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.

Mechanochemical Feedback Loops in Development and Disease.

There is increasing evidence that both mechanical and biochemical signals play important roles in development and disease. The development of complex organisms, in particular, has been proposed to rely on the feedback between mechanical and biochemical patterning events. This feedback occurs at the molecular level via mechanosensation but can also arise as an emergent property of the system at the cellular and tissue level. In recent years, dynamic changes in tissue geometry, flow, rheology, and cell fate specification have emerged as key platforms of mechanochemical feedback loops in multiple processes. Here, we review recent experimental and theoretical advances in understanding how these feedbacks function in development and disease.

mTORC1 Controls Phase Separation and the Biophysical Properties of the Cytoplasm by Tuning Crowding.

Macromolecular crowding has a profound impact on reaction rates and the physical properties of the cell interior, but the mechanisms that regulate crowding are poorly understood. We developed genetically encoded multimeric nanoparticles (GEMs) to dissect these mechanisms. GEMs are homomultimeric scaffolds fused to a fluorescent protein that self-assemble into bright, stable particles of defined size and shape. By combining tracking of GEMs with genetic and pharmacological approaches, we discovered that the mTORC1 pathway can modulate the effective diffusion coefficient of particles ≥20 nm in diameter more than 2-fold by tuning ribosome concentration, without any discernable effect on the motion of molecules ≤5 nm. This change in ribosome concentration affected phase separation both in vitro and in vivo. Together, these results establish a role for mTORC1 in controlling both the mesoscale biophysical properties of the cytoplasm and biomolecular condensation.

Mucins and Their Role in Shaping the Functions of Mucus Barriers.

We review what is currently understood about how the structure of the primary solid component of mucus, the glycoprotein mucin, gives rise to the mechanical and biochemical properties of mucus that are required for it to perform its diverse physiological roles. Macroscale processes such as lubrication require mucus of a certain stiffness and spinnability, which are set by structural features of the mucin network, including the identity and density of cross-links and the degree of glycosylation. At the microscale, these same features affect the mechanical environment experienced by small particles and play a crucial role in establishing an interaction-based filter. Finally, mucin glycans are critical for regulating microbial interactions, serving as receptor binding sites for adhesion, as nutrient sources, and as environmental signals. We conclude by discussing how these structural principles can be used in the design of synthetic mucin-mimetic materials and provide suggestions for directions of future work in this field.

Hemodynamic Control of Endothelial Cell Fates in Development.

Biomechanical forces are emerging as critical regulators of embryogenesis, particularly in the developing cardiovascular system. From the onset of blood flow, the embryonic vasculature is continuously exposed to a variety of hemodynamic forces. These biomechanical stimuli are key determinants of vascular cell specification and remodeling and the establishment of vascular homeostasis. In recent years, major advances have been made in our understanding of mechano-activated signaling networks that control both spatiotemporal and structural aspects of vascular development. It has become apparent that a major site for mechanotransduction is situated at the interface of blood and the vessel wall and that this process is controlled by the vascular endothelium. In this review, we discuss the hemodynamic control of endothelial cell fates, focusing on arterial-venous specification, lymphatic development, and the endothelial-to-hematopoietic transition, and present some recent insights into the mechano-activated pathways driving these cell fate decisions in the developing embryo.

Topography of mountain belts controlled by rheology and surface processes.

It is widely recognized that collisional mountain belt topography is generated by crustal thickening and lowered by river bedrock erosion, linking climate and tectonics1-4. However, whether surface processes or lithospheric strength control mountain belt height, shape and longevity remains uncertain. Additionally, how to reconcile high erosion rates in some active orogens with long-term survival of mountain belts for hundreds of millions of years remains enigmatic. Here we investigate mountain belt growth and decay using a new coupled surface process5,6 and mantle-scale tectonic model7. End-member models and the new non-dimensional Beaumont number, Bm, quantify how surface processes and tectonics control the topographic evolution of mountain belts, and enable the definition of three end-member types of growing orogens: type 1, non-steady state, strength controlled (Bm > 0.5); type 2, flux steady state8, strength controlled (Bm ≈ 0.4-0.5); and type 3, flux steady state, erosion controlled (Bm < 0.4). Our results indicate that tectonics dominate in Himalaya-Tibet and the Central Andes (both type 1), efficient surface processes balance high convergence rates in Taiwan (probably type 2) and surface processes dominate in the Southern Alps of New Zealand (type 3). Orogenic decay is determined by erosional efficiency and can be subdivided into two phases with variable isostatic rebound characteristics and associated timescales. The results presented here provide a unified framework explaining how surface processes and lithospheric strength control the height, shape, and longevity of mountain belts.

