In vivo quantification of spatially varying mechanical properties in developing tissues

Multimodal mechano-microscopy reveals mechanical phenotypes of breast cancer spheroids in three dimensions

Cancer cell invasion relies on an equilibrium between cell deformability and the biophysical constraints imposed by the extracellular matrix (ECM). However, there is little consensus on the nature of the local biomechanical alterations in cancer cell dissemination in the context of three-dimensional (3D) tumor microenvironments (TMEs). While the shortcomings of two-dimensional (2D) models in replicating in situ cell behavior are well known, 3D TME models remain underutilized because contemporary mechanical quantification tools are limited to surface measurements. Here, we overcome this major challenge by quantifying local mechanics of cancer cell spheroids in 3D TMEs. We achieve this using multimodal mechano-microscopy, integrating optical coherence microscopy-based elasticity imaging with confocal fluorescence microscopy. We observe that non-metastatic cancer spheroids show no invasion while showing increased peripheral cell elasticity in both stiff and soft environments. Metastatic cancer spheroids, however, show ECM-mediated softening in a stiff microenvironment and, in a soft environment, initiate cell invasion with peripheral softening associated with early metastatic dissemination. This exemplar of live-cell 3D mechanotyping supports that invasion increases cell deformability in a 3D context, illustrating the power of multimodal mechano-microscopy for quantitative mechanobiology in situ.

Photo-induced changes in tissue stiffness alter epithelial budding morphogenesis in the embryonic lung

Extracellular matrix (ECM) stiffness has been shown to influence the differentiation of progenitor cells in culture, but a lack of tools to perturb the mechanical properties within intact embryonic organs has made it difficult to determine how changes in tissue stiffness influence organ patterning and morphogenesis. Photocrosslinking of the ECM has been successfully used to stiffen soft tissues, such as the cornea and skin, which are optically accessible, but this technique has not yet been applied to developing embryos. Here, we use photocrosslinking with Rose Bengal (RB) to locally and ectopically stiffen the pulmonary mesenchyme of explanted embryonic lungs cultured ex vivo . This change in mechanical properties was sufficient to suppress FGF-10-mediated budding morphogenesis along the embryonic airway, without negatively impacting patterns of cell proliferation or apoptosis. A computational model of airway branching was used to determine that FGF-10-induced buds form via a growth-induced buckling mechanism and that increased mesenchymal stiffness is sufficient to inhibit epithelial buckling. Taken together, our data demonstrate that photocrosslinking can be used to create regional differences in mechanical properties within intact embryonic organs and that these differences influence epithelial morphogenesis and patterning. Further, this photocrosslinking assay can be readily adapted to other developing tissues and model systems.

Actomyosin forces in cell migration: Moving beyond cell body retraction

In textbook illustrations of migrating cells, actomyosin contractility is typically depicted as the contraction force necessary for cell body retraction. This dogma has been transformed by the molecular clutch model, which acknowledges that actomyosin traction forces also generate and transmit biomechanical signals at the leading edge, enabling cells to sense and shape their migratory path in mechanically complex environments. To fulfill these complementary functions, the actomyosin system assembles a gradient of contractile energy along the front-rear axis of migratory cells. Here, we highlight the hierarchic assembly and self-regulatory network structure of the actomyosin system and explain how the kinetics of different nonmuscle myosin II (NM II) paralogs synergize during contractile force generation. Our aim is to emphasize how protrusion formation, cell adhesion, contraction, and retraction are spatiotemporally integrated during different modes of migration, including chemotaxis and durotaxis. Finally, we hypothesize how different NM II paralogs might tune aspects of migration in vivo, highlighting future research directions.

Mechanical state transitions in the regulation of tissue form and function

From embryonic development, postnatal growth and adult homeostasis to reparative and disease states, cells and tissues undergo constant changes in genome activity, cell fate, proliferation, movement, metabolism and growth. Importantly, these biological state transitions are coupled to changes in the mechanical and material properties of cells and tissues, termed mechanical state transitions. These mechanical states share features with physical states of matter, liquids and solids. Tissues can switch between mechanical states by changing behavioural dynamics or connectivity between cells. Conversely, these changes in tissue mechanical properties are known to control cell and tissue function, most importantly the ability of cells to move or tissues to deform. Thus, tissue mechanical state transitions are implicated in transmitting information across biological length and time scales, especially during processes of early development, wound healing and diseases such as cancer. This Review will focus on the biological basis of tissue-scale mechanical state transitions, how they emerge from molecular and cellular interactions, and their roles in organismal development, homeostasis, regeneration and disease.

Substrate Rigidity Modulates Segmentation Clock Dynamics in Isolated Presomitic Mesoderm Cells

The segmentation clock, a genetic oscillator in the presomitic mesoderm (PSM), is known to be influenced by biochemical signals, yet its potential regulation by mechanical cues remains unclear. The complex PSM microenvironment has made it challenging to isolate the effects of mechanical perturbations on clock behavior. Here we investigated how mechanical stimuli affect clock oscillations by culturing zebrafish PSM cells on PDMS micropost arrays with tunable rigidities (0.6-1200 kPa). We observed an inverse sigmoidal relationship between surface rigidity and both the percentage of oscillating cells and the number of oscillation cycles, with a switching threshold between 3-6 kPa. The periods of oscillating cells showed a consistently broad distribution across rigidity changes. Moreover, these cells exhibited distinct biophysical properties, such as reduced motility, contractility, and sustained circularity. These findings highlight the crucial role of cell-substrate interactions in regulating segmentation clock behavior, providing insights into the mechanobiology of somitogenesis.

An emerging role for tissue plasticity in developmental precision

Reproducible tissue morphology is a fundamental feature of embryonic development. To ensure such robustness during tissue morphogenesis, inherent noise in biological processes must be buffered. While redundant genes, parallel signaling pathways and intricate network topologies are known to reduce noise, over the last few years, mechanical properties of tissues have been shown to play a vital role. Here, taking the example of somite shape changes, I will discuss how tissues are highly plastic in their ability to change shapes leading to increased precision and reproducibility.

