Electrostatic tweezer for droplet manipulation

Various physical tweezers for manipulating liquid droplets based on optical, electrical, magnetic, acoustic, or other external fields have emerged and revolutionized research and application in medical, biological, and environmental fields. Despite notable progress, the existing modalities for droplet control and manipulation are still limited by the extra responsive additives and relatively poor controllability in terms of droplet motion behaviors, such as distance, velocity, and direction. Herein, we report a versatile droplet electrostatic tweezer (DEST) for remotely and programmatically trapping or guiding the liquid droplets under diverse conditions, such as in open and closed spaces and on flat and tilted surfaces as well as in oil medium. DEST, leveraging on the coulomb attraction force resulting from its electrostatic induction to a droplet, could manipulate droplets of various compositions, volumes, and arrays on various substrates, offering a potential platform for a series of applications, such as high-throughput surface-enhanced Raman spectroscopy detection with single measuring time less than 20 s.

Since the emergence of optical tweezers that are capable of trapping and manipulating microparticles in a remote and noninvasive manner in 1986 (1), the tweezers have evolved to diverse forms, such as magnetic tweezers (2) and acoustic tweezers (3). These tweezers have been widely used to manipulate many kinds of micro-/nanometal particles, bioparticles, liquid droplets, and so on. In particular, well-controlled liquid droplet manipulation is essential to various practical fields (4–7), such as printing technology (8), heat management (9–11), water harvesting (12, 13), biological assays (14), chemical reactions (15, 16), and frost prevention (17, 18). Despite remarkable significances, the droplet manipulation using these physical tweezers has achieved less progress, probably owing to the fluidic nature of droplets, which are soft and deformable in diverse operating conditions and mediums. Current approaches to manipulating droplets mainly take advantage of surface force gradient (3, 4, 9, 19–27) or the force directly applied to droplets, which always demands the responsiveness of substrates or droplets for force sources. As one of the most important physical fields to generate driving force, the electric field offers the intrinsic advantage that most types of droplets and conductive substrates (28, 29), unlike other external stimuli such as magnetism (30) or light (31, 32), respectively.Among various electric-based manipulations, electrowetting on dielectric has been widely explored (33–35). However, these conventional electric-based droplet manipulations are deeply dependent on sophisticated electrode patterns and rational electric circuit control, which increase the complexity of manipulation platforms. Other methods eliminating the need for electrode groups, such as surface charge printing or electrostatic repulsion methods (26, 27), are susceptible to the extra steps to generate charges on substrates or droplets and therefore, are accompanied by manipulation instability due to undesirable triboelectrification during the droplet motion.Here, we report a versatile droplet electrostatic tweezer (DEST) for remote and noninvasive manipulation of droplets on the basis of electrostatic induction. Due to the inherent responsiveness of liquid droplets to the electrostatic field, the droplets on conductive superhydrophobic surfaces obtain temporary and adjustable induced charges, and therefore, they could be trapped and guided by a noncontact tweezer, which is further proven by the diverse droplet types on diverse substrates. Such a DEST allows us to maneuver the droplets with a wide volume range (from tens of nanoliters to several milliliters) and amount range (from one to seven or more droplets) on both open surface and closed channels, even under oil. DEST could also programmatically manipulate droplets with high velocity (81.6 mm/s or faster), unlimited distance, agile direction steering, and a precise droplet stopping point without the need for any responsive agents in droplets and substrates, which offers a potential platform for the chemical reaction carrying solid cargo, surface-cleaning, and high-throughput surface-enhanced Raman spectroscopy (SERS) detection.     

