Curvature-dependent constraints drive remodeling of epithelia

Mapping mechanical stress in curved epithelia of designed size and shape

The function of organs such as lungs, kidneys and mammary glands relies on the three-dimensional geometry of their epithelium. To adopt shapes such as spheres, tubes and ellipsoids, epithelia generate mechanical stresses that are generally unknown. Here we engineer curved epithelial monolayers of controlled size and shape and map their state of stress. We design pressurized epithelia with circular, rectangular and ellipsoidal footprints. We develop a computational method, called curved monolayer stress microscopy, to map the stress tensor in these epithelia. This method establishes a correspondence between epithelial shape and mechanical stress without assumptions of material properties. In epithelia with spherical geometry we show that stress weakly increases with areal strain in a size-independent manner. In epithelia with rectangular and ellipsoidal cross-section we find pronounced stress anisotropies that impact cell alignment. Our approach enables a systematic study of how geometry and stress influence epithelial fate and function in three-dimensions.

Curvature in Biological Systems: Its Quantification, Emergence, and Implications across the Scales

Surface curvature both emerges from, and influences the behavior of, living objects at length scales ranging from cell membranes to single cells to tissues and organs. The relevance of surface curvature in biology is supported by numerous experimental and theoretical investigations in recent years. In this review, first, a brief introduction to the key ideas of surface curvature in the context of biological systems is given and the challenges that arise when measuring surface curvature are discussed. Giving an overview of the emergence of curvature in biological systems, its significance at different length scales becomes apparent. On the other hand, summarizing current findings also shows that both single cells and entire cell sheets, tissues or organisms respond to curvature by modulating their shape and their migration behavior. Finally, the interplay between the distribution of morphogens or micro-organisms and the emergence of curvature across length scales is addressed with examples demonstrating these key mechanistic principles of morphogenesis. Overall, this review highlights that curved interfaces are not merely a passive by-product of the chemical, biological, and mechanical processes but that curvature acts also as a signal that co-determines these processes.

Bioengineered 3D Tissue Model of Intestine Epithelium with Oxygen Gradients to Sustain Human Gut Microbiome

The human gut microbiome is crucial to hosting physiology and health. Therefore, stable in vitro coculture of primary human intestinal cells with a microbiome community is essential for understanding intestinal disease progression and revealing novel therapeutic targets. Here, a three-dimensional scaffold system is presented to regenerate an in vitro human intestinal epithelium that recapitulates many functional characteristics of the native small intestines. The epithelium, derived from human intestinal enteroids, contains mature intestinal epithelial cells and possesses selectively permeable barrier functions. Importantly, by properly positioning the scaffolds cultured under normal atmospheric conditions, two physiologically relevant oxygen gradients, a proximal-to-distal oxygen gradient along the gastrointestinal (GI) tract, and a radial oxygen gradient across the epithelium, are distinguished in the tissues when the lumens are faced up and down in cultures, respectively. Furthermore, the presence of the low oxygen gradients supported the coculture of intestinal epithelium along with a complex living commensal gut microbiome (including obligate anaerobes) to simulate temporal microbiome dynamics in the native human gut. This unique silk scaffold platform may enable the exploration of microbiota-related mechanisms of disease pathogenesis and host-pathogen dynamics in infectious diseases including the potential to explore the human microbiome-gut-brain axis and potential novel microbiome-based therapeutics.

Thickness of epithelia on wavy substrates: measurements and continuous models

We measured the thickness of MDCK epithelia grown on substrates with a sinusoidal profile. We show that while at long wavelength the profile of the epithelium follows that of the substrate, at short wavelengths cells are thicker in valleys than on ridges. This is reminiscent of the so-called «healing length in the case of a thin liquid film wetting a rough solid substrate. We explore the ability of continuum mechanics models to account for these observations. Modeling the epithelium as a thin liquid film, with surface tension, does not fully account for the measurements. Neither does modeling the epithelium as a thin incompressible elastic film. On the contrary, the addition of an apical active stress gives satisfactory agreement with measurements, with one fitting parameter, the ratio between the active stress and the elastic modulus.

