding apical domains. The cells had a biased orientation along the anteroposterior (AP) axis. This apical domain heterogeneity required planar cell polarity (PCP) signaling and was especially pronounced at neural plate hinges. Vertex model simulations suggested that spatially dispersed isotropically constricting cells cause the elongation of their non-constricting counterparts along the AP axis. Consistent with this hypothesis, cell-autonomous induction of apical constriction in Xenopus ectoderm cells was accompanied by the expansion of adjacent non-constricting cells. Our observations indicate that a subset of isotropically constricting cells can initiate neural plate bending, whereas a 'tug-of-war' contest between the force-generating and responding cells reduces its shrinking along the AP axis. This mechanism is an alternative to anisotropic shrinking of cell junctions that are perpendicular to the body axis. We propose that neural folding relies on PCP-dependent transduction of mechanical signals between neuroepithelial cells.

How dynamic prestress governs the shape of living systems, from the subcellular to tissue scale

Cells and tissues change shape both to carry out their function and during pathology. In most cases, these deformations are driven from within the systems themselves. This is permitted by a range of molecular actors, such as active crosslinkers and ion pumps, whose activity is biologically controlled in space and time. The resulting stresses are propagated within complex and dynamical architectures like networks or cell aggregates. From a mechanical point of view, these effects can be seen as the generation of prestress or prestrain, resulting from either a contractile or growth activity. In this review, we present this concept of prestress and the theoretical tools available to conceptualize the statics and dynamics of living systems. We then describe a range of phenomena where prestress controls shape changes in biopolymer networks (especially the actomyosin cytoskeleton and fibrous tissues) and cellularized tissues. Despite the diversity of scale and organization, we demonstrate that these phenomena stem from a limited number of spatial distributions of prestress, which can be categorized as heterogeneous, anisotropic or differential. We suggest that in addition to growth and contraction, a third type of prestress-topological prestress-can result from active processes altering the microstructure of tissue.

Continuum soft tissue models from upscaling of arrays of hyperelastic cells

Constitutive models for soft tissue mechanics are typically constructed by fitting phenomenological models to experimental measurements. However, a significant challenge is to rationally construct soft tissue models that encode the properties of the constituent cells and their extracellular matrix. This work presents a framework to derive multiscale soft tissue models that incorporate properties of individual cells without assuming homogeneity or periodicity at the cell level. We consider a viscoelastic model for each cell (which can deform, grow and divide), that we couple to form a network description of a one-dimensional line of cells. We use a discrete-to-continuum approach to form (nonlinear) continuum partial differential equation models for the tissue. These models elucidate the contrasting role of the two forms of dissipation: substrate dissipation localizes the deformation to the neighbourhood of the free boundary and inhibits morphoelastic growth, whereas internal cell dissipation promotes spatial uniformity and does not influence the elongation length. Furthermore, cell division is shown to increase the rate of elongation of the array compared with growth alone, provided the substrate dissipation is proportional to the cell surface area.

Mechanical regulation of tissues that reproduces wrinkle patterns of gastrointestinal tracts

Gastrointestinal tracts exhibit a number of surface morphologies including zigzags, labyrinths, protrusions, and invaginations which are associated with digestive functions and are suggested to be formed by mechanical mechanisms. In this study, we investigate loading conditions and mechanical properties of tissues that reproduce different wrinkle patterning of gastrointestinal tracts on cell culture platforms. Numerical simulations of wrinkling dynamics are performed for a layered model consisting of an anisotropic epithelial layer resting on a bimodular soft substrate, which in turn adheres to a rigid foundation. Motivated by the patterning of intestinal villi of chicks and mice, we examine two-step compression, where the epithelial layer is subjected to uniaxial compression followed by biaxial compression, and one-step compression, where the epithelial layer is compressed in biaxial directions. Under different mechanical conditions of tissues, a wide variety of surface patterns are displayed that reproduce luminal patterns of digestive tracts. These results suggest possible conditions for mechanical regulation of tissues to duplicate gastrointestinal surface patterns in vitro and provide insight into mechanistic understandings of biological tissues.

Geometrical characterization of active contraction pulses in epithelial cells using the two-dimensional vertex model

Several models have been proposed to describe the dynamics of epithelial tissues undergoing morphogenetic changes driven by apical constriction pulses, which differ in where the constriction is applied, either at the perimeter or in the medial regions. To help discriminate between these models, we analyse the impact of where constriction is applied on the final geometry of the active contracted cell, using the two-dimensional vertex model. We find that medial activity, characterized by a reduction in the reference area, generates anisotropic cell shapes, whereas isotropic cell shapes are produced when the reference perimeter is reduced. When plasticity is included, sufficiently slow processes of medial contractile activity, compared with the characteristic times of elasticity and plasticity, cells can achieve less elongated shapes. Similarly, for perimeter activity, the highest level of contraction is achieved. Finally, we apply the model to describe the apical contractile pulses observed within the epithelial enveloping cell layer during the pre-epiboly of the annual killifish Austrolebias nigripinnis. The analysis of the cell shape changes allowed a global fit of all parameters of the vertex model, with the pulses being quantitatively captured using perimeter activity and area plasticity.

