Rigidity percolation uncovers a structural basis for embryonic tissue phase transitions.

Embryo morphogenesis is impacted by dynamic changes in tissue material properties, which have been proposed to occur via processes akin to phase transitions (PTs). Here, we show that rigidity percolation provides a simple and robust theoretical framework to predict material/structural PTs of embryonic tissues from local cell connectivity. By using percolation theory, combined with directly monitoring dynamic changes in tissue rheology and cell contact mechanics, we demonstrate that the zebrafish blastoderm undergoes a genuine rigidity PT, brought about by a small reduction in adhesion-dependent cell connectivity below a critical value. We quantitatively predict and experimentally verify hallmarks of PTs, including power-law exponents and associated discontinuities of macroscopic observables. Finally, we show that this uniform PT depends on blastoderm cells undergoing meta-synchronous divisions causing random and, consequently, uniform changes in cell connectivity. Collectively, our theoretical and experimental findings reveal the structural basis of material PTs in an organismal context.

Not Going with the Flow: How Cells Adapt Internal Physics.

Defining the principles underlying the organization of biomolecules within cells is a key challenge of current cell biology research. Persson et al. now identify a powerful layer of regulation that allows cells to decouple diffusion from temperature by modulating their intracellular viscosity. This so-called viscoadaptation is mediated through trehalose and glycogen activities, which alter diffusion dynamics and self-assembly propensity inside the cell globally.

Cellular Control of Viscosity Counters Changes in Temperature and Energy Availability.

Cellular functioning requires the orchestration of thousands of molecular interactions in time and space. Yet most molecules in a cell move by diffusion, which is sensitive to external factors like temperature. How cells sustain complex, diffusion-based systems across wide temperature ranges is unknown. Here, we uncover a mechanism by which budding yeast modulate viscosity in response to temperature and energy availability. This "viscoadaptation" uses regulated synthesis of glycogen and trehalose to vary the viscosity of the cytosol. Viscoadaptation functions as a stress response and a homeostatic mechanism, allowing cells to maintain invariant diffusion across a 20°C temperature range. Perturbations to viscoadaptation affect solubility and phase separation, suggesting that viscoadaptation may have implications for multiple biophysical processes in the cell. Conditions that lower ATP trigger viscoadaptation, linking energy availability to rate regulation of diffusion-controlled processes. Viscoadaptation reveals viscosity to be a tunable property for regulating diffusion-controlled processes in a changing environment.

Matrix viscoelasticity promotes liver cancer progression in the pre-cirrhotic liver.

Type 2 diabetes mellitus is a major risk factor for hepatocellular carcinoma (HCC). Changes in extracellular matrix (ECM) mechanics contribute to cancer development1,2, and increased stiffness is known to promote HCC progression in cirrhotic conditions3,4. Type 2 diabetes mellitus is characterized by an accumulation of advanced glycation end-products (AGEs) in the ECM; however, how this affects HCC in non-cirrhotic conditions is unclear. Here we find that, in patients and animal models, AGEs promote changes in collagen architecture and enhance ECM viscoelasticity, with greater viscous dissipation and faster stress relaxation, but not changes in stiffness. High AGEs and viscoelasticity combined with oncogenic ß-catenin signalling promote HCC induction, whereas inhibiting AGE production, reconstituting the AGE clearance receptor AGER1 or breaking AGE-mediated collagen cross-links reduces viscoelasticity and HCC growth. Matrix analysis and computational modelling demonstrate that lower interconnectivity of AGE-bundled collagen matrix, marked by shorter fibre length and greater heterogeneity, enhances viscoelasticity. Mechanistically, animal studies and 3D cell cultures show that enhanced viscoelasticity promotes HCC cell proliferation and invasion through an integrin-ß1-tensin-1-YAP mechanotransductive pathway. These results reveal that AGE-mediated structural changes enhance ECM viscoelasticity, and that viscoelasticity can promote cancer progression in vivo, independent of stiffness.

3D trajectories adopted by coding and regulatory DNA elements: first-passage times for genomic interactions.