Intestinal villus structure contributes to even shedding of epithelial cells

In the intestinal epithelium, proliferated epithelial cells ascend the crypts and villi and shed at the villus tips into the gut lumen. In this study, we theoretically investigate the roles of the villi on cell turnover. We present a stochastic model that focuses on the duration over which cells migrate the shortest paths between the crypt orifices and the villus tips, where shedding cells are randomly chosen from among those older than the shortest-path cell migration times. By extending the length of the shortest path to delay cell shedding, the finger-like shape of the villus would tightly regulate shedding-cell ages compared with flat surfaces and shorter projections; the villus allows epithelial cells to shed at around the same age, which limits them from shedding early or staying in the epithelium for long periods. Computational simulations of cell dynamics agreed well with the predictions. We also examine various mechanical conditions of cells and confirm that coordinated collective cell migration supports the predictions. These results suggest the important roles of the villi in homeostatic maintenance of the small intestine, and we discuss the applicability of our approach to other tissues with collective cell movement.

Adaptive architecture and mechanoresponse of epithelial cells on a torus

Curvature is a geometric feature widely observed in the epithelia and critical to the performance of fundamental biological functions. Understanding curvature-related biophysical phenomena remains challenging partly owing to the difficulty of quantitatively tuning and measuring curvatures of interfacing individual cells. In this study, we prepared confluent wild-type Madin-Darby canine kidney cells on a torus structure presenting positive, zero, and negative Gaussian curvatures with a tubule diameter of 2-7 cells and quantified the mechanobiological characteristics of individual cells. Cells on the torus surface exhibited topological sensing ability both as an individual cell and collective cell organization. Both cell bodies and nuclei, adapted on the torus, exhibited local Gaussian curvature-dependent preferential orientation. The cells on the torus demonstrated significant adjustment in the nuclear area and exhibited asymmetric nuclear position depending on the local Gaussian curvature. Moreover, cells on top of the torus, where local Gaussian curvature is near zero, exhibited more sensitive morphological adaptations than the nuclei depending on the Gaussian curvature gradient. Furthermore, the spatial heterogeneity of intermediate filament proteins related to mechanoresponsive expression of the cell body and nucleus, vimentin, keratin and lamin A, revealed local Gaussian curvature as a key factor of cellular adaptation on curved surfaces.

Mapping cellular-scale internal mechanics in 3D tissues with thermally responsive hydrogel probes

Local tissue mechanics play a critical role in cell function, but measuring these properties at cellular length scales in living 3D tissues can present considerable challenges. Here we present thermoresponsive, smart material microgels that can be dispersed or injected into tissues and optically assayed to measure residual tissue elasticity after creep over several weeks. We first develop and characterize the sensors, and demonstrate that internal mechanical profiles of live multicellular spheroids can be mapped at high resolutions to reveal broad ranges of rigidity within the tissues, which vary with subtle differences in spheroid aggregation method. We then show that small sites of unexpectedly high rigidity develop in invasive breast cancer spheroids, and in an in vivo mouse model of breast cancer progression. These focal sites of increased intratumoral rigidity suggest new possibilities for how early mechanical cues that drive cancer cells towards invasion might arise within the evolving tumor microenvironment.

Topographical curvature is sufficient to control epithelium elongation

How biophysical cues can control tissue morphogenesis is a central question in biology and for the development of efficient tissue engineering strategies. Recent data suggest that specific topographies such as grooves and ridges can trigger anisotropic tissue growth. However, the specific contribution of biologically relevant topographical features such as cell-scale curvature is still unclear. Here we engineer a series of grooves and ridges model topographies exhibiting specific curvature at the ridge/groove junctions and monitored the growth of epithelial colonies on these surfaces. We observe a striking proportionality between the maximum convex curvature of the ridges and the elongation of the epithelium. This is accompanied by the anisotropic distribution of F-actin and nuclei with partial exclusion of both in convex regions as well as the curvature-dependent reorientation of pluricellular protrusions and mitotic spindles. This demonstrates that curvature itself is sufficient to trigger and modulate the oriented growth of epithelia through the formation of convex “topographical barriers” and establishes curvature as a powerful tuning parameter for tissue engineering and biomimetic biomaterial design.