Air-stable droplet interface bilayers on oil-infused surfaces

Droplet interface bilayers are versatile model membranes useful for synthetic biology and biosensing; however, to date they have always been confined to fluid reservoirs. Here, we demonstrate that when two or more water droplets collide on an oil-infused substrate, they exhibit noncoalescence due to the formation of a thin oil film that gets squeezed between the droplets from the bottom up. We show that when phospholipids are included in the water droplets, a stable droplet interface bilayer forms between the noncoalescing water droplets. As with traditional oil-submerged droplet interface bilayers, we were able to characterize ion channel transport by incorporating peptides into each droplet. Our findings reveal that droplet interface bilayers can function in ambient environments, which could potentially enable biosensing of airborne matter.Inspired by the pitcher plant (1), it was recently found that nano/microstructured hydrophobic substrates can be impregnated with lubricating fluids to create slippery surfaces for droplets (2–5). In contrast to dry, superomniphobic surfaces (6), lubricant-infused surfaces demonstrate stable liquid repellency at extreme pressures and temperatures (5, 7), are self-healing to mechanical damage (5), and their wettability and optical properties can be tuned (7, 8). A wide variety of applications are being explored for lubricant-infused surfaces, such as enhancing condensation heat transfer (9, 10), self-cleaning (11), fog harvesting (12), and omniphobic textiles (13), or minimizing ice nucleation (14, 15), ice adhesion (16, 17), and biofouling (18). Though previous studies have characterized the dynamics and possible wetting states of isolated droplets on lubricant-infused surfaces (5, 19–22), the interactive behavior of multiple droplets has not been reported.For the more traditional scenario of water droplets completely submerged in a reservoir of immiscible fluid, the physics of droplet–droplet interactions are well known. Water droplets submerged in crude oil can exhibit stable noncoalescence; this is because the crude oil contains surface-active components, such as resins and asphaltenes, which congregate at the droplet interfaces (23). When amphiphilic phospholipids are introduced into an oil reservoir containing water droplets, droplet interface bilayers (DIBs) can form between adjacent water droplets (24, 25). Recently, DIBs have emerged as an ideal model membrane system due to attractive features such as durability (26, 27), tunable size and curvature (28–30), deformability (31), facile electrical characterization of ion channels (32–35), the option to introduce asymmetry into the system (36), and droplet interchangeability (26, 32). In the absence of any stabilizing agents, water droplets colliding in an immiscible fluid will exhibit coalescence when their interaction time exceeds the time required to drain the film of fluid trapped between the droplets (37, 38). Droplet collision is typically controlled by applying a constant force (i.e., gravity) (39, 40), constant approach velocity (41, 42), or constant flow rate (43, 44). For experimental studies in pure oil baths, the time required for colliding water droplets to exhibit film rupture and coalesce typically ranges from 10⁻³ to 10² s, depending on parameters such as oil viscosity, droplet size, and the flow field (40, 42–44).Here, we show that water droplets in an ambient environment exhibit noncoalescence when colliding on an oil-infused surface, even in the absence of any surfactants. This phenomenon is due to the oil meniscus that surrounds each water droplet; when the oil menisci of neighboring droplets overlap, the menisci spontaneously merge together to minimize their surface energies and an oil film is squeezed upward to form a barrier between the colliding droplets. Though droplet coalescence will eventually occur due to film drainage, the time required for film rupture is several hours for moderate-viscosity [∼100 centistokes (cSt)] oils and is 1–3 orders of magnitude longer compared with droplets submerged in an oil bath (40, 42–44). These findings should refine the understanding of using oil-infused substrates for processes involving droplet–droplet interactions, such as condensation (9, 10) and fog harvesting (12).When incorporating amphiphilic phospholipids into the water droplets, we demonstrate that the thinning oil membrane between noncoalescing droplets gets replaced by a stable lipid bilayer, somewhat analogous to the formation of a black lipid membrane in an aperture painted with oil (45). To our knowledge, this is the first report of producing droplet interface bilayers in an ambient environment. We show that air-stable DIBs still allow for the robust electrical characterization of ion channels inserted in the lipid bilayer. Previously, it has been demonstrated that black lipid membranes or DIBs can be used for biosensing (46–50), light sensing (26), microscale biobatteries (26), electrical circuits (51, 52), and engineering tissue-like material (53). However, these suspended lipid bilayers have always been confined to fluid reservoirs (25, 45). We suggest that our air-stable DIBs will allow for an unprecedented degree of control regarding the fabrication, manipulation, transportation, and utilization of functional droplet networks.     

