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.

Cell Membranes Resist Flow.

The fluid-mosaic model posits a liquid-like plasma membrane, which can flow in response to tension gradients. It is widely assumed that membrane flow transmits local changes in membrane tension across the cell in milliseconds, mediating long-range signaling. Here, we show that propagation of membrane tension occurs quickly in cell-attached blebs but is largely suppressed in intact cells. The failure of tension to propagate in cells is explained by a fluid dynamical model that incorporates the flow resistance from cytoskeleton-bound transmembrane proteins. Perturbations to tension propagate diffusively, with a diffusion coefficient Dσ ∼0.024 µm2/s in HeLa cells. In primary endothelial cells, local increases in membrane tension lead only to local activation of mechanosensitive ion channels and to local vesicle fusion. Thus, membrane tension is not a mediator of long-range intracellular signaling, but local variations in tension mediate distinct processes in sub-cellular domains.

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.

A modified viscous flow law for natural glacier ice: Scaling from laboratories to ice sheets.

Glacier flow modulates sea level and is governed largely by the viscous deformation of ice. Multiple molecular-scale mechanisms facilitate viscous deformation, but it remains unclear how each contributes to glacier-scale deformation. Here, we present a model of ice deformation that bridges laboratory and glacier scales, unifies existing estimates of the viscous parameters, and provides a framework for estimating the parameters from observations and incorporating flow laws derived from laboratory observations into glacier-flow models. Our results yield a map of the dominant deformation mechanisms in the Antarctic Ice Sheet, showing that, contrary to long-standing assumptions, dislocation creep, characterized by a value of the stress exponent [Formula: see text], likely dominates in all fast-flowing areas. This increase from the canonical value of [Formula: see text] dramatically alters the climate conditions under which marine ice sheets may become unstable and drive rapid rates of sea-level rise.

Elasticity and rheology of auxetic granular metamaterials.

The flowing, jamming, and avalanche behavior of granular materials is satisfyingly universal and vexingly hard to tune: A granular flow is typically intermittent and will irremediably jam if too confined. Here, we show that granular metamaterials made from particles with a negative Poisson's ratio yield more easily and flow more smoothly than ordinary granular materials. We first create a collection of auxetic grains based on a re-entrant mechanism and show that each grain exhibits a negative Poisson's ratio regardless of the direction of compression. Interestingly, we find that the elastic and yielding properties are governed by the high compressibility of granular metamaterials: At a given confinement, they exhibit lower shear modulus, lower yield stress, and more frequent, smaller avalanches than materials made from ordinary grains. We further demonstrate that granular metamaterials promote flow in more complex confined geometries, such as intruder and hopper geometries, even when the packing contains only a fraction of auxetic grains. Moreover, auxetic granular metamaterials exhibit enhanced impact absorption. Our findings blur the boundary between complex fluids and metamaterials and could help in scenarios that involve process, transport, and reconfiguration of granular materials.

Probing active nematics with in situ microfabricated elastic inclusions.

In this work, we report a direct measurement of the forces exerted by a tubulin/kinesin active nematic gel as well as its complete rheological characterization, including the quantification of its shear viscosity, η, and its activity parameter, α. For this, we develop a method that allows us to rapidly photo-polymerize compliant elastic inclusions in the continuously remodeling active system. Moreover, we quantitatively settle long-standing theoretical predictions, such as a postulated relationship encoding the intrinsic time scale of the active nematic in terms of η and α. In parallel, we infer a value for the nematic elasticity constant, K, by combining our measurements with the theorized scaling of the active length scale. On top of the microrheology capabilities, we demonstrate strategies for defect encapsulation, quantification of defect mechanics, and defect interactions, enabled by the versatility of the microfabrication strategy that allows to combine elastic motifs of different shapes and stiffnesses that are fabricated in situ.

Soft matter mechanics of baseball's Rubbing Mud.

Researchers looking for sustainable materials with optimal mechanical properties may draw inspiration from a baseball tradition. For nearly 100 y, a mysterious mud harvested from an undisclosed river site in New Jersey (USA) has been the agent of choice in the USA's Major League Baseball for "de-glossing" new baseballs. It is unclear, however, what makes this "Rubbing Mud" work. Here, we perform a multiscale investigation of the rheology and tribology of this mud material under baseball-relevant conditions and identify three mechanisms by which the mud alters the surface properties of the baseball. First, the mud creates a more uniform baseball surface by filling in pores in the leather; this is possible because of its relatively high cohesion (clays and organics) making the material remarkably shear thinning. Second, the residue of cohesive particles coating the baseball effectively doubles contact adhesion. Third, a sparse population of angular sand grains are bonded to the baseball by clay-sized particles, leaving a studded surface that enhances friction. The proportions of cohesive, frictional, and viscous elements in Rubbing Mud conspire to create a soft material with an unusual mix of properties, that could find other applications in the development of sustainable geomaterials. Our improved understanding of the flow and friction of natural muds may also find use in modeling natural hazards such as mudslides and for locomotion in muddy environments.