Deformable microlaser force sensing

Mechanical forces are key regulators of cellular behavior and function, affecting many fundamental biological processes such as cell migration, embryogenesis, immunological responses, and pathological states. Specialized force sensors and imaging techniques have been developed to quantify these otherwise invisible forces in single cells and in vivo. However, current techniques rely heavily on high-resolution microscopy and do not allow interrogation of optically dense tissue, reducing their application to 2D cell cultures and highly transparent biological tissue. Here, we introduce DEFORM, deformable microlaser force sensing, a spectroscopic technique that detects sub-nanonewton forces with unprecedented spatio-temporal resolution. DEFORM is based on the spectral analysis of laser emission from dye-doped oil microdroplets and uses the force-induced lifting of laser mode degeneracy in these droplets to detect nanometer deformations. Following validation by atomic force microscopy and development of a model that links changes in laser spectrum to applied force, DEFORM is used to measure forces in 3D and at depths of hundreds of microns within tumor spheroids and late-stage Drosophila larva. We furthermore show continuous force sensing with single-cell spatial and millisecond temporal resolution, thus paving the way for non-invasive studies of biomechanical forces in advanced stages of embryogenesis, tissue remodeling, and tumor invasion.

Dynamic monitoring soft tissue healing via visualized Gd-crosslinked double network MRI microspheres

By integrating magnetic resonance-visible components with scaffold materials, hydrogel microspheres (HMs) become visible under magnetic resonance imaging(MRI), allowing for non-invasive, continuous, and dynamic monitoring of the distribution, degradation, and relationship of the HMs with local tissues. However, when these visualization components are physically blended into the HMs, it reduces their relaxation rate and specificity under MRI, weakening the efficacy of real-time dynamic monitoring. To achieve MRI-guided in vivo monitoring of HMs with tissue repair functionality, we utilized airflow control and photo-crosslinking methods to prepare alginate-gelatin-based dual-network hydrogel microspheres (G-AlgMA HMs) using gadolinium ions (Gd (III)), a paramagnetic MRI contrast agent, as the crosslinker. When the network of G-AlgMA HMs degrades, the cleavage of covalent bonds causes the release of Gd (III), continuously altering the arrangement and movement characteristics of surrounding water molecules. This change in local transverse and longitudinal relaxation times results in variations in MRI signal values, thus enabling MRI-guided in vivo monitoring of the HMs. Additionally, in vivo data show that the degradation and release of polypeptide (K2 (SL)6 K2 (KK)) from G-AlgMA HMs promote local vascular regeneration and soft tissue repair. Overall, G-AlgMA HMs enable non-invasive, dynamic in vivo monitoring of biomaterial degradation and tissue regeneration through MRI, which is significant for understanding material degradation mechanisms, evaluating biocompatibility, and optimizing material design.

Lightsheet microscopy integrates single-cell optical visco-elastography and fluorescence cytometry of 3D live tissues

Most common cytometry methods, including flow cytometry, observe suspended or fixed cells and cannot evaluate their structural roles in 3D tissues. However, cellular physical interactions are critical in physiological, developmental, and pathological processes. Here, we present a novel optical visco-elastography that characterizes single-cellular physical interactions by applying in-situ micro-mechanical perturbation to live microtissues under 3D lightsheet microscopy. The 4D digital image correlation (DIC) analysis of ~20,000 nodes tracked the compressive deformation of 3D tissues containing ~500 cells. The computational 3D image segmentation allowed cell-by-cell qualitative observation and statistical analysis, directly correlating multi-channel fluorescence and viscoelasticity. To represent epithelia-stroma interactions, we used a 3D organoid model of maternal-fetal interface and visualized solid-like, well-aligned displacement and liquid-like random motion between individual cells. The statistical analysis through our unique cytometry confirmed that endometrial stromal fibroblasts stiffen in response to decidualization. Moreover, we demonstrated in the 3D model that interaction with placental extravillous trophoblasts partially reverses the attained stiffness, which was supported by the gene expression analysis. Placentation shares critical cellular and molecular significance with various fundamental biological events such as cancer metastasis, wound healing, and gastrulation. Our analysis confirmed existing beliefs and discovered new insights, proving the broad applicability of our method.

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.

Macrophage mediated mesoscale brain mechanical homeostasis mechanically imaged via optical tweezers and Brillouin microscopy in vivo

Tissues are active materials where epithelial turnover, immune surveillance, and remodeling of stromal cells such as macrophages all regulate form and function. Scattering modalities such as Brillouin microscopy (BM) can non-invasively access mechanical signatures at GHz. However, our traditional understanding of tissue material properties is derived mainly from modalities which probe mechanical properties at different frequencies. Thus, reconciling measurements amongst these modalities remains an active area. Here, we compare optical tweezer active microrheology (OT-AMR) and Brillouin microscopy (BM) to longitudinally map brain development in the larval zebrafish. We determine that each measurement is able to detect a mechanical signature linked to functional units of the brain. We demonstrate that the corrected BM-Longitudinal modulus using a density factor correlates well with OT-AMR storage modulus at lower frequencies. We also show that the brain tissue mechanical properties are dependent on both the neuronal architecture and the presence of macrophages. Moreover, the BM technique is able to delineate the contributions to mechanical properties of the macrophage from that due to colony stimulating factor 1 receptor (CSF1R) mediated stromal remodeling. Here, our data suggest that macrophage remodeling is instrumental in the maintenance of tissue mechanical homeostasis during development. Moreover, the strong agreement between the OT-AM and BM further demonstrates that scattering-based technique is sensitive to both large and minute structural modification in vivo.

Multiscale elasticity mapping of biological samples in 3D at optical resolution

The mechanical properties of biological tissues have emerged as an integral determinant of tissue function in health and disease. Nonetheless, characterizing the elasticity of biological samples in 3D and at high resolution remains challenging. Here, we present a µElastography platform: a scalable elastography system that maps the elastic properties of tissues from cellular to organ scales. The platform leverages the use of a biocompatible, thermo-responsive hydrogel to deliver compressive stress to a biological sample and track its resulting deformation. By surrounding the specimen with a reference hydrogel of known Young's modulus, we are able to map the absolute values of elastic properties in biological samples. We validate the experimental and computational components of the platform using a hydrogel phantom and verify the system's ability to detect internal mechanical heterogeneities. We then apply the platform to map the elasticity of multicellular spheroids and the murine lymph node. With these applications, we demonstrate the platform's ability to map tissue elasticity at internal planes of interest, as well as capture mechanical heterogeneities neglected by most macroscale characterization techniques. The µElastography platform, designed to be implementable in any biology lab with access to 3D microscopy (e.g., confocal, multiphoton, or optical coherence microscopy), will provide the capability to characterize the mechanical properties of biological samples to labs across the large community of biological sciences by eliminating the need of specialized instruments such as atomic force microscopy. STATEMENT OF SIGNIFICANCE: Understanding the elasticity of biological tissues is of great importance, but characterizing these properties typically requires highly specialized equipment. Utilizing stimulus-responsive hydrogels, we present a scalable, hydrogel-based elastography method that uses readily available reagents and imaging modalities to generate resolved maps of internal elasticity within biomaterials and biological samples at optical resolution. This new approach is capable of detecting internal stiffness heterogeneities within the 3D bulk of samples and is highly scalable across both imaging modalities and biological length scales. Thus, it will have significant impact on the measurement capabilities of labs studying engineered biomaterials, mechanobiology, disease progression, and tissue engineering and development.