Adhesion-regulated junction slippage controls cell intercalation dynamics in an Apposed-Cortex Adhesion Model

Cell intercalation is a key cell behaviour of morphogenesis and wound healing, where local cell neighbour exchanges can cause dramatic tissue deformations such as body axis extension. Substantial experimental work has identified the key molecular players facilitating intercalation, but there remains a lack of consensus and understanding of their physical roles. Existing biophysical models that represent cell-cell contacts with single edges cannot study cell neighbour exchange as a continuous process, where neighbouring cell cortices must uncouple. Here, we develop an Apposed-Cortex Adhesion Model (ACAM) to understand active cell intercalation behaviours in the context of a 2D epithelial tissue. The junctional actomyosin cortex of every cell is modelled as a continuous viscoelastic rope-loop, explicitly representing cortices facing each other at bicellular junctions and the adhesion molecules that couple them. The model parameters relate directly to the properties of the key subcellular players that drive dynamics, providing a multi-scale understanding of cell behaviours. We show that active cell neighbour exchanges can be driven by purely junctional mechanisms. Active contractility and cortical turnover in a single bicellular junction are sufficient to shrink and remove a junction. Next, a new, orthogonal junction extends passively. The ACAM reveals how the turnover of adhesion molecules regulates tension transmission and junction deformation rates by controlling slippage between apposed cell cortices. The model additionally predicts that rosettes, which form when a vertex becomes common to many cells, are more likely to occur in actively intercalating tissues with strong friction from adhesion molecules.

Generation of anisotropic strain dysregulates wild-type cell division at the interface between host and oncogenic tissue

Epithelial tissues are highly sensitive to anisotropies in mechanical force, with cells altering fundamental behaviors, such as cell adhesion, migration, and cell division.1-5 It is well known that, in the later stages of carcinoma (epithelial cancer), the presence of tumors alters the mechanical properties of a host tissue and that these changes contribute to disease progression.6-9 However, in the earliest stages of carcinoma, when a clonal cluster of oncogene-expressing cells first establishes in the epithelium, the extent to which mechanical changes alter cell behavior in the tissue as a whole remains unclear. This is despite knowledge that many common oncogenes, such as oncogenic Ras, alter cell stiffness and contractility.10-13 Here, we investigate how mechanical changes at the cellular level of an oncogenic cluster can translate into the generation of anisotropic strain across an epithelium, altering cell behavior in neighboring host tissue. We generated clusters of oncogene-expressing cells within otherwise normal in vivo epithelium, using Xenopus laevis embryos. We find that cells in kRasV12, but not cMYC, clusters have increased contractility, which introduces radial stress in the tissue and deforms surrounding host cells. The strain imposed by kRasV12 clusters leads to increased cell division and altered division orientation in neighboring host tissue, effects that can be rescued by reducing actomyosin contractility specifically in the kRasV12 cells. Our findings indicate that some oncogenes can alter the mechanical and proliferative properties of host tissue from the earliest stages of cancer development, changes that have the potential to contribute to tumorigenesis.

Vertex model instabilities for tissues subject to cellular activity or applied stresses

The vertex model is widely used to describe the dynamics of epithelial tissues, because of its simplicity and versatility and the direct inclusion of biophysical parameters. Here, it is shown that quite generally, when cells modify their equilibrium perimeter due to their activity, or the tissue is subject to external stresses, the tissue becomes unstable with deformations that couple pure shear or deviatoric modes, with rotation and expansion modes. For short times, these instabilities deform cells, increasing their ellipticity, while at longer times cells become nonconvex, indicating that the vertex model ceases to be a valid description for tissues under these conditions. The agreement between the analytic calculations performed for a regular hexagonal tissue and the simulations of disordered tissues is excellent due to the homogenization of the tissue at long wavelengths.

Apical stress fibers enable a scaling between cell mechanical response and area in epithelial tissue

Biological systems tailor their properties and behavior to their size throughout development and in numerous aspects of physiology. However, such size scaling remains poorly understood as it applies to cell mechanics and mechanosensing. By examining how the Drosophila pupal dorsal thorax epithelium responds to morphogenetic forces, we found that the number of apical stress fibers (aSFs) anchored to adherens junctions scales with cell apical area to limit larger cell elongation under mechanical stress. aSFs cluster Hippo pathway components, thereby scaling Hippo signaling and proliferation with area. This scaling is promoted by tricellular junctions mediating an increase in aSF nucleation rate and lifetime in larger cells. Development, homeostasis, and repair entail epithelial cell size changes driven by mechanical forces; our work highlights how, in turn, mechanosensitivity scales with cell size.