Parenchymal border macrophages regulate the flow dynamics of the cerebrospinal fluid.

Macrophages are important players in the maintenance of tissue homeostasis1. Perivascular and leptomeningeal macrophages reside near the central nervous system (CNS) parenchyma2, and their role in CNS physiology has not been sufficiently well studied. Given their continuous interaction with the cerebrospinal fluid (CSF) and strategic positioning, we refer to these cells collectively as parenchymal border macrophages (PBMs). Here we demonstrate that PBMs regulate CSF flow dynamics. We identify a subpopulation of PBMs that express high levels of CD163 and LYVE1 (scavenger receptor proteins), closely associated with the brain arterial tree, and show that LYVE1+ PBMs regulate arterial motion that drives CSF flow. Pharmacological or genetic depletion of PBMs led to accumulation of extracellular matrix proteins, obstructing CSF access to perivascular spaces and impairing CNS perfusion and clearance. Ageing-associated alterations in PBMs and impairment of CSF dynamics were restored after intracisternal injection of macrophage colony-stimulating factor. Single-nucleus RNA sequencing data obtained from patients with Alzheimer's disease (AD) and from non-AD individuals point to changes in phagocytosis, endocytosis and interferon-γ signalling on PBMs, pathways that are corroborated in a mouse model of AD. Collectively, our results identify PBMs as new cellular regulators of CSF flow dynamics, which could be targeted pharmacologically to alleviate brain clearance deficits associated with ageing and AD.

Extreme flow simulations reveal skeletal adaptations of deep-sea sponges.

Since its discovery1,2, the deep-sea glass sponge Euplectella aspergillum has attracted interest in its mechanical properties and beauty. Its skeletal system is composed of amorphous hydrated silica and is arranged in a highly regular and hierarchical cylindrical lattice that begets exceptional flexibility and resilience to damage3-6. Structural analyses dominate the literature, but hydrodynamic fields that surround and penetrate the sponge have remained largely unexplored. Here we address an unanswered question: whether, besides improving its mechanical properties, the skeletal motifs of E. aspergillum underlie the optimization of the flow physics within and beyond its body cavity. We use extreme flow simulations based on the 'lattice Boltzmann' method7, featuring over fifty billion grid points and spanning four spatial decades. These in silico experiments reproduce the hydrodynamic conditions on the deep-sea floor where E. aspergillum lives8-10. Our results indicate that the skeletal motifs reduce the overall hydrodynamic stress and support coherent internal recirculation patterns at low flow velocity. These patterns are arguably beneficial to the organism for selective filter feeding and sexual reproduction11,12. The present study reveals mechanisms of extraordinary adaptation to live in the abyss, paving the way towards further studies of this type at the intersection between fluid mechanics, organism biology and functional ecology.

Viscoelastic control of spatiotemporal order in bacterial active matter.