During B lymphocyte development, immunoglobulin heavy-chain variable (VH), diversity (DH), and joining (JH) segments assemble to generate a diverse antigen receptor repertoire. Here, we have marked the distal VH and DH-JH-Eµ regions with Tet-operator binding sites and traced their 3D trajectories in pro-B cells transduced with a retrovirus encoding Tet-repressor-EGFP. We found that these elements displayed fractional Langevin motion (fLm) due to the viscoelastic hindrance from the surrounding network of proteins and chromatin fibers. Using fractional Langevin dynamics modeling, we found that, with high probability, DHJH elements reach a VH element within minutes. Spatial confinement emerged as the dominant parameter that determined the frequency of such encounters. We propose that the viscoelastic nature of the nuclear environment causes coding elements and regulatory elements to bounce back and forth in a spring-like fashion until specific genomic interactions are established and that spatial confinement of topological domains largely controls first-passage times for genomic interactions.

Extreme dynamics in a biomolecular condensate.

Proteins and nucleic acids can phase-separate in the cell to form concentrated biomolecular condensates1-4. The functions of condensates span many length scales: they modulate interactions and chemical reactions at the molecular scale5, organize biochemical processes at the mesoscale6 and compartmentalize cells4. Understanding the underlying mechanisms of these processes will require detailed knowledge of the rich dynamics across these scales7. The mesoscopic dynamics of biomolecular condensates have been extensively characterized8, but their behaviour at the molecular scale has remained more elusive. Here, as an example of biomolecular phase separation, we study complex coacervates of two highly and oppositely charged disordered human proteins9. Their dense phase is 1,000 times more concentrated than the dilute phase, and the resulting percolated interaction network10 leads to a bulk viscosity 300 times greater than that of water. However, single-molecule spectroscopy optimized for measurements within individual droplets reveals that at the molecular scale, the disordered proteins remain exceedingly dynamic, with their chain configurations interconverting on submicrosecond timescales. Massive all-atom molecular dynamics simulations reproduce the experimental observations and explain this apparent discrepancy: the underlying interactions between individual charged side chains are short-lived and exchange on a pico- to nanosecond timescale. Our results indicate that, despite the high macroscopic viscosity of phase-separated systems, local biomolecular rearrangements required for efficient reactions at the molecular scale can remain rapid.

Extracellular fluid viscosity enhances cell migration and cancer dissemination.

Cells respond to physical stimuli, such as stiffness1, fluid shear stress2 and hydraulic pressure3,4. Extracellular fluid viscosity is a key physical cue that varies under physiological and pathological conditions, such as cancer5. However, its influence on cancer biology and the mechanism by which cells sense and respond to changes in viscosity are unknown. Here we demonstrate that elevated viscosity counterintuitively increases the motility of various cell types on two-dimensional surfaces and in confinement, and increases cell dissemination from three-dimensional tumour spheroids. Increased mechanical loading imposed by elevated viscosity induces an actin-related protein 2/3 (ARP2/3)-complex-dependent dense actin network, which enhances Na+/H+ exchanger 1 (NHE1) polarization through its actin-binding partner ezrin. NHE1 promotes cell swelling and increased membrane tension, which, in turn, activates transient receptor potential cation vanilloid 4 (TRPV4) and mediates calcium influx, leading to increased RHOA-dependent cell contractility. The coordinated action of actin remodelling/dynamics, NHE1-mediated swelling and RHOA-based contractility facilitates enhanced motility at elevated viscosities. Breast cancer cells pre-exposed to elevated viscosity acquire TRPV4-dependent mechanical memory through transcriptional control of the Hippo pathway, leading to increased migration in zebrafish, extravasation in chick embryos and lung colonization in mice. Cumulatively, extracellular viscosity is a physical cue that regulates both short- and long-term cellular processes with pathophysiological relevance to cancer biology.

Stiffness Sensing by Cells.

Physical stimuli are essential for the function of eukaryotic cells, and changes in physical signals are important elements in normal tissue development as well as in disease initiation and progression. The complexity of physical stimuli and the cellular signals they initiate are as complex as those triggered by chemical signals. One of the most important, and the focus of this review, is the effect of substrate mechanical properties on cell structure and function. The past decade has produced a nearly exponentially increasing number of mechanobiological studies to define how substrate stiffness alters cell biology using both purified systems and intact tissues. Here we attempt to identify common features of mechanosensing in different systems while also highlighting the numerous informative exceptions to what in early studies appeared to be simple rules by which cells respond to mechanical stresses.

Differential proliferation regulates multi-tissue morphogenesis during embryonic axial extension: integrating viscous modeling and experimental approaches.