Mechanical stress can regulate temporomandibular joint cavitation via signalling pathways

The temporomandibular joint (TMJ), composed of temporal fossa, mandibular condyle and a fibrocartilage disc with upper and lower cavities, is the biggest synovial joint and biomechanical hinge of the craniomaxillofacial musculoskeletal system. The initial events that give rise to TMJ cavities across diverse species are not fully understood. Most studies focus on the pivotal role of molecules such as Indian hedgehog (Ihh) and hyaluronic acid (HA) in TMJ cavitation. Although biologists have observed that mechanical stress plays an irreplaceable role in the development of biological tissues and organs, few studies have been concerned with how mechanical stress regulates TMJ cavitation. Based on the evidence from human or other animal embryos today, it is implicated that mechanical stress plays an essential role in TMJ cavitation. In this review, we discuss the relationship between mechanical stress and TMJ cavitation from evo-devo perspectives and review the clinical features and potential pathogenesis of TMJ dysplasia.

How great thou ART: biomechanical properties of oocytes and embryos as indicators of quality in assisted reproductive technologies

Assisted Reproductive Technologies (ART) have revolutionized infertility treatment and animal breeding, but their success largely depends on selecting high-quality oocytes for fertilization and embryos for transfer. During preimplantation development, embryos undergo complex morphogenetic processes, such as compaction and cavitation, driven by cellular forces dependent on cytoskeletal dynamics and cell-cell interactions. These processes are pivotal in dictating an embryo's capacity to implant and progress to full-term development. Hence, a comprehensive grasp of the biomechanical attributes characterizing healthy oocytes and embryos is essential for selecting those with higher developmental potential. Various noninvasive techniques have emerged as valuable tools for assessing biomechanical properties without disturbing the oocyte or embryo physiological state, including morphokinetics, analysis of cytoplasmic movement velocity, or quantification of cortical tension and elasticity using microaspiration. By shedding light on the cytoskeletal processes involved in chromosome segregation, cytokinesis, cellular trafficking, and cell adhesion, underlying oogenesis, and embryonic development, this review explores the significance of embryo biomechanics in ART and its potential implications for improving clinical IVF outcomes, offering valuable insights and research directions to enhance oocyte and embryo selection procedures.

Measurement of adhesion and traction of cells at high yield (MATCHY) reveals an energetic ratchet driving nephron condensation

Engineering of embryonic strategies for tissue-building has extraordinary promise for regenerative medicine. This has led to a resurgence in interest in the relationship between cell biophysical properties and morphological transitions. However, mapping gene or protein expression data to cell biophysical properties to physical morphogenesis remains challenging with current techniques. Here we present MATCHY (multiplexed adhesion and traction of cells at high yield). MATCHY advances the multiplexing and throughput capabilities of existing traction force and cell-cell adhesion assays using microfabrication and an automated computation scheme with machine learning-driven cell segmentation. Both biophysical assays are coupled with serial downstream immunofluorescence to extract cell type/signaling state information. MATCHY is especially suited to complex primary tissue-, organoid-, or biopsy-derived cell mixtures since it does not rely on a priori knowledge of cell surface markers, cell sorting, or use of lineage-specific reporter animals. We first validate MATCHY on canine kidney epithelial cells engineered for RET tyrosine kinase expression and quantify a relationship between downstream signaling and cell traction. We go on to create a biophysical atlas of primary cells dissociated from the mouse embryonic kidney and use MATCHY to identify distinct biophysical states along the nephron differentiation trajectory. Our data complement expression-level knowledge of adhesion molecule changes that accompany nephron differentiation with quantitative biophysical information. These data reveal an 'energetic ratchet' that explains spatial nephron progenitor cell condensation from the niche as they differentiate, which we validate through agent-based computational simulation. MATCHY offers automated cell biophysical characterization at >104-cell throughput, a highly enabling advance for fundamental studies and new synthetic tissue design strategies for regenerative medicine.

Engineering the Physical Microenvironment into Neural Organoids for Neurogenesis and Neurodevelopment

Understanding the signals from the physical microenvironment is critical for deciphering the processes of neurogenesis and neurodevelopment. The discovery of how surrounding physical signals shape human developing neurons is hindered by the bottleneck of conventional cell culture and animal models. Notwithstanding neural organoids provide a promising platform for recapitulating human neurogenesis and neurodevelopment, building neuronal physical microenvironment that accurately mimics the native neurophysical features is largely ignored in current organoid technologies. Here, it is discussed how the physical microenvironment modulates critical events during the periods of neurogenesis and neurodevelopment, such as neural stem cell fates, neural tube closure, neuronal migration, axonal guidance, optic cup formation, and cortical folding. Although animal models are widely used to investigate the impacts of physical factors on neurodevelopment and neuropathy, the important roles of human stem cell-derived neural organoids in this field are particularly highlighted. Considering the great promise of human organoids, building neural organoid microenvironments with mechanical forces, electrophysiological microsystems, and light manipulation will help to fully understand the physical cues in neurodevelopmental processes. Neural organoids combined with cutting-edge techniques, such as advanced atomic force microscopes, microrobots, and structural color biomaterials might promote the development of neural organoid-based research and neuroscience.