Active matter consists of units that generate mechanical work by consuming energy1. Examples include living systems (such as assemblies of bacteria2-5 and biological tissues6,7), biopolymers driven by molecular motors8-11 and suspensions of synthetic self-propelled particles12-14. A central goal is to understand and control the self-organization of active assemblies in space and time. Most active systems exhibit either spatial order mediated by interactions that coordinate the spatial structure and the motion of active agents12,14,15 or the temporal synchronization of individual oscillatory dynamics2. The simultaneous control of spatial and temporal organization is more challenging and generally requires complex interactions, such as reaction-diffusion hierarchies16 or genetically engineered cellular circuits2. Here we report a simple technique to simultaneously control the spatial and temporal self-organization of bacterial active matter. We confine dense active suspensions of Escherichia coli cells and manipulate a single macroscopic parameter-namely, the viscoelasticity of the suspending fluid- through the addition of purified genomic DNA. This reveals self-driven spatial and temporal organization in the form of a millimetre-scale rotating vortex with periodically oscillating global chirality of tunable frequency, reminiscent of a torsional pendulum. By combining experiments with an active-matter model, we explain this behaviour in terms of the interplay between active forcing and viscoelastic stress relaxation. Our findings provide insight into the influence of bacterial motile behaviour in complex fluids, which may be of interest in health- and ecology-related research, and demonstrate experimentally that rheological properties can be harnessed to control active-matter flows17,18. We envisage that our millimetre-scale, tunable, self-oscillating bacterial vortex may be coupled to actuation systems to act a 'clock generator' capable of providing timing signals for rhythmic locomotion of soft robots and for programmed microfluidic pumping19, for example, by triggering the action of a shift register in soft-robotic logic devices20.

Mechanistic framework for reduced-order models in soft materials: Application to three-dimensional granular intrusion.

Soft materials often display complex behaviors that transition through apparent solid- and fluid-like regimes. While a growing number of microscale simulation methods exist for these materials, reduced-order models that encapsulate the macroscale physics are often desired to predict how external bodies interact with soft media. Such an approach could provide direct insights in diverse situations from impact and penetration problems to locomotion over natural terrains. This work proposes a systematic program to develop three-dimensional (3D) reduced-order models for soft materials from a fundamental basis using continuum symmetries and rheological principles. In particular, we derive a reduced-order, 3D resistive force theory (3D-RFT), which is capable of accurately and quickly predicting the resistive stress distribution on arbitrary-shaped bodies intruding through granular media. Aided by a continuum description of the granular medium, a comprehensive set of spatial symmetry constraints, and a limited amount of reference data, we develop a self-consistent and accurate 3D-RFT. We verify the model capabilities in a wide range of cases and show that it can be quickly recalibrated to different media and intruder surface types. The premises leading to 3D-RFT anticipate application to other soft materials with strongly hyperlocalized intrusion behavior.

Viscous relaxation as a probe of heat flux and crustal plateau composition on Venus.

It has recently been suggested that deformed crustal plateaus on Venus may be composed of felsic (silica-rich) rocks, possibly supporting the idea of an ancient ocean there. However, these plateaus have a tendency to collapse owing to flow of the viscous lower crust. Felsic minerals, especially water-bearing ones, are much weaker and thus lead to more rapid collapse, than more mafic minerals. We model plateau topographic evolution using a non-Newtonian viscous relaxation code. Despite uncertainties in the likely crustal thickness and surface heat flux, we find that quartz-dominated rheologies relax too rapidly to be plausible plateau-forming material. For plateaus dominated by a dry anorthite rheology, survival is possible only if the background crustal thickness is less than 29 km, unless the heat flux on Venus is less than the radiogenic lower bound of 34 [Formula: see text]. Future spacecraft determinations of plateau crustal thickness and mineralogy will place firmer constraints on Venus's heat flux.

The liquid-to-solid transition of FUS is promoted by the condensate surface.

A wide range of macromolecules can undergo phase separation, forming biomolecular condensates in living cells. These membraneless organelles are typically highly dynamic, formed reversibly, and carry out essential functions in biological systems. Crucially, however, a further liquid-to-solid transition of the condensates can lead to irreversible pathological aggregation and cellular dysfunction associated with the onset and development of neurodegenerative diseases. Despite the importance of this liquid-to-solid transition of proteins, the mechanism by which it is initiated in normally functional condensates is unknown. Here we show, by measuring the changes in structure, dynamics, and mechanics in time and space, that single-component FUS condensates do not uniformly convert to a solid gel, but rather that liquid and gel phases coexist simultaneously within the same condensate, resulting in highly inhomogeneous structures. Furthermore, our results show that this transition originates at the interface between the condensate and the dilute continuous phase, and once initiated, the gelation process propagates toward the center of the condensate. To probe such spatially inhomogeneous rheology during condensate aging, we use a combination of established micropipette aspiration experiments together with two optical techniques, spatial dynamic mapping and reflective confocal dynamic speckle microscopy. These results reveal the importance of the spatiotemporal dimension of the liquid-to-solid transition and highlight the interface of biomolecular condensates as a critical element in driving pathological protein aggregation.