Quantifying electron transport in aggregated colloidal suspensions in the strong flow regime.

Electron transport in complex fluids, biology, and soft matter is a valuable characteristic in processes ranging from redox reactions to electrochemical energy storage. These processes often employ conductor-insulator composites in which electron transport properties are fundamentally linked to the microstructure and dynamics of the conductive phase. While microstructure and dynamics are well recognized as key determinants of the electrical properties, a unified description of their effect has yet to be determined, especially under flowing conditions. In this work, the conductivity and shear viscosity are measured for conductive colloidal suspensions to build a unified description by exploiting both recent quantification of the effect of flow-induced dynamics on electron transport and well-established relationships between electrical properties, microstructure, and flow. These model suspensions consist of conductive carbon black (CB) particles dispersed in fluids of varying viscosities and dielectric constants. In a stable, well-characterized shear rate regime where all suspensions undergo self-similar agglomerate breakup, competing relationships between conductivity and shear rate were observed. To account for the role of variable agglomerate size, equivalent microstructural states were identified using a dimensionless fluid Mason number, [Formula: see text], which allowed for isolation of the role of dynamics on the flow-induced electron transport rate. At equivalent microstructural states, shear-enhanced particle-particle collisions are found to dominate the electron transport rate. This work rationalizes seemingly contradictory experimental observations in literature concerning the shear-dependent electrical properties of CB suspensions and can be extended to other flowing composite systems.

Constraining Earth's nonlinear mantle viscosity using plate-boundary resolving global inversions.

Variable viscosity in Earth's mantle exerts a fundamental control on mantle convection and plate tectonics, yet rigorously constraining the underlying parameters has remained a challenge. Inverse methods have not been sufficiently robust to handle the severe viscosity gradients and nonlinearities (arising from dislocation creep and plastic failure) while simultaneously resolving the megathrust and bending slabs globally. Using global plate motions as constraints, we overcome these challenges by combining a scalable nonlinear Stokes solver that resolves the key tectonic features with an adjoint-based Bayesian approach. Assuming plate cooling, variations in the thickness of continental lithosphere, slabs, and broad scale lower mantle structure as well as a constant grain size through the bulk of the upper mantle, a good fit to global plate motions is found with a nonlinear upper mantle stress exponent of 2.43 [Formula: see text] 0.25 (mean [Formula: see text] SD). A relatively low yield stress of 151 [Formula: see text] 19 MPa is required for slabs to bend during subduction and transmit a slab pull that generates asymmetrical subduction. The recovered long-term strength of megathrusts (plate interfaces) varies between different subduction zones, with South America having a larger strength and Vanuatu and Central America having lower values with important implications for the stresses driving megathrust earthquakes.

Unbiased construction of constitutive relations for soft materials from experiments via rheology-informed neural networks.

The ability to concisely describe the dynamical behavior of soft materials through closed-form constitutive relations holds the key to accelerated and informed design of materials and processes. The conventional approach is to construct constitutive relations through simplifying assumptions and approximating the time- and rate-dependent stress response of a complex fluid to an imposed deformation. While traditional frameworks have been foundational to our current understanding of soft materials, they often face a twofold existential limitation: i) Constructed on ideal and generalized assumptions, precise recovery of material-specific details is usually serendipitous, if possible, and ii) inherent biases that are involved by making those assumptions commonly come at the cost of new physical insight. This work introduces an approach by leveraging recent advances in scientific machine learning methodologies to discover the governing constitutive equation from experimental data for complex fluids. Our rheology-informed neural network framework is found capable of learning the hidden rheology of a complex fluid through a limited number of experiments. This is followed by construction of an unbiased material-specific constitutive relation that accurately describes a wide range of bulk dynamical behavior of the material. While extremely efficient in closed-form model discovery for a real-world complex system, the model also provides insight into the underpinning physics of the material.

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.

Phase separation and ripening in a viscoelastic gel.