Magneto-acoustic protein nanostructures for non-invasive imaging of tissue mechanics in vivo

Measuring cellular and tissue mechanics inside intact living organisms is essential for interrogating the roles of force in physiological and disease processes. Current agents for studying the mechanobiology of intact, living organisms are limited by poor light penetration and material stability. Magnetomotive ultrasound is an emerging modality for real-time in vivo imaging of tissue mechanics. Nonetheless, it has poor sensitivity and spatiotemporal resolution. Here we describe magneto-gas vesicles (MGVs), protein nanostructures based on gas vesicles and magnetic nanoparticles that produce differential ultrasound signals in response to varying mechanical properties of surrounding tissues. These hybrid nanomaterials significantly improve signal strength and detection sensitivity. Furthermore, MGVs enable non-invasive, long-term and quantitative measurements of mechanical properties within three-dimensional tissues and in vivo fibrosis models. Using MGVs as novel contrast agents, we demonstrate their potential for non-invasive imaging of tissue elasticity, offering insights into mechanobiology and its application to disease diagnosis and treatment.

Quantifying local stiffness and forces in soft biological tissues using droplet optical microcavities

Mechanical properties of biological tissues fundamentally underlie various biological processes and noncontact, local, and microscopic methods can provide fundamental insights. Here, we present an approach for quantifying the local mechanical properties of biological materials at the microscale, based on measuring the spectral shifts of the optical resonances in droplet microcavities. Specifically, the developed method allows for measurements of deformations in dye-doped oil droplets embedded in soft materials or biological tissues with an error of only 1 nm, which in turn enables measurements of anisotropic stress inside tissues as small as a few pN/μm2. Furthermore, by applying an external strain, Young's modulus can be measured in the range from 1 Pa to 35 kPa, which covers most human soft tissues. Using multiple droplet microcavities, our approach could enable mapping of stiffness and forces in inhomogeneous soft tissues and could also be applied to in vivo and single-cell experiments. The developed method can potentially lead to insights into the mechanics of biological tissues.

Directional Cell Migration Guided by a Strain Gradient

Strain gradients widely exist in development and physiological activities. The directional movement of cells is essential for proper cell localization, and directional cell migration in responses to gradients of chemicals, rigidity, density, and topography of extracellular matrices have been well-established. However; it is unclear whether strain gradients imposed on cells are sufficient to drive directional cell migration. In this work, a programmable uniaxial cell stretch device is developed that creates controllable strain gradients without changing substrate stiffness or ligand distributions. It is demonstrated that over 60% of the single rat embryonic fibroblasts migrate toward the lower strain side in static and the 0.1 Hz cyclic stretch conditions at ≈4% per mm strain gradients. It is confirmed that such responses are distinct from durotaxis or haptotaxis. Focal adhesion analysis confirms higher rates of contact area and protrusion formation on the lower strain side of the cell. A 2D extended motor-clutch model is developed to demonstrate that the strain-introduced traction force determines integrin fibronectin pairs' catch-release dynamics, which drives such directional migration. Together, these results establish strain gradient as a novel cue to regulate directional cell migration and may provide new insights in development and tissue repairs.

Quantifying Spatial Patterns of Tissue Stiffness Within the Embryonic Mouse Kidney

Biophysical factors, including changes in mechanical stiffness, have been shown to influence the morphogenesis of developing organs. There is a lack of experimental techniques, however, that can probe the mechanical properties of embryonic tissues-especially those which are not mechanically or optically accessible, such as the visceral organs of the developing mouse embryo. Here, using the embryonic kidney as a model system, we describe a method to use microindentation to quantify tissue-level regional differences in the mechanical properties of an embryonic organ. This technique is generalizable and can be used to quantify patterns of tissue stiffness within other developing organ systems. Going forward, these data will enable new experimental studies of the role of biophysical cues during organogenesis.

Discontinuous Shear Thickening in Biological Tissue Rheology

During embryonic morphogenesis, tissues undergo dramatic deformations in order to form functional organs. Similarly, in adult animals, living cells and tissues are continually subjected to forces and deformations. Therefore, the success of embryonic development and the proper maintenance of physiological functions rely on the ability of cells to withstand mechanical stresses as well as their ability to flow in a collective manner. During these events, mechanical perturbations can originate from active processes at the single-cell level, competing with external stresses exerted by surrounding tissues and organs. However, the study of tissue mechanics has been somewhat limited to either the response to external forces or to intrinsic ones. In this work, we use an active vertex model of a 2D confluent tissue to study the interplay of external deformations that are applied globally to a tissue with internal active stresses that arise locally at the cellular level due to cell motility. We elucidate, in particular, the way in which this interplay between globally external and locally internal active driving determines the emergent mechanical properties of the tissue as a whole. For a tissue in the vicinity of a solid-fluid jamming or unjamming transition, we uncover a host of fascinating rheological phenomena, including yielding, shear thinning, continuous shear thickening, and discontinuous shear thickening. These model predictions provide a framework for understanding the recently observed nonlinear rheological behaviors in vivo.

Elastic fibers define embryonic tissue stiffness to enable buckling morphogenesis of the small intestine

During embryonic development, tissues must possess precise material properties to ensure that cell-generated forces give rise to the stereotyped morphologies of developing organs. However, the question of how material properties are established and regulated during development remains understudied. Here, we aim to address these broader questions through the study of intestinal looping, a process by which the initially straight intestinal tube buckles into loops, permitting ordered packing within the body cavity. Looping results from elongation of the tube against the constraint of an attached tissue, the dorsal mesentery, which is elastically stretched by the elongating tube to nearly triple its length. This elastic energy storage allows the mesentery to provide stable compressive forces that ultimately buckle the tube into loops. Beginning with a transcriptomic analysis of the mesentery, we identified widespread upregulation of extracellular matrix related genes during looping, including genes related to elastic fiber deposition. Combining molecular and mechanical analyses, we conclude that elastin confers tensile stiffness to the mesentery, enabling its mechanical role in organizing the developing small intestine. These results shed light on the role of elastin as a driver of morphogenesis that extends beyond its more established role in resisting cyclic deformation in adult tissues.

Mapping morphogenesis and mechanics in embryo models

Recent methodological advances in measurements of geometry and forces in the early embryo and its models are enabling a deeper understanding of the complex interplay of genetics, mechanics and geometry during development.

