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.

RNA-driven phase transitions in biomolecular condensates.

RNAs and RNA-binding proteins can undergo spontaneous or active condensation into phase-separated liquid-like droplets. These condensates are cellular hubs for various physiological processes, and their dysregulation leads to diseases. Although RNAs are core components of many cellular condensates, the underlying molecular determinants for the formation, regulation, and function of ribonucleoprotein condensates have largely been studied from a protein-centric perspective. Here, we highlight recent developments in ribonucleoprotein condensate biology with a particular emphasis on RNA-driven phase transitions. We also present emerging future directions that might shed light on the role of RNA condensates in spatiotemporal regulation of cellular processes and inspire bioengineering of RNA-based therapeutics.

A conceptual framework for understanding phase separation and addressing open questions and challenges.

Macromolecular phase separation is being recognized for its potential importance and relevance as a driver of spatial organization within cells. Here, we describe a framework based on synergies between networking (percolation or gelation) and density (phase separation) transitions. Accordingly, the phase transitions in question are referred to as phase separation coupled to percolation (PSCP). The condensates that result from PSCP are viscoelastic network fluids. Such systems have sequence-, composition-, and topology-specific internal network structures that give rise to time-dependent interplays between viscous and elastic properties. Unlike pure phase separation, the process of PSCP gives rise to sequence-, chemistry-, and structure-specific distributions of clusters that can form at concentrations that lie well below the threshold concentration for phase separation. PSCP, influenced by specific versus solubility-determining interactions, also provides a bridge between different observations and helps answer questions and address challenges that have arisen regarding the role of macromolecular phase separation in biology.

Rigidity percolation in a random tensegrity via analytic graph theory.

Functional structures from across the engineered and biological world combine rigid elements such as bones and columns with flexible ones such as cables, fibers, and membranes. These structures are known loosely as tensegrities, since these cable-like elements have the highly nonlinear property of supporting only extensile tension. Marginally rigid systems are of particular interest because the number of structural constraints permits both flexible deformation and the support of external loads. We present a model system in which tensegrity elements are added at random to a regular backbone. This system can be solved analytically via a directed graph theory, revealing a mechanical critical point generalizing that of Maxwell. We show that even the addition of a few cable-like elements fundamentally modifies the nature of this transition point, as well as the later transition to a fully rigid structure. Moreover, the tensegrity network displays a collective avalanche behavior, in which the addition of a single cable leads to the elimination of multiple floppy modes, a phenomenon that becomes dominant at the transition point. These phenomena have implications for systems with nonlinear mechanical constraints, from biopolymer networks to soft robots to jammed packings to origami sheets.

Early path dominance as a principle for neurodevelopment.

We perform targeted attack, a systematic computational unlinking of the network, to analyze its effects on global communication across the brain network through its giant cluster. Across diffusion magnetic resonance images from individuals in the UK Biobank, Adolescent Brain Cognitive Development Study and Developing Human Connectome Project, we find that targeted attack procedures on increasing white matter tract lengths and densities are remarkably invariant to aging and disease. Time-reversing the attack computation suggests a mechanism for how brains develop, for which we derive an analytical equation using percolation theory. Based on a close match between theory and experiment, our results demonstrate that tracts are limited to emanate from regions already in the giant cluster and tracts that appear earliest in neurodevelopment are those that become the longest and densest.

Strong connectivity in real directed networks.

In many real, directed networks, the strongly connected component of nodes which are mutually reachable is very small. This does not fit with current theory, based on random graphs, according to which strong connectivity depends on mean degree and degree-degree correlations. And it has important implications for other properties of real networks and the dynamical behavior of many complex systems. We find that strong connectivity depends crucially on the extent to which the network has an overall direction or hierarchical ordering-a property measured by trophic coherence. Using percolation theory, we find the critical point separating weakly and strongly connected regimes and confirm our results on many real-world networks, including ecological, neural, trade, and social networks. We show that the connectivity structure can be disrupted with minimal effort by a targeted attack on edges which run counter to the overall direction. This means that many dynamical processes on networks can depend significantly on a small fraction of edges.