The process of phase separation in elastic solids and viscous fluids is of fundamental importance to the stability and function of soft materials. We explore the dynamics of phase separation and domain growth in a viscoelastic material such as a polymer gel. Using analytical theory and Monte Carlo simulations, we report a domain growth regime in which the domain size increases algebraically with a ripening exponent [Formula: see text] that depends on the viscoelastic properties of the material. For a prototypical Maxwell material, we obtain [Formula: see text], which is markedly different from the well-known Ostwald ripening process with [Formula: see text]. We generalize our theory to systems with arbitrary power-law relaxation behavior and discuss our findings in the context of the long-term stability of materials as well as recent experimental results on phase separation in cross-linked networks and cytoskeleton.

Scientific machine learning for modeling and simulating complex fluids.

The formulation of rheological constitutive equations-models that relate internal stresses and deformations in complex fluids-is a critical step in the engineering of systems involving soft materials. While data-driven models provide accessible alternatives to expensive first-principles models and less accurate empirical models in many engineering disciplines, the development of similar models for complex fluids has lagged. The diversity of techniques for characterizing non-Newtonian fluid dynamics creates a challenge for classical machine learning approaches, which require uniformly structured training data. Consequently, early machine-learning based constitutive equations have not been portable between different deformation protocols or mechanical observables. Here, we present a data-driven framework that resolves such issues, allowing rheologists to construct learnable models that incorporate essential physical information, while remaining agnostic to details regarding particular experimental protocols or flow kinematics. These scientific machine learning models incorporate a universal approximator within a materially objective tensorial constitutive framework. By construction, these models respect physical constraints, such as frame-invariance and tensor symmetry, required by continuum mechanics. We demonstrate that this framework facilitates the rapid discovery of accurate constitutive equations from limited data and that the learned models may be used to describe more kinematically complex flows. This inherent flexibility admits the application of these "digital fluid twins" to a range of material systems and engineering problems. We illustrate this flexibility by deploying a trained model within a multidimensional computational fluid dynamics simulation-a task that is not achievable using any previously developed data-driven rheological equation of state.

Bonded straight and helical flagellar filaments form ultra-low-density glasses.

We study how the three-dimensional shape of rigid filaments determines the microscopic dynamics and macroscopic rheology of entangled semidilute Brownian suspensions. To control the filament shape we use bacterial flagella, which are microns-long helical or straight filaments assembled from flagellin monomers. We compare the dynamics of straight rods, helical filaments, and shape-diblock copolymers composed of seamlessly joined straight and helical segments. Caged by their neighbors, straight rods preferentially diffuse along their long axis, but exhibit significantly suppressed rotational diffusion. Entangled helical filaments escape their confining tube by corkscrewing through the dense obstacles created by other filaments. By comparison, the adjoining segments of the rod-helix shape-diblocks suppress both the translation and the corkscrewing dynamics. Consequently, the shape-diblock filaments become permanently jammed at exceedingly low densities. We also measure the rheological properties of semidilute suspensions and relate their mechanical properties to the microscopic dynamics of constituent filaments. In particular, rheology shows that an entangled suspension of shape rod-helix copolymers forms a low-density glass whose elastic modulus can be estimated by accounting for how shear deformations reduce the entropic degrees of freedom of constrained filaments. Our results demonstrate that the three-dimensional shape of rigid filaments can be used to design rheological properties of semidilute fibrous suspensions.

Investigation of the yielding transition in concentrated colloidal systems via rheo-XPCS.

We probe the microstructural yielding dynamics of a concentrated colloidal system by performing creep/recovery tests with simultaneous collection of coherent scattering data via X-ray Photon Correlation Spectroscopy (XPCS). This combination of rheology and scattering allows for time-resolved observations of the microstructural dynamics as yielding occurs, which can be linked back to the applied rheological deformation to form structure-property relations. Under sufficiently small applied creep stresses, examination of the correlation in the flow direction reveals that the scattering response recorrelates with its predeformed state, indicating nearly complete microstructural recovery, and the dynamics of the system under these conditions slows considerably. Conversely, larger creep stresses increase the speed of the dynamics under both applied creep and recovery. The data show a strong connection between the microstructural dynamics and the acquisition of unrecoverable strain. By comparing this relationship to that predicted from homogeneous, affine shearing, we find that the yielding transition in concentrated colloidal systems is highly heterogeneous on the microstructural level.

Evolution of interfacial mechanics of lung surfactant mimics progression of acute respiratory distress syndrome.

