Conserved physical mechanisms of cell and tissue elongation.

Living organisms have the ability to self-shape into complex structures appropriate for their function. The genetic and molecular mechanisms that enable cells to do this have been extensively studied in several model and non-model organisms. In contrast, the physical mechanisms that shape cells and tissues have only recently started to emerge, in part thanks to new quantitative in vivo measurements of the physical quantities guiding morphogenesis. These data, combined with indirect inferences of physical characteristics, are starting to reveal similarities in the physical mechanisms underlying morphogenesis across different organisms. Here, we review how physics contributes to shape cells and tissues in a simple, yet ubiquitous, morphogenetic transformation: elongation. Drawing from observed similarities across species, we propose the existence of conserved physical mechanisms of morphogenesis.

Proliferation-driven mechanical compression induces signalling centre formation during mammalian organ development.

Localized sources of morphogens, called signalling centres, play a fundamental role in coordinating tissue growth and cell fate specification during organogenesis. However, how these signalling centres are established in tissues during embryonic development is still unclear. Here we show that the main signalling centre orchestrating development of rodent incisors, the enamel knot (EK), is specified by a cell proliferation-driven buildup in compressive stresses (mechanical pressure) in the tissue. Direct mechanical measurements indicate that the stresses generated by cell proliferation are resisted by the surrounding tissue, creating a circular pattern of mechanical anisotropy with a region of high compressive stress at its centre that becomes the EK. Pharmacological inhibition of proliferation reduces stresses and suppresses EK formation, and application of external pressure in proliferation-inhibited conditions rescues the formation of the EK. Mechanical information is relayed intracellularly through YAP protein localization, which is cytoplasmic in the region of compressive stress that establishes the EK and nuclear in the stretched anisotropic cells that resist the pressure buildup around the EK. Together, our data identify a new role for proliferation-driven mechanical compression in the specification of a model signalling centre during mammalian organ development.

Adherens junctions as molecular regulators of emergent tissue mechanics.

Tissue and organ development during embryogenesis relies on the collective and coordinated action of many cells. Recent studies have revealed that tissue material properties, including transitions between fluid and solid tissue states, are controlled in space and time to shape embryonic structures and regulate cell behaviours. Although the collective cellular flows that sculpt tissues are guided by tissue-level physical changes, these ultimately emerge from cellular-level and subcellular-level molecular mechanisms. Adherens junctions are key subcellular structures, built from clusters of classical cadherin receptors. They mediate physical interactions between cells and connect biochemical signalling to the physical characteristics of cell contacts, hence playing a fundamental role in tissue morphogenesis. In this Review, we take advantage of the results of recent, quantitative measurements of tissue mechanics to relate the molecular and cellular characteristics of adherens junctions, including adhesion strength, tension and dynamics, to the emergent physical state of embryonic tissues. We focus on systems in which cell-cell interactions are the primary contributor to morphogenesis, without significant contribution from cell-matrix interactions. We suggest that emergent tissue mechanics is an important direction for future research, bridging cell biology, developmental biology and mechanobiology to provide a holistic understanding of morphogenesis in health and disease.

In situ quantification of osmotic pressure within living embryonic tissues.

Mechanics is known to play a fundamental role in many cellular and developmental processes. Beyond active forces and material properties, osmotic pressure is believed to control essential cell and tissue characteristics. However, it remains very challenging to perform in situ and in vivo measurements of osmotic pressure. Here we introduce double emulsion droplet sensors that enable local measurements of osmotic pressure intra- and extra-cellularly within 3D multicellular systems, including living tissues. After generating and calibrating the sensors, we measure the osmotic pressure in blastomeres of early zebrafish embryos as well as in the interstitial fluid between the cells of the blastula by monitoring the size of droplets previously inserted in the embryo. Our results show a balance between intracellular and interstitial osmotic pressures, with values of approximately 0.7 MPa, but a large pressure imbalance between the inside and outside of the embryo. The ability to measure osmotic pressure in 3D multicellular systems, including developing embryos and organoids, will help improve our understanding of its role in fundamental biological processes.

Synthesis of Fluorous Ferrofluids and Effects of the Nanoparticle Coatings on Field- and Temperature-Dependent Magnetizations.