Quantifying the environmental limits to fire spread in grassy ecosystems.

Modeling fire spread as an infection process is intuitive: An ignition lights a patch of fuel, which infects its neighbor, and so on. Infection models produce nonlinear thresholds, whereby fire spreads only when fuel connectivity and infection probability are sufficiently high. These thresholds are fundamental both to managing fire and to theoretical models of fire spread, whereas applied fire models more often apply quasi-empirical approaches. Here, we resolve this tension by quantifying thresholds in fire spread locally, using field data from individual fires (n = 1,131) in grassy ecosystems across a precipitation gradient (496 to 1,442 mm mean annual precipitation) and evaluating how these scaled regionally (across 533 sites) and across time (1989 to 2012 and 2016 to 2018) using data from Kruger National Park in South Africa. An infection model captured observed patterns in individual fire spread better than competing models. The proportion of the landscape that burned was well described by measurements of grass biomass, fuel moisture, and vapor pressure deficit. Regionally, averaging across variability resulted in quasi-linear patterns. Altogether, results suggest that models aiming to capture fire responses to global change should incorporate nonlinear fire spread thresholds but that linear approximations may sufficiently capture medium-term trends under a stationary climate.

Self-consistent dispersal puts tight constraints on the spatiotemporal organization of species-rich metacommunities.

Biodiversity is often attributed to a dynamic equilibrium between the immigration and extinction of species. This equilibrium forms a common basis for studying ecosystem assembly from a static reservoir of migrants-the mainland. Yet, natural ecosystems often consist of many coupled communities (i.e., metacommunities), and migration occurs between these communities. The pool of migrants then depends on what is sustained in the ecosystem, which, in turn, depends on the dynamic migrant pool. This chicken-and-egg problem of survival and dispersal is poorly understood in communities of many competing species, except for the neutral case-the "unified neutral theory of biodiversity." Employing spatiotemporal simulations and mean-field analyses, we show that self-consistent dispersal puts rather tight constraints on the dynamic migration-extinction equilibrium. When the number of species is large, species are pushed to the edge of their global extinction, even when competition is weak. As a consequence, the overall diversity is highly sensitive to perturbations in demographic parameters, including growth and dispersal rates. When dispersal is short range, the resulting spatiotemporal abundance patterns follow broad scale-free distributions that correspond to a directed percolation phase transition. The qualitative agreement of our results for short-range and long-range dispersal suggests that this self-organization process is a general property of species-rich metacommunities. Our study shows that self-sustaining metacommunities are highly sensitive to environmental change and provides insights into how biodiversity can be rescued and maintained.

Indirect influence in social networks as an induced percolation phenomenon.

Percolation theory has been widely used to study phase transitions in network systems. It has also successfully explained various macroscopic spreading phenomena across different fields. Yet, the theoretical frameworks have been focusing on direct interactions among nodes, while recent empirical observations have shown that indirect interactions are common in many network systems like social and ecological networks, among others. By investigating the detailed mechanism of both direct and indirect influence on scientific collaboration networks, here we show that indirect influence can play the dominant role in behavioral influence. To address the lack of theoretical understanding of such indirect influence on the macroscopic behavior of the system, we propose a percolation mechanism of indirect interactions called induced percolation. Surprisingly, our model exhibits a unique anisotropy property. Specifically, directed networks show first-order abrupt transitions as opposed to the second-order continuous transition in the same network structure but with undirected links. A mix of directed and undirected links leads to rich hybrid phase transitions. Furthermore, a unique feature of the nonmonotonic pattern is observed in network connectivities near the critical point. We also present an analytical framework to characterize the proposed induced percolation, paving the way to further understanding network dynamics with indirect interactions.

High conductivity Sepia melanin ink films for environmentally benign printed electronics.