Artificial intelligence velocimetry reveals in vivo flow rates, pressure gradients, and shear stresses in murine perivascular flows.

Quantifying the flow of cerebrospinal fluid (CSF) is crucial for understanding brain waste clearance and nutrient delivery, as well as edema in pathological conditions such as stroke. However, existing in vivo techniques are limited to sparse velocity measurements in pial perivascular spaces (PVSs) or low-resolution measurements from brain-wide imaging. Additionally, volume flow rate, pressure, and shear stress variation in PVSs are essentially impossible to measure in vivo. Here, we show that artificial intelligence velocimetry (AIV) can integrate sparse velocity measurements with physics-informed neural networks to quantify CSF flow in PVSs. With AIV, we infer three-dimensional (3D), high-resolution velocity, pressure, and shear stress. Validation comes from training with 70% of PTV measurements and demonstrating close agreement with the remaining 30%. A sensitivity analysis on the AIV inputs shows that the uncertainty in AIV inferred quantities due to uncertainties in the PVS boundary locations inherent to in vivo imaging is less than 30%, and the uncertainty from the neural net initialization is less than 1%. In PVSs of N = 4 wild-type mice we find mean flow speed 16.33 ± 11.09 µm/s, volume flow rate 2.22 ± 1.983 × 103 µm3/s, axial pressure gradient ( - 2.75 ± 2.01)×10-4 Pa/µm (-2.07 ± 1.51 mmHg/m), and wall shear stress (3.00 ± 1.45)×10-3 Pa (all mean ± SE). Pressure gradients, flow rates, and resistances agree with prior predictions. AIV infers in vivo PVS flows in remarkable detail, which will improve fluid dynamic models and potentially clarify how CSF flow changes with aging, Alzheimer's disease, and small vessel disease.

A microfluidic platform to investigate the role of mechanical constraints on tissue reorganization.

Mechanical constraints have a high impact on development processes, and there is a need for new tools to investigate the role of mechanosensitive pathways in tissue reorganization during development. We present here experiments in which embryonic cell aggregates are aspired through constrictions in microfluidic channels, generating highly heterogeneous flows and large cell deformations that can be imaged using two-photon microscopy. This approach provides a way to measure in situ local viscoelastic properties of 3D tissues and connect them to intracellular and intercellular events, such as cell shape changes and cell rearrangements. These methods could be applied to organoids to investigate and quantify rheological properties of tissues, and to understand how constraints affect development.

Collective intercellular communication through ultra-fast hydrodynamic trigger waves.

The biophysical relationships between sensors and actuators1-5 have been fundamental to the development of complex life forms. Swimming organisms generate abundant flows that persist in aquatic environments6-13, and responding promptly to external stimuli is key to survival14-19. Here we present the discovery of 'hydrodynamic trigger waves' in cellular communities of the protist Spirostomum ambiguum that propagate-in a manner similar to a chain reaction20-22-hundreds of times faster than their swimming speed. By coiling its cytoskeleton, Spirostomum can contract its long body by 60% within milliseconds23, experiencing accelerations that can reach forces of 14g. We show that a single cellular contraction (the transmitter) generates long-ranged vortex flows at intermediate Reynolds numbers that can, in turn, trigger neighbouring cells (the receivers). To measure the sensitivity to hydrodynamic signals in these receiver cells, we present a high-throughput suction-flow device for probing mechanosensitive ion channels24 by back-calculating the microscopic forces on the cell membrane. We analyse and quantitatively model the ultra-fast hydrodynamic trigger waves in a universal framework of antenna and percolation theory25,26, and reveal a phase transition that requires a critical colony density to sustain collective communication. Our results suggest that this signalling could help to organize cohabiting communities over large distances and influence long-term behaviour through gene expression (comparable to quorum sensing16). In more immediate terms, because contractions release toxins27, synchronized discharges could facilitate the repulsion of large predators or immobilize large prey. We postulate that numerous aquatic organisms other than protists could coordinate their behaviour using variations of hydrodynamic trigger waves.