Single and two-cells shape analysis from energy functionals for three-dimensional vertex models

Vertex models have been extensively used for simulating the evolution of multicellular systems, and have given rise to important global properties concerning their macroscopic rheology or jamming transitions. These models are based on the definition of an energy functional, which fully determines the cellular response and conclusions. While two-dimensional vertex models have been widely employed, three-dimensional models are far more scarce, mainly due to the large amount of configurations that they may adopt and the complex geometrical transitions they undergo. We here investigate the shape of single and two-cells configurations as a function of the energy terms, and we study the dependence of the final shape on the model parameters: namely the exponent of the term penalising cell-cell adhesion and surface contractility. In single cell analysis, we deduce analytically the radius and limit values of the contractility for linear and quadratic surface energy terms, in 2D and 3D. In two-cells systems, symmetrical and asymmetrical, we deduce the evolution of the aspect ratio and the relative radius. While in functionals with linear surface terms yield the same aspect ratio in 2D and 3D, the configurations when using quadratic surface terms are distinct. We relate our results with well-known solutions from capillarity theory, and verify our analytical findings with a three-dimensional vertex model.

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.

Untethered Micro/Nanorobots for Remote Sensing: Toward Intelligent Platform

Untethered micro/nanorobots that can wirelessly control their motion and deformation state have gained enormous interest in remote sensing applications due to their unique motion characteristics in various media and diverse functionalities. Researchers are developing micro/nanorobots as innovative tools to improve sensing performance and miniaturize sensing systems, enabling in situ detection of substances that traditional sensing methods struggle to achieve. Over the past decade of development, significant research progress has been made in designing sensing strategies based on micro/nanorobots, employing various coordinated control and sensing approaches. This review summarizes the latest developments on micro/nanorobots for remote sensing applications by utilizing the self-generated signals of the robots, robot behavior, microrobotic manipulation, and robot-environment interactions. Providing recent studies and relevant applications in remote sensing, we also discuss the challenges and future perspectives facing micro/nanorobots-based intelligent sensing platforms to achieve sensing in complex environments, translating lab research achievements into widespread real applications.

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.

A comprehensive model of Drosophila epithelium reveals the role of embryo geometry and cell topology in mechanical responses

In order to understand morphogenesis, it is necessary to know the material properties or forces shaping the living tissue. In spite of this need, very few in vivo measurements are currently available. Here, using the early Drosophila embryo as a model, we describe a novel cantilever-based technique which allows for the simultaneous quantification of applied force and tissue displacement in a living embryo. By analyzing data from a series of experiments in which embryonic epithelium is subjected to developmentally relevant perturbations, we conclude that the response to applied force is adiabatic and is dominated by elastic forces and geometric constraints, or system size effects. Crucially, computational modeling of the experimental data indicated that the apical surface of the epithelium must be softer than the basal surface, a result which we confirmed experimentally. Further, we used the combination of experimental data and comprehensive computational model to estimate the elastic modulus of the apical surface and set a lower bound on the elastic modulus of the basal surface. More generally, our investigations revealed important general features that we believe should be more widely addressed when quantitatively modeling tissue mechanics in any system. Specifically, different compartments of the same cell can have very different mechanical properties; when they do, they can contribute differently to different mechanical stimuli and cannot be merely averaged together. Additionally, tissue geometry can play a substantial role in mechanical response, and cannot be neglected.

A programmable ferrofluidic droplet robot

Soft miniature robots have wide potential applications in lab-on-a-chip and biomedical sciences due to their deformability, safety, and remarkable controllability. However, current ferrofluidic droplet robots have some problems, such as easy broken, limited motion range and high energy consumption. Therefore, the objective of this study is to propose a programmable ferrofluidic flexible droplet robot (PFDR) with control strategies for elongation, splitting and merging behaviors by designing an actuation system consisting of a row of electromagnets and a robotic arm or a coordinate robot. The PFDR can not only deform actively to prevent itself from breaking, but also deform passively to fit the profile of channels or tubes to move efficiently. The actuation system can make PFDR have larger motion range as well as lower energy consumption. The design concept and the operating principle of PFDR are presented. The magnetic actuation system is developed. The lag of PFDR is analyzed in theoretical and experimental ways. The splitting and merging behaviors are investigated and other functionalities are studied as well.

From cells to form: A roadmap to study shape emergence in vivo

Organogenesis arises from the collective arrangement of cells into progressively 3D-shaped tissue. The acquisition of a correctly shaped organ is then the result of a complex interplay between molecular cues, responsible for differentiation and patterning, and the mechanical properties of the system, which generate the necessary forces that drive correct shape emergence. Nowadays, technological advances in the fields of microscopy, molecular biology, and computer science are making it possible to see and record such complex interactions in incredible, unforeseen detail within the global context of the developing embryo. A quantitative and interdisciplinary perspective of developmental biology becomes then necessary for a comprehensive understanding of morphogenesis. Here, we provide a roadmap to quantify the events that lead to morphogenesis from imaging to image analysis, quantification, and modeling, focusing on the discrete cellular and tissue shape changes, as well as their mechanical properties.

Actin polymerization and depolymerization in developing vertebrates

Development is a complex process that occurs throughout the life cycle. F-actin, a major component of the cytoskeleton, is essential for the morphogenesis of tissues and organs during development. F-actin is formed by the polymerization of G-actin, and the dynamic balance of polymerization and depolymerization ensures proper cellular function. Disruption of this balance results in various abnormalities and defects or even embryonic lethality. Here, we reviewed recent findings on the structure of G-actin and F-actin and the polymerization of G-actin to F-actin. We also focused on the functions of actin isoforms and the underlying mechanisms of actin polymerization/depolymerization in cellular and organic morphogenesis during development. This information will extend our understanding of the role of actin polymerization in the physiologic or pathologic processes during development and may open new avenues for developing therapeutics for embryonic developmental abnormalities or tissue regeneration.

Evidence that tissue recoil in the early Drosophila embryo is a passive not active process

Understanding tissue morphogenesis is impossible without knowing the mechanical properties of the tissue being shaped. Although techniques for measuring tissue material properties are continually being developed, methods for determining how individual proteins contribute to mechanical properties are very limited. Here, we developed two complementary techniques for the acute inactivation of spaghetti squash (the Drosophila myosin regulatory light chain), one based on the recently introduced (auxin-inducible degron 2 (AID2) system, and the other based on a novel method for conditional protein aggregation that results in nearly instantaneous protein inactivation. Combining these techniques with rheological measurements, we show that passive material properties of the cellularization-stage Drosophila embryo are essentially unaffected by myosin activity. These results suggest that this tissue is elastic, not predominantly viscous, on the developmentally relevant timescale.