A major challenge in biology is to understand how mechanical interactions and cellular behavior affect the shapes of tissues and embryo morphology. The extension of the neural tube and paraxial mesoderm, which form the spinal cord and musculoskeletal system, respectively, results in the elongated shape of the vertebrate embryonic body. Despite our understanding of how each of these tissues elongates independently of the others, the morphogenetic consequences of their simultaneous growth and mechanical interactions are still unclear. Our study investigates how differential growth, tissue biophysical properties and mechanical interactions affect embryonic morphogenesis during axial extension using a 2D multi-tissue continuum-based mathematical model. Our model captures the dynamics observed in vivo by time-lapse imaging of bird embryos, and reveals the underestimated influence of differential tissue proliferation rates. We confirmed this prediction in quail embryos by showing that decreasing the rate of cell proliferation in the paraxial mesoderm affects long-term tissue dynamics, and shaping of both the paraxial mesoderm and the neighboring neural tube. Overall, our work provides a new theoretical platform upon which to consider the long-term consequences of tissue differential growth and mechanical interactions on morphogenesis.

Size- and position-dependent cytoplasm viscoelasticity through hydrodynamic interactions with the cell surface.

Many studies of cytoplasm rheology have focused on small components in the submicrometer scale. However, the cytoplasm also baths large organelles like nuclei, microtubule asters, or spindles that often take significant portions of cells and move across the cytoplasm to regulate cell division or polarization. Here, we translated passive components of sizes ranging from few up to ~50 percents of the cell diameter, through the vast cytoplasm of live sea urchin eggs, with calibrated magnetic forces. Creep and relaxation responses indicate that for objects larger than the micron size, the cytoplasm behaves as a Jeffreys material, viscoelastic at short timescales, and fluidizing at longer times. However, as component size approached that of cells, cytoplasm viscoelastic resistance increased in a nonmonotonic manner. Flow analysis and simulations suggest that this size-dependent viscoelasticity emerges from hydrodynamic interactions between the moving object and the static cell surface. This effect also yields to position-dependent viscoelasticity with objects initially closer to the cell surface being harder to displace. These findings suggest that the cytoplasm hydrodynamically couples large organelles to the cell surface to restrain their motion, with important implications for cell shape sensing and cellular organization.

Multicurvature viscous streaming: Flow topology and particle manipulation.

Viscous streaming refers to the rectified, steady flows that emerge when a liquid oscillates around an immersed microfeature. Relevant to microfluidics, the resulting local, strong inertial effects allow manipulation of fluid and particles effectively, within short time scales and compact footprints. Nonetheless, practically, viscous streaming has been stymied by a narrow set of achievable flow topologies, limiting scope and application. Here, by moving away from classically employed microfeatures of uniform curvature, we experimentally show how multicurvature designs, computationally obtained, give rise, instead, to rich flow repertoires. The potential utility of these flows is then illustrated in compact, robust, and tunable devices for enhanced manipulation, filtering, and separation of both synthetic and biological particles. Overall, our mixed computational/experimental approach expands the scope of viscous streaming application, with opportunities in manufacturing, environment, health, and medicine, from particle self-assembly to microplastics removal.

Magnetohydrodynamic levitation for high-performance flexible pumps.

We use magnetohydrodynamic levitation as a means to create a soft, elastomeric, solenoid-driven pump (ESP). We present a theoretical framework and fabrication of a pump designed to address the unique challenges of soft robotics, maintaining pumping performance under deformation. Using a permanent magnet as a piston and ferrofluid as a liquid seal, we model and construct a deformable displacement pump. The magnet is driven back and forth along the length of a flexible core tube by a series of solenoids made of thin conductive wire. The magnet piston is kept concentric within the tube by Maxwell stresses within the ferrofluid and magnetohydrodynamic levitation, as viscous lift pressure is created due to its forward velocity. The centering of the magnet reduces shear stresses during pumping and improves efficiency. We provide a predictive model and capture the transient nonlinear dynamics of the magnet during operation, leading to a parametric performance curve characterizing the ESP, enabling goal-driven design. In our experimental validation, we report a shut-off pressure of 2 to 8 kPa and run-out flow rate of 50 to 320 mL⋅min-1, while subject to deformation of its own length scale, drawing a total of 0.17 W. This performance leads to the highest reported duty point (i.e., pressure and flow rate provided under load) for a pump that operates under deformation of its own length scale. We then integrate the pump into an elastomeric chassis and squeeze it through a tortuous pathway while providing continuous fluid pressure and flow rate; the vehicle then emerges at the other end and propels itself swimming.