Emergence of tissue-like mechanics from fibrous networks confined by close-packed cells.

The viscoelasticity of the crosslinked semiflexible polymer networks-such as the internal cytoskeleton and the extracellular matrix-that provide shape and mechanical resistance against deformation is assumed to dominate tissue mechanics. However, the mechanical responses of soft tissues and semiflexible polymer gels differ in many respects. Tissues stiffen in compression but not in extension1-5, whereas semiflexible polymer networks soften in compression and stiffen in extension6,7. In shear deformation, semiflexible polymer gels stiffen with increasing strain, but tissues do not1-8. Here we use multiple experimental systems and a theoretical model to show that a combination of nonlinear polymer network elasticity and particle (cell) inclusions is essential to mimic tissue mechanics that cannot be reproduced by either biopolymer networks or colloidal particle systems alone. Tissue rheology emerges from an interplay between strain-stiffening polymer networks and volume-conserving cells within them. Polymer networks that soften in compression but stiffen in extension can be converted to materials that stiffen in compression but not in extension by including within the network either cells or inert particles to restrict the relaxation modes of the fibrous networks that surround them. Particle inclusions also suppress stiffening in shear deformation; when the particle volume fraction is low, they have little effect on the elasticity of the polymer networks. However, as the particles become more closely packed, the material switches from compression softening to compression stiffening. The emergence of an elastic response in these composite materials has implications for how tissue stiffness is altered in disease and can lead to cellular dysfunction9-11. Additionally, the findings could be used in the design of biomaterials with physiologically relevant mechanical properties.

Rheology of debris flow materials is controlled by the distance from jamming.

Debris flows are dense and fast-moving complex suspensions of soil and water that threaten lives and infrastructure. Assessing the hazard potential of debris flows requires predicting yield and flow behavior. Reported measurements of rheology for debris flow slurries are highly variable and sometimes contradictory due to heterogeneity in particle composition and volume fraction ([Formula: see text]) and also inconsistent measurement methods. Here we examine the composition and flow behavior of source materials that formed the postwildfire debris flows in Montecito, CA, in 2018, for a wide range of [Formula: see text] that encapsulates debris flow formation by overland flow. We find that shear viscosity and yield stress are controlled by the distance from jamming, [Formula: see text], where the jamming fraction [Formula: see text] is a material parameter that depends on grain size polydispersity and friction. By rescaling shear and viscous stresses to account for these effects, the data collapse onto a simple nondimensional flow curve indicative of a Bingham plastic (viscoplastic) fluid. Given the highly nonlinear dependence of rheology on [Formula: see text], our findings suggest that determining the jamming fraction for natural materials will significantly improve flow models for geophysical suspensions such as hyperconcentrated flows and debris flows.

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.

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.

Scale-Dependent Rheology of Synovial Fluid Lubricating Macromolecules.

Synovial fluid (SF) is the complex biofluid that facilitates the exceptional lubrication of articular cartilage in joints. Its primary lubricating macromolecules, the linear polysaccharide hyaluronic acid (HA) and the mucin-like glycoprotein proteoglycan 4 (PRG4 or lubricin), interact synergistically to reduce boundary friction. However, the precise manner in which these molecules influence the rheological properties of SF remains unclear. This study aimed to elucidate this by employing confocal microscopy and multiscale rheometry to examine the microstructure and rheology of solutions containing recombinant human PRG4 (rhPRG4) and HA. Contrary to previous assumptions of an extensive HA-rhPRG4 network, it is discovered that rhPRG4 primarily forms stiff, gel-like aggregates. The properties of these aggregates, including their size and stiffness, are found to be influenced by the viscoelastic characteristics of the surrounding HA matrix. Consequently, the rheology of this system is not governed by a single length scale, but instead responds as a disordered, hierarchical network with solid-like rhPRG4 aggregates distributed throughout the continuous HA phase. These findings provide new insights into the biomechanical function of PRG4 in cartilage lubrication and may have implications in the development of HA-based therapies for joint diseases like osteoarthritis.