Ferrofluids have been extensively employed in industrial, environmental, and biomedical areas. Among them, fluorous ferrofluids are of particular interest because of the biorthogonal nature of perfluorocarbons (PFCs). However, the noninteracting nature of PFCs as well as challenges in functionalization of nanoparticle surfaces with fluorous ligands has limited their applications, especially in biomedicine. In particular, commercially available fluorous ferrofluids are stabilized using ionic surfactants with charged groups that physically interact with a wide range of charged biological molecules. In this paper, we developed a unique two-phase ligand attachment strategy to render stable fluorous ferrofluids using nonionic surfactants. The superparamagnetic Fe3O4 or MnFe2O4 core of the magnetic nanoparticles, the magnetic component of the ferrofluid, was coated with a silica shell containing abundant surface hydroxyl groups, thereby enabling the installation of fluorous ligands through stable covalent, neutral, siloxane bonds. We explored chemistry-material relationships between different ligands and PFC solvents and found that low-molecular-weight ligands can assist with the installation of high-molecular-weight ligands (4000-8000 g/mol), allowing us to systematically control the size and thickness of ligand functionalization on the nanoparticle surface. By zero-field-cooled magnetization measurements, we studied how the ligands affect magnetic dipole orientation forces and observed a curve flattening that is only associated with the ferrofluids. This work provided insight into ferrofluids' dependence on interparticle interactions and contributed a methodology to synthesize fluorous ferrofluids with nonionic surfactants that exhibit both magnetic and chemical stability. We believe that the doped MnFe2O4 fluorous ferrofluid has the highest combination of stability and magnetization reported to date.

Mechanics of the cellular microenvironment as probed by cells in vivo during zebrafish presomitic mesoderm differentiation.

Tissue morphogenesis, homoeostasis and repair require cells to constantly monitor their three-dimensional microenvironment and adapt their behaviours in response to local biochemical and mechanical cues. Yet the mechanical parameters of the cellular microenvironment probed by cells in vivo remain unclear. Here, we report the mechanics of the cellular microenvironment that cells probe in vivo and in situ during zebrafish presomitic mesoderm differentiation. By quantifying both endogenous cell-generated strains and tissue mechanics, we show that individual cells probe the stiffness associated with deformations of the supracellular, foam-like tissue architecture. Stress relaxation leads to a perceived microenvironment stiffness that decreases over time, with cells probing the softest regime. We find that most mechanical parameters, including those probed by cells, vary along the anteroposterior axis as mesodermal progenitors differentiate. These findings expand our understanding of in vivo mechanosensation and might aid the design of advanced scaffolds for tissue engineering applications.

Macromolecular Crowding as an Intracellular Stimulus for Responsive Nanomaterials.

Stimuli-responsive materials are exploited in biological, materials, and sensing applications. We introduce a new endogenous stimulus, biomacromolecule crowding, which we achieve by leveraging changes in thermoresponsive properties of polymers upon high concentrations of crowding agents. We prepare poly(2-oxazoline) amphiphiles that exhibit lower critical solution temperatures (LCST) in serum above physiological temperature. These amphiphiles stabilize oil-in-water nanoemulsions at temperatures below the LCST but are ineffective surfactants above the LCST, resulting in emulsion fusion. We find that the transformations observed upon heating nanoemulsions above their surfactant's LCST can instead be induced at physiological temperatures through the addition of polymers and protein, rendering thermoresponsive materials "crowding responsive." We demonstrate that the cytosol is a stimulus for nanoemulsions, with droplet fusion occurring upon injection into cells of living zebrafish embryos. This report sets the stage for classes of thermoresponsive materials to respond to macromolecule concentration rather than temperature changes.

Mechanical feedback defines organizing centers to drive digit emergence.

During embryonic development, digits gradually emerge in a periodic pattern. Although genetic evidence indicates that digit formation results from a self-organizing process, the underlying mechanisms are still unclear. Here, we find that convergent-extension tissue flows driven by active stresses underlie digit formation. These active stresses simultaneously shape cartilage condensations and lead to the emergence of a compressive stress region that promotes high activin/p-SMAD/SOX9 expression, thereby defining digit-organizing centers via a mechanical feedback. In Wnt5a mutants, such mechanical feedback is disrupted due to the loss of active stresses, organizing centers do not emerge, and digit formation is precluded. Thus, digit emergence does not result solely from molecular interactions, as was previously thought, but requires a mechanical feedback that ensures continuous coupling between phalanx specification and elongation. Our work, which links mechanical and molecular signals, provides a mechanistic context for the emergence of organizing centers that may underlie various developmental processes.

Embryonic Tissues as Active Foams.