Melanins (from the Greek µÎ­λας, mélas, black) are bio-pigments ubiquitous in flora and fauna. Eumelanin is an insoluble brown-black type of melanin, found in vertebrates and invertebrates alike, among which Sepia (cuttlefish) is noteworthy. Sepia melanin is a type of bio-sourced eumelanin that can readily be extracted from the ink sac of cuttlefish. Eumelanin features broadband optical absorption, metal-binding affinity and antioxidative and radical-scavenging properties. It is a prototype of benign material for sustainable organic electronics technologies. Here, we report on an electronic conductivity as high as 10-3 S cm-1 in flexographically printed Sepia melanin films; such values for the conductivity are typical for well-established high-performance organic electronic polymers but quite uncommon for bio-sourced organic materials. Our studies show the potential of bio-sourced materials for emerging electronic technologies with low human- and eco-toxicity.

An Alternating-Electric-Field-Driven Assembly of DNA Nanoparticles into FCC Crystals.

Using an alternating electric field is a versatile way to control particle assembly. Programming DNA-AuNP assembly via an electric field remains a significant challenge despite the negative charge of DNA. In DNA-AuNP assembly, a critical percolation state is delicately constructed, where the DNA bond is loosely connected and sensitive to electric fields. In this state, an FCC crystal structure can be successfully constructed by applying a high-frequency electric field to assemble DNA-AuNPs without altering the temperature, which is favorable for temperature-sensitive systems. In addition, the regulation of electric fields can be adjusted through parameters such as the frequency and voltage, which offers more precise control than temperature regulation does. The frequency and voltage can be used to precisely tune the phase structure of DNA-AuNPs from dissolved to disordered or FCC. These findings broaden the potential of DNA-based crystal engineering, revealing new opportunities in electronic nanocomposites and devices.

Fast-Charging, Binder-Free Lithium Battery Cathodes Enabled via Multidimensional Conductive Networks.

To meet the growing demands in both energy and power densities of lithium ion batteries, electrode structures must be capable of facile electron and ion transport while minimizing the content of electrochemically inactive components. Herein, binder-free LiFePO4 (LFP) cathodes are fabricated with a multidimensional conductive architecture that allows for fast-charging capability, reaching a specific capacity of 94 mAh g-1 at 4 C. Such multidimensional networks consist of active material particles wrapped by 1D single-walled carbon nanotubes (CNTs) and bound together using 2D MXene (Ti3C2Tx) nanosheets. The CNTs form a porous coating layer and improve local electron transport across the LFP surface, while the Ti3C2Tx nanosheets provide simultaneously high electrode integrity and conductive pathways through the bulk of the electrode. This work highlights the ability of multidimensional conductive fillers to realize simultaneously superior electrochemical and mechanical properties, providing useful insights into future fast-charging electrode designs for scalable electrochemical systems.

Quantum Gas-Enabled Direct Mapping of Active Current Density in Percolating Networks of Nanowires.

Electrically percolating nanowire networks are among the most promising candidates for next-generation transparent electrodes. Scientific interest in these materials stems from their intrinsic current distribution heterogeneity, leading to phenomena like percolating pathway rerouting and localized self-heating, which can cause irreversible damage. Without an experimental technique to resolve the current distribution and an underpinning nonlinear percolation model, one relies on empirical rules and safety factors to engineer materials. We introduce Bose-Einstein condensate microscopy to address the longstanding problem of imaging active current flow in 2D materials. We report on performance improvement of this technique whereby observation of dynamic redistribution of current pathways becomes feasible. We show how this, combined with existing thermal imaging methods, eliminates the need for assumptions between electrical and thermal properties. This will enable testing and modeling individual junction behavior and hot-spot formation. Investigating both reversible and irreversible mechanisms will contribute to improved performance and reliability of devices.

Making the Case for Disordered Proteins and Biomolecular Condensates in Bacteria.

Intrinsically disordered proteins/regions (IDPs/IDRs) contribute to a diverse array of molecular functions in eukaryotic systems. There is also growing recognition that membraneless biomolecular condensates, many of which are organized or regulated by IDPs/IDRs, can enable spatial and temporal regulation of complex biochemical reactions in eukaryotes. Motivated by these findings, we assess if (and how) membraneless biomolecular condensates and IDPs/IDRs are functionally involved in key cellular processes and molecular functions in bacteria. We summarize the conceptual underpinnings of condensate assembly and leverage these concepts by connecting them to recent findings that implicate specific types of condensates and IDPs/IDRs in important cellular level processes and molecular functions in bacterial systems.