Geometric trade-off between contractile force and viscous drag determines the actomyosin-based motility of a cell-sized droplet.

Cell migration in confined environments is fundamental for diverse biological processes from cancer invasion to leukocyte trafficking. The cell body is propelled by the contractile force of actomyosin networks transmitted from the cell membrane to the external substrates. However, physical determinants of actomyosin-based migration capacity in confined environments are not fully understood. Here, we develop an in vitro migratory cell model, where cytoplasmic actomyosin networks are encapsulated into droplets surrounded by a lipid monolayer membrane. We find that the droplet can move when the actomyosin networks are bound to the membrane, in which the physical interaction between the contracting actomyosin networks and the membrane generates a propulsive force. The droplet moves faster when it has a larger contact area with the substrates, while narrower confinement reduces the migration speed. By combining experimental observations and active gel theory, we propose a mechanism where the balance between sliding friction force, which is a reaction force of the contractile force, and viscous drag determines the migration speed, providing a physical basis of actomyosin-based motility in confined environments.

Contribution of cytoplasm viscoelastic properties to mitotic spindle positioning.

Cells are filled with macromolecules and polymer networks that set scale-dependent viscous and elastic properties to the cytoplasm. Although the role of these parameters in molecular diffusion, reaction kinetics, and cellular biochemistry is being increasingly recognized, their contributions to the motion and positioning of larger organelles, such as mitotic spindles for cell division, remain unknown. Here, using magnetic tweezers to displace and rotate mitotic spindles in living embryos, we uncovered that the cytoplasm can impart viscoelastic reactive forces that move spindles, or passive objects with similar size, back to their original positions. These forces are independent of cytoskeletal force generators yet reach hundreds of piconewtons and scale with cytoplasm crowding. Spindle motion shears and fluidizes the cytoplasm, dissipating elastic energy and limiting spindle recoils with functional implications for asymmetric and oriented divisions. These findings suggest that bulk cytoplasm material properties may constitute important control elements for the regulation of division positioning and cellular organization.

Aggregated eosinophils and neutrophils characterize the properties of mucus in chronic rhinosinusitis.

BACKGROUND: Airway obstruction caused by viscous mucus is an important pathophysiologic characteristic of persistent inflammation, which can result in organ damage. OBJECTIVE: We investigated the hypothesis that the biophysical characteristics of accumulating granulocytes affect the clinical properties of mucus. METHODS: Surgically acquired nasal mucus samples from patients with eosinophilic chronic rhinosinusitis and neutrophil-dominant, noneosinophilic chronic rhinosinusitis were evaluated in terms of computed tomography density, viscosity, water content, wettability, and protein composition. Isolated human eosinophils and neutrophils were stimulated to induce the formation of extracellular traps, followed by the formation of aggregates. The biophysical properties of the aggregated cells were also examined. RESULTS: Mucus from patients with eosinophilic chronic rhinosinusitis had significantly higher computed tomography density, viscosity, dry weight, and hydrophobicity compared to mucus from patients with noneosinophilic chronic rhinosinusitis. The levels of eosinophil-specific proteins in mucus correlated with its physical properties. Eosinophil and neutrophil aggregates showed physical and pathologic characteristics resembling those of mucus. Cotreatment with deoxyribonuclease and heparin, which slenderizes the structure of eosinophil extracellular traps, efficiently induced reductions in the viscosity and hydrophobicity of both eosinophil aggregates and eosinophilic mucus. CONCLUSIONS: The present study elucidated the pathogenesis of mucus stasis in infiltrated granulocyte aggregates from a novel perspective. These findings may contribute to the development of treatment strategies for eosinophilic airway diseases.

Mechanical characterization of regenerating Hydra tissue spheres.

Hydra vulgaris, long known for its remarkable regenerative capabilities, is also a long-standing source of inspiration for models of spontaneous patterning. Recently it became clear that early patterning during Hydra regeneration is an integrated mechanochemical process whereby morphogen dynamics is influenced by tissue mechanics. One roadblock to understanding Hydra self-organization is our lack of knowledge about the mechanical properties of these organisms. In this study, we combined microfluidic developments to perform parallelized microaspiration rheological experiments and numerical simulations to characterize these mechanical properties. We found three different behaviors depending on the applied stresses: an elastic response, a viscoelastic response, and tissue rupture. Using models of deformable shells, we quantify their Young's modulus, shear viscosity, and the critical stresses required to switch between behaviors. Based on these experimental results, we propose a description of the tissue mechanics during normal regeneration. Our results provide a first step toward the development of original mechanochemical models of patterning grounded in quantitative experimental data.