The physical state of embryonic tissues emerges from non-equilibrium, collective interactions among constituent cells. Cellular jamming, rigidity transitions and characteristics of glassy dynamics have all been observed in multicellular systems, but it is unclear how cells control these emergent tissue states and transitions, including tissue fluidization. Combining computational and experimental methods, here we show that tissue fluidization in posterior zebrafish tissues is controlled by the stochastic dynamics of tensions at cell-cell contacts. We develop a computational framework that connects cell behavior to embryonic tissue dynamics, accounting for the presence of extracellular spaces, complex cell shapes and cortical tension dynamics. We predict that tissues are maximally rigid at the structural transition between confluent and non-confluent states, with actively-generated tension fluctuations controlling stress relaxation and tissue fluidization. By directly measuring strain and stress relaxation, as well as the dynamics of cell rearrangements, in elongating posterior zebrafish tissues, we show that tension fluctuations drive active cell rearrangements that fluidize the tissue. These results highlight a key role of non-equilibrium tension dynamics in developmental processes.

Mechanical control of tissue shape and morphogenetic flows during vertebrate body axis elongation.

Shaping embryonic tissues into their functional morphologies requires cells to control the physical state of the tissue in space and time. While regional variations in cellular forces or cell proliferation have been typically assumed to be the main physical factors controlling tissue morphogenesis, recent experiments have revealed that spatial variations in the tissue physical (fluid/solid) state play a key role in shaping embryonic tissues. Here we theoretically study how the regional control of fluid and solid tissue states guides morphogenetic flows to shape the extending vertebrate body axis. Our results show that both the existence of a fluid-to-solid tissue transition along the anteroposterior axis and the tissue surface tension determine the shape of the tissue and its ability to elongate unidirectionally, with large tissue tensions preventing unidirectional elongation and promoting blob-like tissue expansions. We predict both the tissue morphogenetic flows and stresses that enable unidirectional axis elongation. Our results show the existence of a sharp transition in the structure of morphogenetic flows, from a flow with no vortices to a flow with two counter-rotating vortices, caused by a transition in the number and location of topological defects in the flow field. Finally, comparing the theoretical predictions to quantitative measurements of both tissue flows and shape during zebrafish body axis elongation, we show that the observed morphogenetic events can be explained by the existence of a fluid-to-solid tissue transition along the anteroposterior axis. These results highlight the role of spatiotemporally-controlled fluid-to-solid transitions in the tissue state as a physical mechanism of embryonic morphogenesis.

Coordinating cell polarization and morphogenesis through mechanical feedback.

Many cellular processes require cell polarization to be maintained as the cell changes shape, grows or moves. Without feedback mechanisms relaying information about cell shape to the polarity molecular machinery, the coordination between cell polarization and morphogenesis, movement or growth would not be possible. Here we theoretically and computationally study the role of a genetically-encoded mechanical feedback (in the Cell Wall Integrity pathway) as a potential coordination mechanism between cell morphogenesis and polarity during budding yeast mating projection growth. We developed a coarse-grained continuum description of the coupled dynamics of cell polarization and morphogenesis as well as 3D stochastic simulations of the molecular polarization machinery in the evolving cell shape. Both theoretical approaches show that in the absence of mechanical feedback (or in the presence of weak feedback), cell polarity cannot be maintained at the projection tip during growth, with the polarization cap wandering off the projection tip, arresting morphogenesis. In contrast, for mechanical feedback strengths above a threshold, cells can robustly maintain cell polarization at the tip and simultaneously sustain mating projection growth. These results indicate that the mechanical feedback encoded in the Cell Wall Integrity pathway can provide important positional information to the molecular machinery in the cell, thereby enabling the coordination of cell polarization and morphogenesis.

Physical constraints on early blastomere packings.

At very early embryonic stages, when embryos are composed of just a few cells, establishing the correct packing arrangements (contacts) between cells is essential for the proper development of the organism. As early as the 4-cell stage, the observed cellular packings in different species are distinct and, in many cases, differ from the equilibrium packings expected for simple adherent and deformable particles. It is unclear what are the specific roles that different physical parameters, such as the forces between blastomeres, their division times, orientation of cell division and embryonic confinement, play in the control of these packing configurations. Here we simulate the non-equilibrium dynamics of cells in early embryos and systematically study how these different parameters affect embryonic packings at the 4-cell stage. In the absence of embryo confinement, we find that cellular packings are not robust, with multiple packing configurations simultaneously possible and very sensitive to parameter changes. Our results indicate that the geometry of the embryo confinement determines the packing configurations at the 4-cell stage, removing degeneracy in the possible packing configurations and overriding division rules in most cases. Overall, these results indicate that physical confinement of the embryo is essential to robustly specify proper cellular arrangements at very early developmental stages.

