Inferring cell junction tension and pressure from cell geometry

The enigma of cell intercalation

Geometric criteria can be used to assess whether cell intercalation is active or passive during the convergent extension of tissue.

Connecting theory and experiment in cell and tissue mechanics

Understanding complex living systems, which are fundamentally constrained by physical phenomena, requires combining experimental data with theoretical physical and mathematical models. To develop such models, collaborations between experimental cell biologists and theoreticians are increasingly important but these two groups often face challenges achieving mutual understanding. To help navigate these challenges, this Perspective discusses different modelling approaches, including bottom-up hypothesis-driven and top-down data-driven models, and highlights their strengths and applications. Using cell mechanics as an example, we explore the integration of specific physical models with experimental data from the molecular, cellular and tissue level up to multiscale input. We also emphasize the importance of constraining model complexity and outline strategies for crosstalk between experimental design and model development. Furthermore, we highlight how physical models can provide conceptual insights and produce unifying and generalizable frameworks for biological phenomena. Overall, this Perspective aims to promote fruitful collaborations that advance our understanding of complex biological systems.

Embryo mechanics cartography: inference of 3D force atlases from fluorescence microscopy

Tissue morphogenesis results from a tight interplay between gene expression, biochemical signaling and mechanics. Although sequencing methods allow the generation of cell-resolved spatiotemporal maps of gene expression, creating similar maps of cell mechanics in three-dimensional (3D) developing tissues has remained a real challenge. Exploiting the foam-like arrangement of cells, we propose a robust end-to-end computational method called 'foambryo' to infer spatiotemporal atlases of cellular forces from fluorescence microscopy images of cell membranes. Our method generates precise 3D meshes of cells' geometry and successively predicts relative cell surface tensions and pressures. We validate it with 3D foam simulations, study its noise sensitivity and prove its biological relevance in mouse, ascidian and worm embryos. 3D force inference allows us to recover mechanical features identified previously, but also predicts new ones, unveiling potential new insights on the spatiotemporal regulation of cell mechanics in developing embryos. Our code is freely available and paves the way for unraveling the unknown mechanochemical feedbacks that control embryo and tissue morphogenesis.

New tools reveal PCP-dependent polarized mechanics in the cortex and cytoplasm of single cells during convergent extension

Understanding biomechanics of biological systems is crucial for unraveling complex processes like tissue morphogenesis. However, current methods for studying cellular mechanics in vivo are limited by the need for specialized equipment and often provide limited spatiotemporal resolution. Here we introduce two new techniques, Tension by Transverse Fluctuation (TFlux) and in vivo microrheology, that overcome these limitations. They both offer time-resolved, subcellular biomechanical analysis using only fluorescent reporters and widely available microscopes. Employing these two techniques, we have revealed a planar cell polarity (PCP)-dependent mechanical gradient both in the cell cortex and the cytoplasm of individual cells engaged in convergent extension. Importantly, the non-invasive nature of these methods holds great promise for its application for uncovering subcellular mechanical variations across a wide array of biological contexts.

Summary

Non-invasive imaging-based techniques providing time-resolved biomechanical analysis at subcellular scales in developing vertebrate embryos.

The mechanics of cephalic furrow formation in the Drosophila embryo

Cephalic furrow formation (CFF) is a major morphogenetic movement during gastrulation in Drosophila melanogaster embryos that gives rise to a deep, transitory epithelial invagination. Recent studies have identified the individual cell shape changes that drive the initiation and progression phases of CFF; however, the underlying mechanics are not yet well understood. During the progression phase, the furrow deepens as columnar cells from both the anterior and posterior directions fold inwards rotating by 90°. To analyze the mechanics of this process, we have developed an advanced two-dimensional lateral vertex model that includes multinode representation of cellular membranes and allows us to capture the membrane curvature associated with pressure variation. Our investigations reveal some key potential mechanical features of CFF, as follows. When cells begin to roll over the cephalic furrow cleft, they become wedge shaped as their apical cortices and overlying membranes expand, lateral cortices and overlying membranes release tension, internal pressures drop, and basal cortices and membranes contract. Then, cells reverse this process by shortening apical cortices and membranes, increasing lateral tension, and causing internal pressures to rise. Since the basal membranes expand, the cells recover their rotated columnar shape once in the furrow. Interestingly, our findings indicate that the basal membranes may be passively reactive throughout the progression phase. We also find that the smooth rolling of cells over the cephalic furrow cleft necessitates that internalized cells provide a solid base through high levels of membrane tension and internal pressure, which allows the transmission of tensile force that pulls new cells into the furrow. These results lead us to suggest that CFF helps to establish a baseline tension across the apical surface of the embryo to facilitate cellular coordination of other morphogenetic movements via mechanical stress feedback mechanisms.

Force propagation between epithelial cells depends on active coupling and mechano-structural polarization

Cell-generated forces play a major role in coordinating the large-scale behavior of cell assemblies, in particular during development, wound healing, and cancer. Mechanical signals propagate faster than biochemical signals, but can have similar effects, especially in epithelial tissues with strong cell-cell adhesion. However, a quantitative description of the transmission chain from force generation in a sender cell, force propagation across cell-cell boundaries, and the concomitant response of receiver cells is missing. For a quantitative analysis of this important situation, here we propose a minimal model system of two epithelial cells on an H-pattern ('cell doublet'). After optogenetically activating RhoA, a major regulator of cell contractility, in the sender cell, we measure the mechanical response of the receiver cell by traction force and monolayer stress microscopies. In general, we find that the receiver cells show an active response so that the cell doublet forms a coherent unit. However, force propagation and response of the receiver cell also strongly depend on the mechano-structural polarization in the cell assembly, which is controlled by cell-matrix adhesion to the adhesive micropattern. We find that the response of the receiver cell is stronger when the mechano-structural polarization axis is oriented perpendicular to the direction of force propagation, reminiscent of the Poisson effect in passive materials. We finally show that the same effects are at work in small tissues. Our work demonstrates that cellular organization and active mechanical response of a tissue are key to maintain signal strength and lead to the emergence of elasticity, which means that signals are not dissipated like in a viscous system, but can propagate over large distances.