Edge current and pairing order transition in chiral bacterial vortices

Bacterial suspensions show turbulence-like spatiotemporal dynamics and vortices moving irregularly inside the suspensions. Understanding these ordered vortices is an ongoing challenge in active matter physics, and their application to the control of autonomous material transport will provide significant development in microfluidics. Despite the extensive studies, one of the key aspects of bacterial propulsion has remained elusive: The motion of bacteria is chiral, i.e., it breaks mirror symmetry. Therefore, the mechanism of control of macroscopic active turbulence by microscopic chirality is still poorly understood. Here, we report the selective stabilization of chiral rotational direction of bacterial vortices in achiral circular microwells sealed by an oil/water interface. The intrinsic chirality of bacterial swimming near the top and bottom interfaces generates chiral collective motions of bacteria at the lateral boundary of the microwell that are opposite in directions. These edge currents grow stronger as bacterial density increases, and, within different top and bottom interfaces, their competition leads to a global rotation of the bacterial suspension in a favored direction, breaking the mirror symmetry of the system. We further demonstrate that chiral edge current favors corotational configurations of interacting vortices, enhancing their ordering. The intrinsic chirality of bacteria is a key feature of the pairing order transition from active turbulence, and the geometric rule of pairing order transition may shed light on the strategy for designing chiral active matter.

Turbulent flows offer a rich variety of structures at large length scales and are usually obtained by driving flows out of equilibrium (1) while overcoming viscous dampening. A peculiar class of out-of-equilibrium fluids from self-propelled colloids to microswimmers and animals, stimulated from the lower scales, also present turbulence-like structures called active turbulence (2–4). For example, a dense bacterial suspension is driven out of equilibrium by the autonomous motion of bacteria suspended therein (5–7). The collective swimming of bacteria shapes the active turbulence into vortices of similar size (8–14). However, this vortical order decays over distance, making it a long-standing issue for the development of ordered dynamics at larger scales. Hence, growing attention is paid to novel strategies to control active turbulence with simple geometric design.Chirality, i.e., the nonequivalence of opposite handedness, is also ubiquitous across scales (15) and is commonly involved in active systems (16–19), either biological, such as bacteria (20–24), cytoskeletons (25–27), and fish (28), or nonbiological, consisting of self-propelled colloids (29–32). One of the effects of chirality is the nonequivalence of clockwise (CW) and counterclockwise (CCW) rotations. As for bacteria, broken mirror symmetry in flagellar rotation (CCW rotation around the tail-to-head direction during swimming) results in the opposite rotation of the cell body, which generates a net torque onto the solid surface the bacterium swims over, and in turn bends its trajectory circularly (20). Despite such intrinsic chirality in individual motion, active turbulence reported in the past showed CW and CCW global rotational directions have equal probability, indicating that mirror symmetry was recovered at the collective level (9–11, 13). Can microscopic chirality of bacterial motion be transferred into the macroscopic order of collective swimming? Such a question is a great challenge that would provide both fundamental understanding of active turbulence and technical applications for controlled material transport (33, 34).In this study, we report the chiral collective swimming of a dense bacterial suspension confined in an asymmetric (different top and bottom interfaces) but achiral (perfectly circular lateral interface) boundary, with a strongly favored rotational direction. That nonequivalence between CW and CCW collective swimming reflects the interplay between the counterrotating collective bacterial motions at each of the top and bottom interfaces. The increase of bacterial density strengthens that interplay, and CCW rotation (with respect to the bottom–top direction, later referred to as “top view”) predominates. Furthermore, we found that the collective swimming of bacteria at the top and bottom interfaces appears near the lateral boundaries and takes the form of an edge current. Its robustness with respect to the shape of the lateral boundary alters the geometric constraints ruling the self-organization of interacting bacterial vortices by promoting corotational configurations. The obtained geometric rule, in excellent agreement with experiments, brings understanding of chiral active matter in order to organize larger-scale flow.     