Fluorous Soluble Cyanine Dyes for Visualizing Perfluorocarbons in Living Systems.

The bioorthogonal nature of perfluorocarbons provides a unique platform for introducing dynamic nano- and microdroplets into cells and organisms. To monitor the localization and deformation of the droplets, fluorous soluble fluorophores that are compatible with standard fluorescent protein markers and applicable to cells, tissues, and small organisms are necessary. Here, we introduce fluorous cyanine dyes that represent the most red-shifted fluorous soluble fluorophores to date. We study the effect of covalently appended fluorous tags on the cyanine scaffold and evaluate the changes in photophysical properties imparted by the fluorous phase. Ultimately, we showcase the utility of the fluorous soluble pentamethine cyanine dye for tracking the localization of perfluorocarbon nanoemulsions in macrophage cells and for measurements of mechanical forces in multicellular spheroids and zebrafish embryonic tissues. These studies demonstrate that the red-shifted cyanine dyes offer spectral flexibility in multiplexed imaging experiments and enhanced precision in force measurements.

Physical control of tissue morphogenesis across scales.

During embryogenesis, tissues and organs are progressively shaped into their functional morphologies. While the information about tissue and organ shape is encoded genetically, the sculpting of embryonic structures in the 3D space is ultimately a physical process. The control of physical quantities involved in tissue morphogenesis originates at cellular and subcellular scales, but it is their emergent behavior at supracellular scales that guides morphogenetic events. In this review, we highlight the physical quantities that can be spatiotemporally tuned at supracellular scales to sculpt tissues and organs during embryonic development of animal species, and connect them to the cellular and molecular mechanisms controlling them.

A fluid-to-solid jamming transition underlies vertebrate body axis elongation.

Just as in clay moulding or glass blowing, physically sculpting biological structures requires the constituent material to locally flow like a fluid while maintaining overall mechanical integrity like a solid. Disordered soft materials, such as foams, emulsions and colloidal suspensions, switch from fluid-like to solid-like behaviours at a jamming transition1-4. Similarly, cell collectives have been shown to display glassy dynamics in 2D and 3D5,6 and jamming in cultured epithelial monolayers7,8, behaviours recently predicted theoretically9-11 and proposed to influence asthma pathobiology8 and tumour progression12. However, little is known about whether these seemingly universal behaviours occur in vivo13 and, specifically, whether they play any functional part during embryonic morphogenesis. Here, by combining direct in vivo measurements of tissue mechanics with analysis of cellular dynamics, we show that during vertebrate body axis elongation, posterior tissues undergo a jamming transition from a fluid-like behaviour at the extending end, the mesodermal progenitor zone, to a solid-like behaviour in the presomitic mesoderm. We uncover an anteroposterior, N-cadherin-dependent gradient in yield stress that provides increasing mechanical integrity to the presomitic mesoderm, consistent with the tissue transiting from a wetter to a dryer foam-like architecture. Our results show that cell-scale stresses fluctuate rapidly (within about 1 min), enabling cell rearrangements and effectively 'melting' the tissue at the growing end. Persistent (more than 0.5 h) stresses at supracellular scales, rather than cell-scale stresses, guide morphogenetic flows in fluid-like tissue regions. Unidirectional axis extension is sustained by the reported rigidification of the presomitic mesoderm, which mechanically supports posterior, fluid-like tissues during remodelling before their maturation. The spatiotemporal control of fluid-like and solid-like tissue states may represent a generic physical mechanism of embryonic morphogenesis.

The effect of cell geometry on polarization in budding yeast.

The localization (or polarization) of proteins on the membrane during the mating of budding yeast (Saccharomyces cerevisiae) is an important model system for understanding simple pattern formation within cells. While there are many existing mathematical models of polarization, for both budding and mating, there are still many aspects of this process that are not well understood. In this paper we set out to elucidate the effect that the geometry of the cell can have on the dynamics of certain models of polarization. Specifically, we look at several spatial stochastic models of Cdc42 polarization that have been adapted from published models, on a variety of tip-shaped geometries, to replicate the shape change that occurs during the growth of the mating projection. We show here that there is a complex interplay between the dynamics of polarization and the shape of the cell. Our results show that while models of polarization can generate a stable polarization cap, its localization at the tip of mating projections is unstable, with the polarization cap drifting away from the tip of the projection in a geometry dependent manner. We also compare predictions from our computational results to experiments that observe cells with projections of varying lengths, and track the stability of the polarization cap. Lastly, we examine one model of actin polarization and show that it is unlikely, at least for the models studied here, that actin dynamics and vesicle traffic are able to overcome this effect of geometry.