Highly Sensitive Soft Pressure Sensors for Wearable Applications Based on Composite Films with Curved 3D Carbon Nanotube Structures.

Soft pressure sensors based on 3D microstructures exhibit high sensitivity in the low-pressure range, which is crucial for various wearable and soft touch applications. However, it is still a challenge to manufacture soft pressure sensors with sufficient sensitivity under small mechanical stimuli for wearable applications. This work presents a novel strategy for extremely sensitive pressure sensors based on the composite film with local changes in curved 3D carbon nanotube (CNT) structure via expandable microspheres. The sensitivity is significantly enhanced by the synergetic effects of heterogeneous contact of the microdome structure and changes of percolation network within the curved 3D CNT structure. The finite-element method simulation is used to comprehend the relationships between the sensitivity and mechanical/electrical behavior of microdome structure under the applied pressure. The sensor shows an excellent sensitivity (571.64 kPa-1 ) with fast response time (85 ms), great repeatability, and long-term stability. Using the developed sensor, a wireless wearable health monitoring system to avoid carpel tunnel syndrome is built, and a multi-array pressure sensor for realizing a variety of movements in real-time is demonstrated.

Synergistic Inclusion Effects of Hard Magnetic Nanorods on the Magnetomechanical Actuation of Soft Magnetic Microsphere-Based Polymer Composites.

The magnetomechanical actuation of micropillars is developed for the contactless manipulation of miniaturized actuators and microtextured surfaces. Anisotropic geometry of micropillars can significantly enhance the magnetic actuation compared with their isotropic counterparts by directional stress distributions. However, this strategy is not viable for triangular micropillars owing to insufficient anisotropy. In this study, a significant improvement in the magnetic actuation of triangular micropillars using composite magnetic particles is reported. A minute and optimal amount of hard magnetic gamma-ferrite nanorods are hybridized with soft magnetic iron microspheres to generate synergistic effects of magnetic coupling and percolation phenomenon on the magnetic actuation of polymer composites. The addition of 1 wt% face-centered cubic-phased gamma-ferrite nanorods suppresses the magnetic coupling interference of body-centered cubic-phased iron microspheres. Furthermore, the nanorods reduce the percolation threshold by participating in the percolation of the microspheres. A systematic compositional study on the magnetization and magnetorheological properties reveals that the coupling effect dominates the percolation effect at a low magnetic field, whereas the percolation effect governs the magnetic actuation at a high magnetic field. This hybrid approach can help in designing material constituents for effective magnetic actuators and robotic systems that can sensitively respond to an external magnetic field.

Diverse Self-assembly Pathways in Nematic Compartment Network: Topological Percolation and Pathfinding.

The self-assembly of nematic molecules in microcompartments with unambiguously defined surface anchoring is well predictable and is likely to have a single stable topological structure. Here, in contrast, a confined nematic system comprising an array of microcompartments interconnected by channels is demonstrated, exhibiting diverse molecular assembly pathways leading to the formation of four types of topological structures and twelve different patterns randomly distributed. Intercompartment communication via channels plays a crucial role in the diversity of patterns and distributions. It determines the sizes and structures of domains separated by channel defects. The domain structure, which features a pathfinding algorithm and reverse tree structure, can be modelled by an isotropically directed bond percolation with additional restrictions. This system serves as a model for controlled randomness and restricted growth of networks, with potential applications in anticounterfeit protection as a physically unclonable function (PUF) with multiple-level communication protocols.

Microstructure Morphology of Chemical and Structural Phase Separation in Thermally treated KxFe2-ySe2 Superconductor.