Two-dimensional electronic–vibrational sum frequency spectroscopy for interactions of electronic and nuclear motions at interfaces

Interactions of electronic and vibrational degrees of freedom are essential for understanding excited-states relaxation pathways of molecular systems at interfaces and surfaces. Here, we present the development of interface-specific two-dimensional electronic–vibrational sum frequency generation (2D-EVSFG) spectroscopy for electronic–vibrational couplings for excited states at interfaces and surfaces. We demonstrate this 2D-EVSFG technique by investigating photoexcited interface-active (E)-4-((4-(dihexylamino) phenyl)diazinyl)-1-methylpyridin-1- lum (AP3) molecules at the air–water interface as an example. Our 2D-EVSFG experiments show strong vibronic couplings of interfacial AP3 molecules upon photoexcitation and subsequent relaxation of a locally excited (LE) state. Time-dependent 2D-EVSFG experiments indicate that the relaxation of the LE state, S₂, is strongly coupled with two high-frequency modes of 1,529.1 and 1,568.1 cm⁻¹. Quantum chemistry calculations further verify that the strong vibronic couplings of the two vibrations promote the transition from the S₂ state to the lower excited state S₁. We believe that this development of 2D-EVSFG opens up an avenue of understanding excited-state dynamics related to interfaces and surfaces.

Electronic and vibrational degrees of freedom are the most important physical quantities in molecular systems at interfaces and surfaces. Knowledge of interactions between electronic and vibrational motions, namely electronic–vibrational couplings, is essential to understanding excited-states relaxation pathways of molecular systems at interfaces and surfaces. Many excited-states relaxation processes occur at interfaces and surfaces, including charge transfer, energy transfer, proton transfer, proton-coupled electron transfer, configurational dynamics, and so on (1–11). These relaxation processes are intimately related to the electronic–vibrational couplings at interfaces and surfaces. Strong electronic–vibrational couplings could promote nonadiabatic evolution of excited potential energy and thus, facilitate chemical reactions or intramolecular structural changes of interfacial molecules (10, 12, 13). Furthermore, these interactions of electronic and vibrational degrees of freedom are subject to solvent environments (e.g., interfaces/surfaces with a restricted environment of unique physical and chemical properties) (9, 14, 15). Despite the importance of interactions of electronic and vibrational motions, little is known about excited-state electronic–vibrational couplings at interfaces and surfaces.Interface-specific electronic and vibrational spectroscopies enable us to characterize the electronic and vibrational structures separately. As interface-specific tools, second-order electronic sum frequency generation (ESFG) and vibrational sum frequency generation (VSFG) spectroscopies have been utilized for investigating molecular structure, orientational configurations, chemical reactions, chirality, static potential, environmental issues, and biological systems at interfaces and surfaces (16–52). Recently, structural dynamics at interfaces and surfaces have been explored using time-resolved ESFG and time-resolved VSFG with a visible pump or an infrared (IR) pump thanks to the development of ultrafast lasers (6–9, 13–15, 49, 53–61). Doubly resonant sum frequency generation (SFG) has been demonstrated to probe both electronic and vibration transitions of interfacial molecular monolayer (15, 62–71). This frequency-domain two-dimensional (2D) interface/surface spectroscopy could provide information regarding electronic–vibrational coupling of interfacial molecules. However, contributions from excited states are too weak to be probed due to large damping rates of vibrational states in excited states (62, 63). As such, the frequency-domain doubly resonant SFG is used only for electronic–vibrational coupling of electronic ground states. Ultrafast interface-specific electronic–vibrational spectroscopy could allow us to gain insights into how specific nuclear motions drive the relaxation of electronic excited states. Therefore, development of interface-specific electronic–vibrational spectroscopy for excited states is needed.In this work, we integrate the specificity of interfaces and surfaces into the capabilities of ultrafast 2D spectroscopy for dynamical electronic–vibrational couplings in excited states of molecules; 2D interface-specific spectroscopies are analogous to those 2D spectra in bulk that spread the information contained in a pump−probe spectrum over two frequency axes. Thus, one can better interpret congested one-dimensional signals. Two-dimensional vibrational sum frequency generation (2D-VSFG) spectroscopy was demonstrated a few year ago (72–74). Furthermore, heterodyne 2D-VSFG spectroscopy using middle infrared (mid-IR) pulse shaping and noncollinear geometry 2D-VSFG experiments have also been developed to study vibrational structures and dynamics at interfaces (31, 75–78). Recently, two-dimensional electronic sum frequency generation (2D-ESFG) spectroscopy has also been demonstrated for surfaces and interfaces (79). On the other hand, bulk two-dimensional electronic–vibrational (2D-EV) spectroscopy has been extensively used to investigate the electronic relaxation and energy transfer dynamics of molecules, biological systems, and nanomaterials (80–90). The 2D-EV technique not only provides electronic and vibrational interactions between excitons or different excited electronic states of systems but also, identifies fast nonradiative transitions through nuclear motions in molecules, aggregations, and nanomaterials. However, an interface-specific technique for two-dimensional electronic–vibrational sum frequency generation (2D-EVSFG) spectroscopy has yet to be developed.Here, we present the development of 2D-EVSFG spectroscopy for the couplings of electronic and nucleic motions at interfaces and surfaces. The purpose of developing 2D-EVSFG spectroscopy is to bridge the gap between the visible and IR regions to reveal how structural dynamics for photoexcited electronic states are coupled with vibrations at interfaces and surfaces. As an example, we applied this 2D-EVSFG experimental method to time evolution of electronic–vibrational couplings at excited states of interface-active molecules at the air–water interface.     