Mechanical feedback coordinates cell wall expansion and assembly in yeast mating morphogenesis.

The shaping of individual cells requires a tight coordination of cell mechanics and growth. However, it is unclear how information about the mechanical state of the wall is relayed to the molecular processes building it, thereby enabling the coordination of cell wall expansion and assembly during morphogenesis. Combining theoretical and experimental approaches, we show that a mechanical feedback coordinating cell wall assembly and expansion is essential to sustain mating projection growth in budding yeast (Saccharomyces cerevisiae). Our theoretical results indicate that the mechanical feedback provided by the Cell Wall Integrity pathway, with cell wall stress sensors Wsc1 and Mid2 increasingly activating membrane-localized cell wall synthases Fks1/2 upon faster cell wall expansion, stabilizes mating projection growth without affecting cell shape. Experimental perturbation of the osmotic pressure and cell wall mechanics, as well as compromising the mechanical feedback through genetic deletion of the stress sensors, leads to cellular phenotypes that support the theoretical predictions. Our results indicate that while the existence of mechanical feedback is essential to stabilize mating projection growth, the shape and size of the cell are insensitive to the feedback.

Geometrical characterization of fluorescently labelled surfaces from noisy 3D microscopy data.

Modern fluorescence microscopy enables fast 3D imaging of biological and inert systems alike. In many studies, it is important to detect the surface of objects and quantitatively characterize its local geometry, including its mean curvature. We present a fully automated algorithm to determine the location and curvatures of an object from 3D fluorescence images, such as those obtained using confocal or light-sheet microscopy. The algorithm aims at reconstructing surface labelled objects with spherical topology and mild deformations from the spherical geometry with high accuracy, rather than reconstructing arbitrarily deformed objects with lower fidelity. Using both synthetic data with known geometrical characteristics and experimental data of spherical objects, we characterize the algorithm's accuracy over the range of conditions and parameters typically encountered in 3D fluorescence imaging. We show that the algorithm can detect the location of the surface and obtain a map of local mean curvatures with relative errors typically below 2% and 20%, respectively, even in the presence of substantial levels of noise. Finally, we apply this algorithm to analyse the shape and curvature map of fluorescently labelled oil droplets embedded within multicellular aggregates and deformed by cellular forces.

Spatiotemporal variation of endogenous cell-generated stresses within 3D multicellular spheroids.

Multicellular spheroids serve as an excellent platform to study tissue behavior and tumor growth in a controlled, three-dimensional (3D) environment. While molecular and cellular studies have long used this platform to study cell behavior in 3D, only recently have studies using multicellular spheroids shown an important role for the mechanics of the microenvironment in a wide range of cellular processes, including during tumor progression. Despite the well-established relevance of mechanical cues to cell behavior and the numerous studies on mechanics using 2D cell culture systems, the spatial and temporal variations in endogenous cellular forces within growing multicellular aggregates remain unknown. Using cell-sized oil droplets with controlled physicochemical properties as force transducers in mesenchymal cell aggregates, we show that the magnitude of cell-generated stresses varies only weakly with spatial location within the spherical aggregate, but it increases considerably over time during aggregate compaction and growth. Moreover, our results indicate that the temporal increase in cellular stresses is due to increasing cell pulling forces transmitted via integrin-mediated cell adhesion, consistent with the need for larger intercellular pulling forces to compact cell aggregates.

Connecting individual to collective cell migration.

Collective cell migration plays a pivotal role in the formation of organs, tissue regeneration, wound healing and many disease processes, including cancer. Despite the considerable existing knowledge on the molecular control of cell movements, it is unclear how the different observed modes of collective migration, especially for small groups of cells, emerge from the known behaviors of individual cells. Here we derive a physical description of collective cellular movements from first principles, while accounting for known phenomenological cell behaviors, such as contact inhibition of locomotion and force-induced cell repolarization. We show that this theoretical description successfully describes the motion of groups of cells of arbitrary numbers, connecting single cell behaviors and parameters (e.g., adhesion and traction forces) to the collective migration of small groups of cells and the expansion of large cell colonies. Specifically, using a common framework, we explain how cells characterized by contact inhibition of locomotion can display coherent collective behavior when in groups, even in the absence of biochemical signaling. We find an optimal group size leading to maximal group persistence and show that cell proliferation prevents the buildup of intercellular forces within cell colonies, enabling their expansion.