Viscoelastic phenotyping of red blood cells.

Red blood cells (RBCs) are the simplest cell types with complex dynamical and viscoelastic phenomenology. While the mechanical rigidity and the flickering noise of RBCs have been extensively investigated, an accurate determination of the constitutive equations of the relaxational kinetics is lacking. Here we measure the force relaxation of RBCs under different types of tensional and compressive extension-jump protocols by attaching an optically trapped bead to the RBC membrane. Relaxational kinetics follows linear response from 60 pN (tensional) to -20 pN (compressive) applied forces, exhibiting a triple exponential function with three well-separated timescales over four decades (0.01-100 s). While the fast timescale (τF∼0.02(1)s) corresponds to the relaxation of the membrane, the intermediate and slow timescales (τI=4(1)s; τS=70(8)s) likely arise from the cortex dynamics and the cytosol viscosity. Relaxation is highly heterogeneous across the RBC population, yet the three relaxation times are correlated, showing dynamical scaling. Finally, we find that glucose depletion and laser illumination of RBCs lead to faster triple exponential kinetics and RBC rigidification. Viscoelastic phenotyping is a promising dynamical biomarker applicable to other cell types and active systems.

Beyond stiffness: Multiscale viscoelastic features as biomechanical markers for assessing cell types and states.

Cell mechanics are pivotal in regulating cellular activities, diseases progression, and cancer development. However, the understanding of how cellular viscoelastic properties vary in physiological and pathological stimuli remains scarce. Here, we develop a hybrid self-similar hierarchical theory-microrheology approach to accurately and efficiently characterize cellular viscoelasticity. Focusing on two key cell types associated with livers fibrosis-the capillarized liver sinusoidal endothelial cells and activated hepatic stellate cells-we uncover a universal two-stage power-law rheology characterized by two distinct exponents, αshort and αlong. The mechanical profiles derived from both exponents exhibit significant potential for discriminating among diverse cells. This finding suggests a potential common dynamic creep characteristic across biological systems, extending our earlier observations in soft tissues. Using a tailored hierarchical model for cellular mechanical structures, we discern significant variations in the viscoelastic properties and their distribution profiles across different cell types and states from the cytoplasm (elastic stiffness E1 and viscosity η), to a single cytoskeleton fiber (elastic stiffness E2), and then to the cell level (transverse expansion stiffness E3). Importantly, we construct a logistic-regression-based machine-learning model using the dynamic parameters that outperforms conventional cell-stiffness-based classifiers in assessing cell states, achieving an area under the curve of 97% vs. 78%. Our findings not only advance a robust framework for monitoring intricate cell dynamics but also highlight the crucial role of cellular viscoelasticity in discerning cell states across a spectrum of liver diseases and prognosis, offering new avenues for developing diagnostic and therapeutic strategies based on cellular viscoelasticity.

Single-cell mechanical assay unveils viscoelastic similarities in normal and neoplastic brain cells.

Understanding cancer cell mechanics allows for the identification of novel disease mechanisms, diagnostic biomarkers, and targeted therapies. In this study, we utilized our previously established fluid shear stress assay to investigate and compare the viscoelastic properties of normal immortalized human astrocytes and invasive human glioblastoma (GBM) cells when subjected to physiological levels of shear stress that are present in the brain microenvironment. We used a parallel-flow microfluidic shear system and a camera-coupled optical microscope to expose single cells to fluid shear stress and monitor the resulting deformation in real time, respectively. From the video-rate imaging, we fed cell deformation information from digital image correlation into a three-parameter generalized Maxwell model to quantify the nuclear and cytoplasmic viscoelastic properties of single cells. We further quantified actin cytoskeleton density and alignment in immortalized human astrocytes and GBM cells via fluorescence microscopy and image analysis techniques. Results from our study show that contrary to the behavior of many extracranial cells, normal and cancerous brain cells do not exhibit significant differences in their viscoelastic properties. Moreover, we also found that the viscoelastic properties of the nucleus and cytoplasm as well as the actin cytoskeletal densities of both brain cell types are similar. Our work suggests that malignant GBM cells exhibit unique mechanical behaviors not seen in other cancer cell types. These results warrant future studies to elucidate the distinct biophysical characteristics of the brain and reveal novel mechanical attributes of GBM and other primary brain tumors.