Targeted mechanical stimulation via magnetic nanoparticles guides in vitro tissue development

Tissues take shape through a series of morphogenetic movements guided by local cell-scale mechanical forces. Current in vitro approaches to recapitulate tissue mechanics rely on uncontrolled self-organization or on the imposition of extrinsic and homogenous forces using matrix or instrument-driven stimulation, thereby failing to recapitulate highly localized and spatially varying forces. Here we develop a method for targeted mechanical stimulation of organoids using embedded magnetic nanoparticles. We show that magnetic clusters within organoids can be produced by sequential aggregation of magnetically labeled and non-labeled human pluripotent stem cells. These clusters impose local mechanical forces on the surrounding cells in response to applied magnetic fields. We show that precise, spatially defined actuation provides short-term mechanical tissue perturbations as well as long-term cytoskeleton remodeling in these organoids, which we term "magnetoids". We demonstrate that targeted magnetic nanoparticle-driven actuation guides asymmetric tissue growth and proliferation, leading to enhanced patterning in human neural magnetoids. This approach, enabled by nanoparticle technology, allows for precise and locally controllable mechanical actuation in human neural tube organoids, and could be widely applicable to interrogate the role of local mechanotransduction in developmental and disease model systems.

Genetic reporter for live tracing fluid flow forces during cell fate segregation in mouse blastocyst development

Mechanical forces are known to be important in mammalian blastocyst formation; however, due to limited tools, specific force inputs and how they relay to first cell fate control of inner cell mass (ICM) and/or trophectoderm (TE) remain elusive. Combining in toto live imaging and various perturbation experiments, we demonstrate and measure fluid flow forces existing in the mouse blastocyst cavity and identify Klf2(Krüppel-like factor 2) as a fluid force reporter with force-responsive enhancers. Long-term live imaging and lineage reconstructions reveal that blastomeres subject to higher fluid flow forces adopt ICM cell fates. These are reinforced by internal ferrofluid-induced flow force assays. We also utilize ex vivo fluid flow force mimicking and pharmacological perturbations to confirm mechanosensing specificity. Together, we report a genetically encoded reporter for continuously monitoring fluid flow forces and cell fate decisions and provide a live imaging framework to infer force information enriched lineage landscape during development. VIDEO ABSTRACT.

ELASTIC FIBERS DEFINE EMBRYONIC TISSUE STIFFNESS TO ENABLE BUCKLING MORPHOGENESIS OF THE SMALL INTESTINE

During embryonic development, tissues must possess precise material properties to ensure that cell-generated forces give rise to the stereotyped morphologies of developing organs. However, the question of how material properties are established and regulated during development remains understudied. Here, we aim to address these broader questions through the study of intestinal looping, a process by which the initially straight intestinal tube buckles into loops, permitting ordered packing within the body cavity. Looping results from elongation of the tube against the constraint of an attached tissue, the dorsal mesentery, which is elastically stretched by the elongating tube to nearly triple its length. This elastic energy storage allows the mesentery to provide stable compressive forces that ultimately buckle the tube into loops. Beginning with a transcriptomic analysis of the mesentery, we identified widespread upregulation of extracellular matrix related genes during looping, including genes related to elastic fiber deposition. Combining molecular and mechanical analyses, we conclude that elastin confers tensile stiffness to the mesentery, enabling its mechanical role in organizing the developing small intestine. These results shed light on the role of elastin as a driver of morphogenesis that extends beyond its more established role in resisting cyclic deformation in adult tissues.

Cell-extracellular matrix mechanotransduction in 3D

Mechanical properties of extracellular matrices (ECMs) regulate essential cell behaviours, including differentiation, migration and proliferation, through mechanotransduction. Studies of cell-ECM mechanotransduction have largely focused on cells cultured in 2D, on top of elastic substrates with a range of stiffnesses. However, cells often interact with ECMs in vivo in a 3D context, and cell-ECM interactions and mechanisms of mechanotransduction in 3D can differ from those in 2D. The ECM exhibits various structural features as well as complex mechanical properties. In 3D, mechanical confinement by the surrounding ECM restricts changes in cell volume and cell shape but allows cells to generate force on the matrix by extending protrusions and regulating cell volume as well as through actomyosin-based contractility. Furthermore, cell-matrix interactions are dynamic owing to matrix remodelling. Accordingly, ECM stiffness, viscoelasticity and degradability often play a critical role in regulating cell behaviours in 3D. Mechanisms of 3D mechanotransduction include traditional integrin-mediated pathways that sense mechanical properties and more recently described mechanosensitive ion channel-mediated pathways that sense 3D confinement, with both converging on the nucleus for downstream control of transcription and phenotype. Mechanotransduction is involved in tissues from development to cancer and is being increasingly harnessed towards mechanotherapy. Here we discuss recent progress in our understanding of cell-ECM mechanotransduction in 3D.

Tissue flows are tuned by actomyosin-dependent mechanics in developing embryos

Rapid epithelial tissue flows are essential to building and shaping developing embryos. However, the mechanical properties of embryonic epithelial tissues and the factors that control these properties are not well understood. Actomyosin generates contractile tensions and contributes to the mechanical properties of cells and cytoskeletal networks in vitro, but it remains unclear how the levels and patterns of actomyosin activity contribute to embryonic epithelial tissue mechanics in vivo. To dissect the roles of cell-generated tensions in the mechanics of flowing epithelial tissues, we use optogenetic tools to manipulate actomyosin contractility with spatiotemporal precision in the Drosophila germband epithelium, which rapidly flows during body axis elongation. We find that manipulating actomyosin-dependent tensions by either optogenetic activation or deactivation of actomyosin alters the solid-fluid mechanical properties of the germband epithelium, leading to changes in cell rearrangements and tissue-level flows. Optogenetically activating actomyosin leads to increases in the overall level but decreases in the anisotropy of tension in the tissue, whereas optogenetically deactivating actomyosin leads to decreases in both the level and anisotropy of tension compared to in wild-type embryos. We find that optogenetically activating actomyosin results in more solid-like (less fluid-like) tissue properties, which is associated with reduced cell rearrangements and tissue flow compared to in wild-type embryos. Optogenetically deactivating actomyosin also results in more solid-like properties than in wild-type embryos but less solid-like properties compared to optogenetically activating actomyosin. Together, these findings indicate that increasing the overall tension level is associated with more solid-like properties in tissues that are relatively isotropic, whereas high tension anisotropy fluidizes the tissue. Our results reveal that epithelial tissue flows in developing embryos involve the coordinated actomyosin-dependent regulation of the mechanical properties of tissues and the tensions driving them to flow in order to achieve rapid tissue remodeling.