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.

Revisiting the relationship between turgor pressure and plant cell growth

Growth is central to plant morphogenesis. Plant cells are encased in rigid cell walls, and they must overcome physical confinement to grow to specific sizes and shapes. Cell wall tension and turgor pressure are the main mechanical components impacting plant cell growth. Cell wall mechanics has been the focus of most plant biomechanical studies, and turgor pressure was often considered as a constant and largely passive component. Nevertheless, it is increasingly accepted that turgor pressure plays a significant role in plant growth. Numerous theoretical and experimental studies suggest that turgor pressure can be both spatially inhomogeneous and actively modulated during morphogenesis. Here, we revisit the pressure-growth relationship by reviewing recent advances in investigating the interactions between cellular/tissular pressure and growth.

The mechanical forces that shape our senses

Developing organs are shaped, in part, by physical interaction with their environment in the embryo. In recent years, technical advances in live-cell imaging and material science have greatly expanded our understanding of the mechanical forces driving organ formation. Here, we provide a broad overview of the types of forces generated during embryonic development and then focus on a subset of organs underlying our senses: the eyes, inner ears, nose and skin. The epithelia in these organs emerge from a common origin: the ectoderm germ layer; yet, they arrive at unique and complex forms over developmental time. We discuss exciting recent animal studies that show a crucial role for mechanical forces in, for example, the thickening of sensory placodes, the coiling of the cochlea and the lengthening of hair. Finally, we discuss how microfabricated organoid systems can now provide unprecedented insights into the physical principles of human development.

Live 3D imaging and mapping of shear stresses within tissues using incompressible elastic beads

To investigate the role of mechanical constraints in morphogenesis and development, we have developed a pipeline of techniques based on incompressible elastic sensors. These techniques combine the advantages of incompressible liquid droplets, which have been used as precise in situ shear stress sensors, and of elastic compressible beads, which are easier to tune and to use. Droplets of a polydimethylsiloxane mix, made fluorescent through specific covalent binding to a rhodamin dye, are produced by a microfluidics device. The elastomer rigidity after polymerization is adjusted to the tissue rigidity. Its mechanical properties are carefully calibrated in situ, for a sensor embedded in a cell aggregate submitted to uniaxial compression. The local shear stress tensor is retrieved from the sensor shape, accurately reconstructed through an active contour method. In vitro, within cell aggregates, and in vivo, in the prechordal plate of the zebrafish embryo during gastrulation, our pipeline of techniques demonstrates its efficiency to directly measure the three dimensional shear stress repartition within a tissue.

Coordination of contractile tension and cell area changes in an epithelial cell monolayer

During tissue development and repair, cells contract and expand in coordination with their neighbors, giving rise to tissue deformations that occur on length scales far larger than that of a single cell. The biophysical mechanisms by which the contractile forces of each cell cause deformations on multicellular length scales are not fully clear. To investigate this question, we began with the principle of force equilibrium, which dictates a balance of tensile forces between neighboring cells. Based on this principle, we hypothesized that coordinated changes in cell area result from tension transmitted across the cell layer. To test this hypothesis, spatial correlations of both contractile tension and the divergence of cell velocities were measured as readouts of coordinated contractility and collective area changes, respectively. Experiments were designed to alter the spatial correlation of contractile tension using three different methods, including disrupting cell-cell adhesions, modulating the alignment of actomyosin stress fibers between neighboring cells, and changing the size of the cell monolayer. In all experiments, the spatial correlations of both tension and divergence increased or decreased together, in agreement with our hypothesis. To relate our findings to the intracellular mechanism connecting changes in cell area to contractile tension, we disrupted activation of extracellular signal-regulated kinase (ERK), which is known to mediate the intracellular relationship between cell area and contraction. Consistent with prior knowledge, a temporal cross-correlation between cell area and tension revealed that ERK was responsible for a proportional relationship between cell area and contraction. Inhibition of ERK activation reduced the spatial correlations of the divergence of cell velocity but not of tension. Together, our findings suggest that coordination of cell contraction and expansion requires transfer of cell tension over space and ERK-mediated coordination between cell area and contraction in time.

Mechanics of neural tube morphogenesis

The neural tube is an important model system of morphogenesis representing the developmental module of out-of-plane epithelial deformation. As the embryonic precursor of the central nervous system, the neural tube also holds keys to many defects and diseases. Recent advances begin to reveal how genetic, cellular and environmental mechanisms work in concert to ensure correct neural tube shape. A physical model is emerging where these factors converge at the regulation of the mechanical forces and properties within and around the tissue that drive tube formation towards completion. Here we review the dynamics and mechanics of neural tube morphogenesis and discuss the underlying cellular behaviours from the viewpoint of tissue mechanics. We will also highlight some of the conceptual and technical next steps.