How acute respiratory distress syndrome progresses from underlying disease or trauma is poorly understood, and there are no generally accepted treatments resulting in a 40% mortality rate. However, during the inflammation that accompanies this disease, the phospholipase A2 concentration increases in the alveolar fluids leading to the hydrolysis of bacterial, viral, and lung surfactant phospholipids into soluble lysolipids. We show that if the lysolipid concentration in the subphase reaches or exceeds its critical micelle concentration, the surface tension, γ, of dipalmitoyl phosphatidylcholine (DPPC) or Curosurf monolayers increases and the dilatational modulus, [Formula: see text], decreases to that of a pure lysolipid interface. This is consistent with DPPC being solubilized in lysolipid micelles and being replaced by lysolipid at the interface. These changes lead to [Formula: see text] which is the criterion for the Laplace instability that can lead to mechanical instabilities during lung inflation, potentially causing alveolar collapse. These findings provide a mechanism behind the alveolar collapse and uneven lung inflation during ARDS.

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.

Accelerated Lung Function Decline and Mucus-Microbe Evolution in Chronic Obstructive Pulmonary Disease.

Rationale: Progressive lung function loss is recognized in chronic obstructive pulmonary disease (COPD); however, no study concurrently evaluates how accelerated lung function decline relates to mucus properties and the microbiome in COPD. Objectives: Longitudinal assessment of mucus and microbiome changes accompanying accelerated lung function decline in patients COPD. Methods: This was a prospective, longitudinal assessment of the London COPD cohort exhibiting the greatest FEV1 decline (n = 30; accelerated decline; 156 ml/yr FEV1 loss) and with no FEV1 decline (n = 28; nondecline; 49 ml/yr FEV1 gain) over time. Lung microbiomes from paired sputum (total 116 specimens) were assessed by shotgun metagenomics and corresponding mucus profiles evaluated for biochemical and biophysical properties. Measurements and Main Results: Biochemical and biophysical mucus properties are significantly altered in the accelerated decline group. Unsupervised principal component analysis showed clear separation, with mucus biochemistry associated with accelerated decline, whereas biophysical mucus characteristics contributed to interindividual variability. When mucus and microbes are considered together, an accelerated decline mucus-microbiome association emerges, characterized by increased mucin (MUC5AC [mucin 5AC] and MUC5B [mucin 5B]) concentration and the presence of Achromobacter and Klebsiella. As COPD progresses, mucus-microbiome shifts occur, initially characterized by low mucin concentration and transition from viscous to elastic dominance accompanied by the commensals Veillonella, Gemella, Rothia, and Prevotella (Global Initiative for Chronic Obstructive Lung Disease [GOLD] A and B) before transition to increased mucus viscosity, mucins, and DNA concentration together with the emergence of pathogenic microorganisms including Haemophilus, Moraxella, and Pseudomonas (GOLD E). Conclusions: Mucus-microbiome associations evolve over time with accelerated lung function decline, symptom progression, and exacerbations affording fresh therapeutic opportunities for early intervention.

Structure of propagating high-stress fronts in a shear-thickening suspension.

We report direct measurements of spatially resolved stress at the boundary of a shear-thickening cornstarch suspension revealing persistent regions of high local stress propagating in the flow direction at the speed of the top boundary. The persistence of these propagating fronts enables precise measurements of their structure, including the profile of boundary stress measured by boundary stress microscopy (BSM) and the nonaffine velocity of particles at the bottom boundary of the suspension measured by particle image velocimetry (PIV). In addition, we directly measure the relative flow between the particle phase and the suspending fluid (fluid migration) and find the migration is highly localized to the fronts and changes direction across the front, indicating that the fronts are composed of a localized region of high dilatant pressure and low particle concentration. The magnitude of the flow indicates that the pore pressure difference driving the fluid migration is comparable to the critical shear stress for the onset of shear thickening. The propagating fronts fully account for the increase in viscosity with applied stress reported by the rheometer and are consistent with the existence of a stable jammed region in contact with one boundary of the system that generates a propagating network of percolated frictional contacts spanning the gap between the rheometer plates and producing strong localized dilatant pressure.

Digital rheometer twins: Learning the hidden rheology of complex fluids through rheology-informed graph neural networks.

SignificanceScience-based data-driven methods that can describe the rheological behavior of complex fluids can be transformative across many disciplines. Digital rheometer twins, which are developed here, can significantly reduce the cost, time, and energy required to characterize complex fluids and predict their future behavior. This is made possible by combining two different methods of informing neural networks with the rheological underpinnings of a system, resulting in quantitative recovery of a gel's response to different flow protocols. The platform developed here is general enough that it can be extended to areas well beyond complex fluids modeling.