In situ sensing physiological properties of biological tissues using wireless miniature soft robots

Implanted electronic sensors, compared with conventional medical imaging, allow monitoring of advanced physiological properties of soft biological tissues continuously, such as adhesion, pH, viscoelasticity, and biomarkers for disease diagnosis. However, they are typically invasive, requiring being deployed by surgery, and frequently cause inflammation. Here we propose a minimally invasive method of using wireless miniature soft robots to in situ sense the physiological properties of tissues. By controlling robot-tissue interaction using external magnetic fields, visualized by medical imaging, we can recover tissue properties precisely from the robot shape and magnetic fields. We demonstrate that the robot can traverse tissues with multimodal locomotion and sense the adhesion, pH, and viscoelasticity on porcine and mice gastrointestinal tissues ex vivo, tracked by x-ray or ultrasound imaging. With the unprecedented capability of sensing tissue physiological properties with minimal invasion and high resolution deep inside our body, this technology can potentially enable critical applications in both basic research and clinical practice.

Magnetic actuation of otoliths allows behavioral and brain-wide neuronal exploration of vestibulo-motor processing in larval zebrafish

The vestibular system in the inner ear plays a central role in sensorimotor control by informing the brain about the orientation and acceleration of the head. However, most experiments in neurophysiology are performed using head-fixed configurations, depriving animals of vestibular inputs. To overcome this limitation, we decorated the utricular otolith of the vestibular system in larval zebrafish with paramagnetic nanoparticles. This procedure effectively endowed the animal with magneto-sensitive capacities: applied magnetic field gradients induced forces on the otoliths, resulting in robust behavioral responses comparable to those evoked by rotating the animal by up to 25°. We recorded the whole-brain neuronal response to this fictive motion stimulation using light-sheet functional imaging. Experiments performed in unilaterally injected fish revealed the activation of a commissural inhibition between the brain hemispheres. This magnetic-based stimulation technique for larval zebrafish opens new perspectives to functionally dissect the neural circuits underlying vestibular processing and to develop multisensory virtual environments, including vestibular feedback.

Engineering tools for quantifying and manipulating forces in epithelia

The integrity of epithelia is maintained within dynamic mechanical environments during tissue development and homeostasis. Understanding how epithelial cells mechanosignal and respond collectively or individually is critical to providing insight into developmental and (patho)physiological processes. Yet, inferring or mimicking mechanical forces and downstream mechanical signaling as they occur in epithelia presents unique challenges. A variety of in vitro approaches have been used to dissect the role of mechanics in regulating epithelia organization. Here, we review approaches and results from research into how epithelial cells communicate through mechanical cues to maintain tissue organization and integrity. We summarize the unique advantages and disadvantages of various reduced-order model systems to guide researchers in choosing appropriate experimental systems. These model systems include 3D, 2D, and 1D micromanipulation methods, single cell studies, and noninvasive force inference and measurement techniques. We also highlight a number of in silico biophysical models that are informed by in vitro and in vivo observations. Together, a combination of theoretical and experimental models will aid future experiment designs and provide predictive insight into mechanically driven behaviors of epithelial dynamics.

Biomechanical models and mechanisms of cellular morphogenesis and cerebral cortical expansion and folding

Morphogenesis of the nervous system involves a highly complex spatio-temporal pattern of physical forces (mainly tension and pressure) acting on cells and tissues that are pliable but have an intricately organized cytoskeletal infrastructure. This review begins by covering basic principles of biomechanics and the core cytoskeletal toolkit used to regulate the shapes of cells and tissues during embryogenesis and neural development. It illustrates how the principle of 'tensegrity' provides a useful conceptual framework for understanding how cells dynamically respond to forces that are generated internally or applied externally. The latter part of the review builds on this foundation in considering the development of mammalian cerebral cortex. The main focus is on cortical expansion and folding - processes that take place over an extended period of prenatal and postnatal development. Cortical expansion and folding are likely to involve many complementary mechanisms, some related to regulating cell proliferation and migration and others related to specific types and patterns of mechanical tension and pressure. Three distinct multi-mechanism models are evaluated in relation to a set of 18 key experimental observations and findings. The Composite Tension Plus (CT+) model is introduced as an updated version of a previous multi-component Differential Expansion Sandwich Plus (DES+) model (Van Essen, 2020); the new CT+ model includes 10 distinct mechanisms and has the greatest explanatory power among published models to date. Much needs to be done in order to validate specific mechanistic components and to assess their relative importance in different species, and important directions for future research are suggested.

The Role of Posterior Neural Plate-Derived Presomitic Mesoderm (PSM) in Trunk and Tail Muscle Formation and Axis Elongation

Elongation of the posterior body axis is distinct from that of the anterior trunk and head. Early drivers of posterior elongation are the neural plate/tube and notochord, later followed by the presomitic mesoderm (PSM), together with the neural tube and notochord. In axolotl, posterior neural plate-derived PSM is pushed posteriorly by convergence and extension of the neural plate. The PSM does not go through the blastopore but turns anteriorly to join the gastrulated paraxial mesoderm. To gain a deeper understanding of the process of axial elongation, a detailed characterization of PSM morphogenesis, which precedes somite formation, and of other tissues (such as the epidermis, lateral plate mesoderm and endoderm) is needed. We investigated these issues with specific tissue labelling techniques (DiI injections and GFP⁺ tissue grafting) in combination with optical tissue clearing and 3D reconstructions. We defined a spatiotemporal order of PSM morphogenesis that is characterized by changes in collective cell behaviour. The PSM forms a cohesive tissue strand and largely retains this cohesiveness even after epidermis removal. We show that during embryogenesis, the PSM, as well as the lateral plate and endoderm move anteriorly, while the net movement of the axis is posterior.

Mechanobiology of cancer cell responsiveness to chemotherapy and immunotherapy: Mechanistic insights and biomaterial platforms

Mechanical forces are central to how cancer treatments such as chemotherapeutics and immunotherapies interact with cells and tissues. At the simplest level, electrostatic forces underlie the binding events that are critical to therapeutic function. However, a growing body of literature points to mechanical factors that also affect whether a drug or an immune cell can reach a target, and to interactions between a cell and its environment affecting therapeutic efficacy. These factors affect cell processes ranging from cytoskeletal and extracellular matrix remodeling to transduction of signals by the nucleus to metastasis of cells. This review presents and critiques the state of the art of our understanding of how mechanobiology impacts drug and immunotherapy resistance and responsiveness, and of the in vitro systems that have been of value in the discovery of these effects.