From biomechanics to mechanobiology: Xenopus provides direct access to the physical principles that shape the embryo

Features of amphibian embryos that have served so well to elucidate the genetics of vertebrate development also enable detailed analysis of the physics that shape morphogenesis and regulate development. Biophysical tools are revealing how genes control mechanical properties of the embryo. The same tools that describe and control mechanical properties are being turned to reveal how dynamic mechanical information and feedback regulate biological programs of development. In this review we outline efforts to explore the various roles of mechanical cues in guiding cilia biology, axonal pathfinding, goblet cell regeneration, epithelial-to-mesenchymal transitions in neural crest, and mesenchymal-to-epithelial transitions in heart progenitors. These case studies reveal the power of Xenopus experimental embryology to expose pathways integrating mechanical cues with programs of development, organogenesis, and regeneration.

Force networks, torque balance and Airy stress in the planar vertex model of a confluent epithelium

The vertex model is a popular framework for modelling tightly packed biological cells, such as confluent epithelia. Cells are described by convex polygons tiling the plane and their equilibrium is found by minimizing a global mechanical energy, with vertex locations treated as degrees of freedom. Drawing on analogies with granular materials, we describe the force network for a localized monolayer and derive the corresponding discrete Airy stress function, expressed for each N-sided cell as N scalars defined over kites covering the cell. We show how a torque balance (commonly overlooked in implementations of the vertex model) requires each internal vertex to lie at the orthocentre of the triangle formed by neighbouring edge centroids. Torque balance also places a geometric constraint on the stress in the neighbourhood of cellular trijunctions, and requires cell edges to be orthogonal to the links of a dual network that connect neighbouring cell centres and thereby triangulate the monolayer. We show how the Airy stress function depends on cell shape when a standard energy functional is adopted, and discuss implications for computational implementations of the model.

Decoupling the Roles of Cell Shape and Mechanical Stress in Orienting and Cueing Epithelial Mitosis

Distinct mechanisms involving cell shape and mechanical force are known to influence the rate and orientation of division in cultured cells. However, uncoupling the impact of shape and force in tissues remains challenging. Combining stretching of Xenopus tissue with mathematical methods of inferring relative mechanical stress, we find separate roles for cell shape and mechanical stress in orienting and cueing division. We demonstrate that division orientation is best predicted by an axis of cell shape defined by the position of tricellular junctions (TCJs), which align with local cell stress rather than tissue-level stress. The alignment of division to cell shape requires functional cadherin and the localization of the spindle orientation protein, LGN, to TCJs but is not sensitive to relative cell stress magnitude. In contrast, proliferation rate is more directly regulated by mechanical stress, being correlated with relative isotropic stress and decoupled from cell shape when myosin II is depleted.

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Tissue stretching increases division rate and reorients divisions with stretch

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Division orientation is regulated by cell shape defined by tricellular junctions

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Cadherin and LGN localize to tricellular junctions aligning division to cell shape

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Division rate is linked to mechanical stress and can be decoupled from cell shape

Qualitative analysis of contribution of intracellular skeletal changes to cellular elasticity

Cells are dynamic structures that continually generate and sustain mechanical forces within their environments. Cells respond to mechanical forces by changing their shape, moving, and differentiating. These reactions are caused by intracellular skeletal changes, which induce changes in cellular mechanical properties such as stiffness, elasticity, viscoelasticity, and adhesiveness. Interdisciplinary research combining molecular biology with physics and mechanical engineering has been conducted to characterize cellular mechanical properties and understand the fundamental mechanisms of mechanotransduction. In this review, we focus on the role of cytoskeletal proteins in cellular mechanics. The specific role of each cytoskeletal protein, including actin, intermediate filaments, and microtubules, on cellular elasticity is summarized along with the effects of interactions between the fibers.

Applying Tensile and Compressive Force to Xenopus Animal Cap Tissue

Over many years, the Xenopus laevis embryo has provided a powerful model system to investigate how mechanical forces regulate cellular function. Here, we describe a system to apply reproducible tensile and compressive force to X. laevis animal cap tissue explants and to simultaneously assess cellular behavior using live confocal imaging.

A Mechanosensitive RhoA Pathway that Protects Epithelia against Acute Tensile Stress

Adherens junctions are tensile structures that couple epithelial cells together. Junctional tension can arise from cell-intrinsic application of contractility or from the cell-extrinsic forces of tissue movement. Here, we report a mechanosensitive signaling pathway that activates RhoA at adherens junctions to preserve epithelial integrity in response to acute tensile stress. We identify Myosin VI as the force sensor, whose association with E-cadherin is enhanced when junctional tension is increased by mechanical monolayer stress. Myosin VI promotes recruitment of the heterotrimeric Gα12 protein to E-cadherin, where it signals for p114 RhoGEF to activate RhoA. Despite its potential to stimulate junctional actomyosin and further increase contractility, tension-activated RhoA signaling is necessary to preserve epithelial integrity. This is explained by an increase in tensile strength, especially at the multicellular vertices of junctions, that is due to mDia1-mediated actin assembly.