Buckling of an Epithelium Growing under Spherical Confinement

Many organs are formed through folding of an epithelium. This change in shape is usually attributed to tissue heterogeneities, for example, local apical contraction. In contrast, compressive stresses have been proposed to fold a homogeneous epithelium by buckling. While buckling is an appealing mechanism, demonstrating that it underlies folding requires measurement of the stress field and the material properties of the tissue, which are currently inaccessible in vivo. Here, we show that monolayers of identical cells proliferating on the inner surface of elastic spherical shells can spontaneously fold. By measuring the elastic deformation of the shell, we infer the forces acting within the monolayer and its elastic modulus. Using analytical and numerical theories linking forces to shape, we find that buckling quantitatively accounts for the shape changes of our monolayers. Our study shows that forces arising from epithelial growth in three-dimensional confinement are sufficient to drive folding by buckling.

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A proliferating epithelium encapsulated in a hollow sphere spontaneously invaginates

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Epithelial proliferation generates compressive stresses that deform the elastic shell

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Coupling between stress and folding shape shows that folding arises from buckling

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Epithelial elastic moduli are inferred from buckling theory and experiments

Mechanical Adaptations of Epithelial Cells on Various Protruded Convex Geometries

The shape of epithelial tissue supports physiological functions of organs such as intestinal villi and corneal epithelium. Despite the mounting evidence showing the importance of geometry in tissue microenvironments, the current understanding on how it affects biophysical behaviors of cells is still elusive. Here, we cultured cells on various protruded convex structure such as triangle, square, and circle shape fabricated using two-photon laser lithography and quantitatively analyzed individual cells. Morphological data indicates that epithelial cells can sense the sharpness of the corner by showing the characteristic cell alignments, which was caused by actin contractility. Cell area was mainly influenced by surface convexity, and Rho-activation increased cell area on circle shape. Moreover, we found that intermediate filaments, vimentin, and cytokeratin 8/18, play important roles in growth and adaptation of epithelial cells by enhancing expression level on convex structure depending on the shape. In addition, microtubule building blocks, α-tubulin, was also responded on geometric structure, which indicates that intermediate filaments and microtubule can cooperatively secure mechanical stability of epithelial cells on convex surface. Altogether, the current study will expand our understanding of mechanical adaptations of cells on out-of-plane geometry.

Effect of luminal flow on doming of mpkCCD cells in a 3D perfusable kidney cortical collecting duct model

The cortical collecting duct (CCD) of the mammalian kidney plays a major role in the maintenance of total body electrolyte, acid/base, and fluid homeostasis by tubular reabsorption and excretion. The mammalian CCD is heterogeneous, composed of Na⁺-absorbing principal cells (PCs) and acid-base-transporting intercalated cells (ICs). Perturbations in luminal flow rate alter hydrodynamic forces to which these cells in the cylindrical tubules are exposed. However, most studies of tubular ion transport have been performed in cell monolayers grown on or epithelial sheets affixed to a flat support, since analysis of transepithelial transport in native tubules by in vitro microperfusion requires considerable expertise. Here, we report on the generation and characterization of an in vitro, perfusable three-dimensional kidney CCD model (3D CCD), in which immortalized mouse PC-like mpkCCD cells are seeded within a cylindrical channel embedded within an engineered extracellular matrix and subjected to luminal fluid flow. We find that a tight epithelial barrier composed of differentiated and polarized PCs forms within 1 wk. Immunofluorescence microscopy reveals the apical epithelial Na⁺ channel ENaC and basolateral Na⁺/K⁺-ATPase. On cessation of luminal flow, benzamil-inhibitable cell doming is observed within these 3D CCDs consistent with the presence of ENaC-mediated Na⁺ absorption. Our 3D CCD provides a geometrically and microphysiologically relevant platform for studying the development and physiology of renal tubule segments.