Polarity mechanisms such as contact inhibition of locomotion regulate persistent rotational motion of mammalian cells on micropatterns

Pairs of endothelial cells on adhesive micropatterns rotate persistently, but pairs of fibroblasts do not; coherent rotation is present in normal mammary acini and kidney cells but absent in cancerous cells. Why? To answer this question, we develop a computational model of pairs of mammalian cells on adhesive micropatterns using a phase field method and study the conditions under which persistent rotational motion (PRM) emerges. Our model couples the shape of the cell, the cell’s internal chemical polarity, and interactions between cells such as volume exclusion and adhesion. We show that PRM can emerge from this minimal model and that the cell-cell interface may be influenced by the nucleus. We study the effect of various cell polarity mechanisms on rotational motion, including contact inhibition of locomotion, neighbor alignment, and velocity alignment, where cells align their polarity to their velocity. These polarity mechanisms strongly regulate PRM: Small differences in polarity mechanisms can create significant differences in collective rotation. We argue that the existence or absence of rotation under confinement may lead to insight into the cell’s methods for coordinating collective cell motility.Collective cell migration is a crucial aspect of wound healing, growth and development of organs and tissues, and cancer invasion (1–3). Cells may move in cohesive groups ranging from small clusters of invading cancerous cells to ducts and branches during morphogenesis to monolayers of epithelial or endothelial cells. Two hallmarks of collective migration are strong cell–cell adhesion and multicellular polarity—an organization of the cellular orientation beyond the single-cell level (1). Cell–cell interactions can lead to collective behavior not evident in any single cell, including chemotaxis in clusters of cells that singly do not chemotax (4). Collective behavior may arise from cell–cell interactions altering the polarity of individual cells (5, 6). Many theories have been proposed for how this multicellular order appears, either in specific biological contexts (7–11) or in simpler, more generic models (12–16). Some authors argue that these dynamics are relatively universal and can be understood with minimal knowledge of the signaling pathways involved (2, 17).Collective rotation is commonly observed in collectively migrating cells, especially in confinement. Persistent rotations have been observed in the slime mold Dictyostelium discoideum (18), canine kidney epithelial cells on adhesive micropatterns (19), and small numbers of endothelial cells on micropatterns (20, 21). Transient swirling patterns are also seen in epithelial monolayers (22). Recent work has also observed that the growth of spherical acini of human mammary epithelial cells in 3D matrix involves a coherent rotation persisting from a single cell to several cells; this rotation is not present in randomly motile cancerous cells (23). Similarly, cancerous cells on adhesive micropatterns do not develop coherent rotation (19). In a recent review of collective migration, Rørth (24) argues that “rotating movement seems to be a feature of normal epithelial cells when cultured under spatially confined conditions”; however, the origin of collective rotation and its controlling factors remain unclear.In this paper, we study a simple example of coordinated motion: the persistent rotational motion (PRM) of small numbers of mammalian cells crawling on micropatterned substrates. Huang et al. (20) and Huang and coworkers (21) observed that pairs of endothelial cells on islands of fibronectin robustly developed PRM in a “yin–yang” shape. By contrast, fibroblasts did not rotate, developing a straight, static interface between the two cells. We develop a computational model of multiple crawling mammalian cells that couples the cells’ mechanical deformations to their biochemical polarity (asymmetry in a chemical species) and includes both mechanical and chemical cell–cell interactions. We use this model as a framework to understand which mechanical and chemical factors regulate robust PRM of cells on micropatterns. This simple system can lead to new insights into cell–cell interactions and multicell polarity and potentially exclude or refine certain mechanisms previously proposed as the cause of collective migration. We also suggest that the yin–yang cell–cell interface shape may reflect the influence of the nucleus, which is often not modeled.     