Direct force measurement and loading on developing tissues in intact avian embryos

Developmental morphogenesis is driven by tissue stresses acting on tissue rheology. Direct measurements of forces in small tissues (100 µm-1 mm) in situ, such as in early embryos, require high spatial precision and minimal invasiveness. Here, we introduce a control-based approach, tissue force microscopy (TiFM), that integrates a mechanical cantilever probe and live imaging with closed-loop feedback control of mechanical loading in early chicken embryos. By testing previously qualitatively characterized force-producing tissues in the elongating body axis, we show that TiFM quantitatively captures stress dynamics with high sensitivity. TiFM also provides the means to apply stable, minimally invasive and physiologically relevant loads to drive tissue deformation and to follow the resulting morphogenetic progression associated with large-scale cell movements. Together, TiFM allows us to control tissue force measurement and manipulation in small developing embryos, and promises to contribute to the quantitative understanding of complex multi-tissue mechanics during development.

Delayed Hopf bifurcation and control of a ferrofluid interface via a time-dependent magnetic field

A ferrofluid droplet confined in a Hele-Shaw cell can be deformed into a stably spinning "gear," using crossed magnetic fields. Previously, fully nonlinear simulation revealed that the spinning gear emerges as a stable traveling wave along the droplet's interface bifurcates from the trivial (equilibrium) shape. In this work, a center manifold reduction is applied to show the geometrical equivalence between a two-harmonic-mode coupled system of ordinary differential equations arising from a weakly nonlinear analysis of the interface shape and a Hopf bifurcation. The rotating complex amplitude of the fundamental mode saturates to a limit cycle as the periodic traveling wave solution is obtained. An amplitude equation is derived from a multiple-time-scale expansion as a reduced model of the dynamics. Then, inspired by the well-known delay behavior of time-dependent Hopf bifurcations, we design a slowly time-varying magnetic field such that the timing and emergence of the interfacial traveling wave can be controlled. The proposed theory allows us to determine the time-dependent saturated state resulting from the dynamic bifurcation and delayed onset of instability. The amplitude equation also reveals hysteresislike behavior upon time reversal of the magnetic field. The state obtained upon time reversal differs from the state obtained during the initial (forward-time) period, yet it can still be predicted by the proposed reduced-order theory.

Morphogenesis-inspired two-dimensional electrowetting in droplet networks

Living tissues dynamically reshape their internal cellular structures through carefully regulated cell-to-cell interactions during morphogenesis. These cellular rearrangement events, such as cell sorting and mutual tissue spreading, have been explained using the differential adhesion hypothesis, which describes the sorting of cells through their adhesive interactions with their neighbors. In this manuscript we explore a simplified form of differential adhesion within a bioinspired lipid-stabilized emulsion approximating cellular tissues. The artificial cellular tissues are created as a collection of aqueous droplets adhered together in a network of lipid membranes. Since this abstraction of the tissue does not retain the ability to locally vary the adhesion of the interfaces through biological mechanisms, instead we employ electrowetting with offsets generated by spatial variations in lipid compositions to capture a simple form of bioelectric control over the tissue characteristics. This is accomplished by first conducting experiments on electrowetting in droplet networks, next creating a model for describing electrowetting in collections of adhered droplets, then validating the model against the experimental measurements. This work demonstrates how the distribution of voltage within a droplet network may be tuned through lipid composition then used to shape directional contraction of the adhered structure using two-dimensional electrowetting events. Predictions from this model were used to explore the governing mechanics for complex electrowetting events in networks, including directional contraction and the formation of new interfaces.

Quantifying stiffness and forces of tumor colonies and embryos using a magnetic microrobot

Stiffness and forces are two fundamental quantities essential to living cells and tissues. However, it has been a challenge to quantify both 3D traction forces and stiffness (or modulus) using the same probe in vivo. Here, we describe an approach that overcomes this challenge by creating a magnetic microrobot probe with controllable functionality. Biocompatible ferromagnetic cobalt-platinum microcrosses were fabricated, and each microcross (about 30 micrometers) was trapped inside an arginine-glycine-apartic acid-conjugated stiff poly(ethylene glycol) (PEG) round microgel (about 50 micrometers) using a microfluidic device. The stiff magnetic microrobot was seeded inside a cell colony and acted as a stiffness probe by rigidly rotating in response to an oscillatory magnetic field. Then, brief episodes of ultraviolet light exposure were applied to dynamically photodegrade and soften the fluorescent nanoparticle-embedded PEG microgel, whose deformation and 3D traction forces were quantified. Using the microrobot probe, we show that malignant tumor-repopulating cell colonies altered their modulus but not traction forces in response to different 3D substrate elasticities. Stiffness and 3D traction forces were measured, and both normal and shear traction force oscillations were observed in zebrafish embryos from blastula to gastrula. Mouse embryos generated larger tensile and compressive traction force oscillations than shear traction force oscillations during blastocyst. The microrobot probe with controllable functionality via magnetic fields could potentially be useful for studying the mechanoregulation of cells, tissues, and embryos.

Extracting, quantifying, and comparing dynamical and biomechanical properties of living matter through single particle tracking

A panoply of new tools for tracking single particles and molecules has led to an explosion of experimental data, leading to novel insights into physical properties of living matter governing cellular development and function, health and disease. In this Perspective, we present tools to investigate the dynamics and mechanics of living systems from the molecular to cellular scale via single-particle techniques. In particular, we focus on methods to measure, interpret, and analyse complex data sets that are associated with forces, materials properties, transport, and emergent organisation phenomena within biological and soft-matter systems. Current approaches, challenges, and existing solutions in the associated fields are outlined in order to support the growing community of researchers at the interface of physics and the life sciences. Each section focuses not only on the general physical principles and the potential for understanding living matter, but also on details of practical data extraction and analysis, discussing limitations, interpretation, and comparison across different experimental realisations and theoretical frameworks. Particularly relevant results are introduced as examples. While this Perspective describes living matter from a physical perspective, highlighting experimental and theoretical physics techniques relevant for such systems, it is also meant to serve as a solid starting point for researchers in the life sciences interested in the implementation of biophysical methods.