The iron-based KxFe2-ySe2 superconductor displays phase separation, leading to the coexisting metallic phase embedded in an antiferromagnetic matrix. The metallic character of the system is believed to arise from a percolative granular network affecting normal as well as superconducting state properties. This network can be manipulated and controlled through thermal treatments. In this study, we have used scanning X-ray micro-fluorescence to visualize morphology of the phase separation and the percolation in KxFe2-ySe2, manipulated by distinct thermal treatments, i.e., fast quenching and slow cooling. We find a differing spatial correlation between Fe and K in differently treated samples, ascribed to different Fe vacancy ordering. We have identified an intermediate phase that acts as an interface between the two phases. The high temperature quenching produces oriented clustered microstructure in which the percolation threshold is lower and hence a more effective network for the transport pathways. Instead, the slow cooling results in larger interfaces around the percolation threshold affecting the superconducting properties of the system. The results provide a quantitative characterization of microstructural morphology of differently grown KxFe2-ySe2 showing potential for the design of electronic devices based on sub-micron scale chemical phase separation, thus opening avenues for further studies of complex heterogeneous structures.

Effect of anisotropy and length dispersity on electrical and optical properties of nanowire network based transparent electrodes: a computational study.

We have studied the impact of nanowire alignment and measurement direction at the percolation threshold on the effective resistance (R) of two-dimensional (2D) films. This helps us to analyze the effect of anisotropy on the conductivity and transmittance of the nanowire-based network characterized by the disorder parameter (s). These optoelectronic properties are determined for systems with monodisperse and bimodal length distribution (a combination of two fixed lengths of nanowires). The 2D systems simulated using our computational approach are assumed to be transparent and conductive in which percolative transport is the primary conduction mechanism. We obtain our results numerically using a computational and geometrical approach, i.e. a Discrete (grid) method that is advantageous in algorithm speed. For a particular disorder parameters, the conductivity and transmittance increase as the length fraction (LF) increases for the bimodal distribution of the length of nanowires in networks. We have observed the maximum conductivity when the nanowires are highly aligned along the measurement direction of percolation, in contrast to the isotropic arrangement of nanowires. Significantly, alignment introduced in nanowires leads to a higher percolation threshold which leads to a decrease in the transmittance of the network. We show that the resistivity of the monodisperse network in the direction parallel (perpendicular) to the alignment decreases (increases) with the disorder parameter and scales ass(s2). This scaling holds true for the bimodal distribution of nanowires as well. For a particularLF, the electrical anisotropy increases withs. The anisotropy is maximum for nearly aligned nanowires in a bimodal network with the highest proportion of the longest wire considered. For the maximally aligned wires and highestLF, we obtained an approximately 50%enhancement in the figure of merit, denoted byφ. Hence, incorporating longer-length wires and increasing the alignment in nanowire networks can increase the conductivity, anisotropy, and figure of merit which may benefit a vast range of applications.

Facile synthesis ofß-Ga2O3based high-performance electronic devices via direct oxidation of solution-processed transition metal dichalcogenides.

Gallium oxide (Ga2O3) is a promising wide bandgap semiconductor that is viewed as a contender for the next generation of high-power electronics due to its high theoretical breakdown electric field and large Baliga's figure of merit. Here, we report a facile route of synthesizingß-Ga2O3via direct oxidation conversion using solution-processed two-dimensional (2D) GaS semiconducting nanomaterial. Higher order of crystallinity in x-ray diffraction patterns and full surface coverage formation in scanning electron microscopy images after annealing were achieved. A direct and wide bandgap of 5 eV was calculated, and the synthesizedß-Ga2O3was fabricated as thin film transistors (TFT). Theß-Ga2O3TFT fabricated exhibits remarkable electron mobility (1.28 cm2Vs-1) and a good current ratio (Ion/Ioff) of 2.06 × 105. To further boost the electrical performance and solve the structural imperfections resulting from the exfoliation process of the 2D nanoflakes, we also introduced and doped graphene inß-Ga2O3TFT devices, increasing the electrical device mobility by ∼8-fold and thereby promoting percolation pathways for the charge transport. We found that electron mobility and conductivity increase directly with the graphene doping concentration. From these results, it can be proved that theß-Ga2O3networks have excellent carrier transport properties. The facile and convenient synthesis method successfully developed in this paper makes an outstanding contribution to applying 2D oxide materials in different and emerging optoelectronic applications.