Overriding native cell coordination enhances external programming of collective cell migration

As collective cell migration is essential in biological processes spanning development, healing, and cancer progression, methods to externally program cell migration are of great value. However, problems can arise if the external commands compete with strong, preexisting collective behaviors in the tissue or system. We investigate this problem by applying a potent external migratory cue—electrical stimulation and electrotaxis—to primary mouse skin monolayers where we can tune cell–cell adhesion strength to modulate endogenous collectivity. Monolayers with high cell–cell adhesion showed strong natural coordination and resisted electrotactic control, with this conflict actively damaging the leading edge of the tissue. However, reducing preexisting coordination in the tissue by specifically inhibiting E-cadherin–dependent cell–cell adhesion, either by disrupting the formation of cell–cell junctions with E-cadherin–specific antibodies or rapidly dismantling E-cadherin junctions with calcium chelators, significantly improved controllability. Finally, we applied this paradigm of weakening existing coordination to improve control and demonstrate accelerated wound closure in vitro. These results are in keeping with those from diverse, noncellular systems and confirm that endogenous collectivity should be considered as a key quantitative design variable when optimizing external control of collective migration.

Collective cell migration enables intricate, coordinated processes that are essential to multicellular life, spanning embryonic development, self-healing upon injury, and cancer invasion modes (1). Control of collective cell migration, therefore, would be a powerful tool for biology and bioengineering as such control would enable fundamentally new ways of regulating these key processes, such as enabling accelerated wound healing. Efficient and precise control over cell motility is becoming increasingly feasible with modern biotechnologies. Tunable chemical gradient generators can redirect chemotaxing cells (2, 3), optogenetics can allow dynamic control of cell contractility (4), micropatterned scaffolds can constrain and direct collective growth (5), and recent work in bioelectric interfaces has even demonstrated truly programmable control over directed cell migration in two dimensions (6, 7). However, despite advances in sophisticated tools, applying them to complex cellular collectives raises a fundamental problem: What happens when we command a tissue to perform a collective behavior that competes with its natural collective behaviors?Paradoxically, those endogenous collective cell behaviors already present in tissues are both a boon and bane for attempts to control and program cell behavior. On the one hand, endogenous collective cell migration means the cells already have established mechanisms for coordinated, directional migration that external cues and control can leverage. For instance, cadherin-mediated cell–cell adhesions in tissues mechanically couple cells together and allow for long-range force transmission and coordinated motion. This coupling allows tissues to migrate collectively and directionally over large distances and maintain cohesion and organization far better than individual cells might (8, 9). On the other hand, imposing a new behavior over an existing collective behavior may generate conflicts. Tight cell coupling can create a “jammed state” or solid-like tissue where cells are so strongly attached and confined that they physically lack the fluidity to migrate as a group (10, 11). Strong coordination established via physical coupling can hinder cells from responding to signals for migration, as shown by the need for zebrafish and other embryos to weaken cell–cell junctions prior to gastrulation to ensure cells collectively migrate to necessary locations (12–14). Hence, how “susceptible” a collective system may be to external control likely depends on a tug-of-war between the resilience and strength of the natural collective processes and the potency of the applied stimulus.Here, we specifically investigate the relationship and interplay between an applied, external command attempting to direct collective cell migration and the strength of the underlying collective behaviors already present in the tissue. We address two key questions. 