A Mechanical Instability in Planar Epithelial Monolayers Leads to Cell Extrusion

In cell extrusion, a cell embedded in an epithelial monolayer loses its apical or basal surface and is subsequently squeezed out of the monolayer by neighboring cells. Cell extrusions occur during apoptosis, epithelial-mesenchymal transition, or precancerous cell invasion. They play important roles in embryogenesis, homeostasis, carcinogenesis, and many other biological processes. Although many of the molecular factors involved in cell extrusion are known, little is known about the mechanical basis of cell extrusion. We used a three-dimensional (3D) vertex model to investigate the mechanical stability of cells arranged in a monolayer with 3D foam geometry. We found that when the cells composing the monolayer have homogeneous mechanical properties, cells are extruded from the monolayer when the symmetry of the 3D geometry is broken because of an increase in cell density or a decrease in the number of topological neighbors around single cells. Those results suggest that mechanical instability inherent in the 3D foam geometry of epithelial monolayers is sufficient to drive epithelial cell extrusion. In the situation in which cells in the monolayer actively generate contractile or adhesive forces under the control of intrinsic genetic programs, the forces act to break the symmetry of the monolayer, leading to cell extrusion that is directed to the apical or basal side of the monolayer by the balance of contractile and adhesive forces on the apical and basal sides. Although our analyses are based on a simple mechanical model, our results are in accordance with observations of epithelial monolayers in vivo and consistently explain cell extrusions under a wide range of physiological and pathophysiological conditions. Our results illustrate the importance of a mechanical understanding of cell extrusion and provide a basis by which to link molecular regulation to physical processes.

Substrate curvature as a cue to guide spatiotemporal cell and tissue organization

Recent evidence clearly shows that cells respond to various physical cues in their environments, guiding many cellular processes and tissue morphogenesis, pathology, and repair. One aspect that is gaining significant traction is the role of local geometry as an extracellular cue. Elucidating how geometry affects cell and tissue behavior is, indeed, crucial to design artificial scaffolds and understand tissue growth and remodeling. Perhaps the most fundamental descriptor of local geometry is surface curvature, and a growing body of evidence confirms that surface curvature affects the spatiotemporal organization of cells and tissues. While well-defined in differential geometry, curvature remains somewhat ambiguously treated in biological studies. Here, we provide a more formal curvature framework, based on the notions of mean and Gaussian curvature, and summarize the available evidence on curvature guidance at the cell and tissue levels. We discuss the involved mechanisms, highlighting the interplay between tensile forces and substrate curvature that forms the foundation of curvature guidance. Moreover, we show that relatively simple computational models, based on some application of curvature flow, are able to capture experimental tissue growth remarkably well. Since curvature guidance principles could be leveraged for tissue regeneration, the implications for geometrical scaffold design are also discussed. Finally, perspectives on future research opportunities are provided.

Cell-Perceived Substrate Curvature Dynamically Coordinates the Direction, Speed, and Persistence of Stromal Cell Migration

Adherent cells residing within tissues or biomaterials are presented with 3D geometrical cues from their environment, often in the form of local surface curvatures. While there is growing evidence that cellular decision-making is influenced by substrate curvature, the effect of physiologically relevant, cell-scale anisotropic curvatures remains poorly understood. This study systematically explores the migration behavior of human bone marrow stromal cells (hBMSCs) on a library of anisotropic curved structures. Analysis of cell trajectories reveals that, on convex cylindrical structures, hBMSC migration speed and persistence are strongly governed by the cellular orientation on the curved structure, while migration on concave cylindrical structures is characterized by fast but non-aligned and non-persistent migration. Concurrent presentation of concave and convex substrates on toroidal structures induces migration in the direction where hBMSCs can most effectively avoid cell bending. These distinct migration behaviors are found to be universally explained by the cell-perceived substrate curvature, which on anisotropic curved structures is dependent on both the temporally varying cell orientation and the 3D cellular morphology. This work demonstrates that cell migration is dynamically guided by the perceived curvature of the underlying substrate, providing an important biomaterial design parameter for instructing cell migration in tissue engineering and regenerative medicine.