1) How much does the strength of an endogenous collective migration behavior in a tissue limit our ability to control its collective cell migration? 2) How can we circumvent such limitations? To investigate these questions, we needed both a programmable perturbation capable of controlling collective migration and a physiologically relevant model system allowing for tunable “collectivity.” Here, we use collectivity to describe how strongly cells are coordinated with their neighbors during migration—highly collective cells exhibit strong, coordinated motion and vice versa. As a perturbation, we harnessed a bioelectric phenomenon called “electrotaxis”—directed cell migration in direct current (DC) electric fields—using our SCHEEPDOG bioreactor (6). Briefly, electrotaxis arises when endogenous, ionic fields form during healing or development (∼1 V/cm) and apply gentle electrophoretic or electrokinetic forces to receptors and structures in cell membranes, causing them to aggregate or change conformation to produce a front–rear polarity cue (15, 16). Components spanning phosphatidylinositol phosphates (PIPs), extracellular signal-regulated kinase (ERK), phosphatidylinositol 3-kinase (PI3K), phosphatase and tensin homolog (PTEN), and small guanosine triphosphate (GTP)ases have been implicated in the transduction process, while gap junctions appear to have an inconclusive role (8, 17–19). Crucially, electrotaxis may be one of the broadest and most conserved migratory cues, having been observed in vitro in over 20 cell types across multiple branches of the tree of life (20–22). As electrotaxis in vitro appears to globally stimulate all cells equally and still induce directional motion, it is distinct from more locally dependent cues such as chemotaxis and haptotaxis. However, as no other reported cue has as much versatility and programmability, electrotaxis is an ideal choice for a broadly applicable cellular control cue in this study.To complement electrotaxis, we chose primary mouse skin for our model system as skin injuries were where the endogenous electrochemical fields that cause electrotaxis were first discovered (in vivo, the wound boundary is negative relative to the surrounding epidermis), and we and others have shown layers of keratinocytes to exhibit strong electrotaxis (6, 23–25). Critically, primary mouse keratinocytes have tunable collectivity in culture as the cadherin-mediated cell–cell adhesion strength in this system can be easily tuned by varying calcium levels in the media—with low-calcium media thought to mimic conditions in the basal layers of the epidermis with weak adhesions and high-calcium media akin to conditions in the uppermost layers of skin with strong adhesions (26–28).Together, these experimental approaches allowed us to precisely explore how the ability to externally “steer” collective migration in a living tissue using a powerful bioelectric cue depends on the native collectivity of the underlying tissue. First, we quantify collective strength in cultured skin layers by measuring neighbor coordination of cellular motion [a standard metric for collective motion adapted from collective theory (29)] and then, validate that the collectivity can be tuned in our model system of mouse keratinocyte monolayers by calibrating junctional E-cadherin levels. Next, we demonstrate how applying the same electrical stimulation conditions to tissues with differing native collectivity results in radically different outputs, with weakly collective tissues precisely responding to our attempts to control their motion, while strongly collective tissues exhibited detrimental supracellular responses resulting in tissue collapse. We then prove that E-cadherin is responsible for these differences, ruling out any effects of calcium signaling per se. Finally, we leverage these findings to develop an approach that allows us to effectively control mature, strongly collective tissues, which we utilize to demonstrate that we can accelerate wound repair in vitro.     

Intermittent collective dynamics emerge from conflicting imperatives in sheep herds

Among the many fascinating examples of collective behavior exhibited by animal groups, some species are known to alternate slow group dispersion in space with rapid aggregation phenomena induced by a sudden behavioral shift at the individual level. We study this phenomenon quantitatively in large groups of grazing Merino sheep under controlled experimental conditions. Our analysis reveals strongly intermittent collective dynamics consisting of fast, avalanche-like regrouping events distributed on all experimentally accessible scales. As a proof of principle, we introduce an agent-based model with individual behavioral shifts, which we show to account faithfully for all collective properties observed. This offers, in turn, an insight on the individual stimulus/response functions that can generate such intermittent behavior. In particular, the intensity of sheep allelomimetic behavior plays a key role in the group’s ability to increase the per capita grazing surface while minimizing the time needed to regroup into a tightly packed configuration. We conclude that the emergent behavior reported probably arises from the necessity to balance two conflicting imperatives: (i) the exploration of foraging space by individuals and (ii) the protection from predators offered by being part of large, cohesive groups. We discuss our results in the context of the current debate about criticality in biology.The social interactions and behavioral mechanisms involved in the coordination of collective movements in animal groups largely determine the animals’ ability to display adapted responses when they face challenges, such as finding, efficiently, food sources (1–4) or safe resting places (5–7) or avoiding predators (8–13). Thus, the diversity of collective motion patterns observed in group-living species reflects the multiple forms of interactions individuals use for coordinating their behavioral actions (14, 15). Deciphering these interactions, their relation with the patterns emerging at the collective level, and their connections with the physiological and ecological constraints peculiar to each group-living species is crucial to understanding the evolution of collective phenomena in biological systems (16–18). So far, only a handful of quantitative datasets have been gathered for large animal groups (19–21). Most of them have focused on elementary cases where the prevailing biological imperative seems to be group cohesion, either to gain protection from potential predators, such as for the spontaneous collective motion exhibited by starling flocks (19, 22) and some fish schools (23–25), or for reproductive purposes, as in swarms of midges (21, 26).One important and, so far, often neglected aspect of collective motion is the existence of individual-level behavioral shifts, which, in turn, may trigger a transition at the collective level. For instance, in many species of fish, groups regularly alternate between a swarming state, in which fish simply aggregate with a low level of polarization, and a schooling state, in which individuals are aligned and move in the same direction (27, 28). This transition is elicited by a sudden change in the velocity of a single or a few individuals that propagates to the whole group. In many cases, the behavioral shift occurs without any perceived threat in the neighborhood, resulting in a spontaneous transition at the collective level that can be interpreted as a consequence of random individual decisions. Such alternating behavioral phases at the collective level have also been reported in refs. 29, 30.Here, we report a quantitative study of the collective behavior of large groups of Merino sheep (Ovis Aries), a highly gregarious domestic breed (31), under controlled experimental conditions. Our analysis reveals an intermittent collective dynamics where long dispersion phases—during which grazing sheep slowly spread out, exploring the foraging field—are punctuated by fast packing events, triggered by an individual-level behavioral shift. We find that these events are distributed on all experimentally accessible scales. To gain insight on the sheep individual stimulus/response function, we introduce an agent-based model that explicitly includes behavioral shifts and strong allelomimetic effects. Our model results suggest that the observed collective behavior can be generated when parameters quantifying allelomimetic behavior are sufficiently large. In this parameter range, sheep regrouping time is minimized, and a large per capita grazing surface is at sheep disposal during dispersion phases.     

Coulomb interaction,phonons, and superconductivity in twisted bilayer graphene

The polarizability of twisted bilayer graphene, due to the combined effect of electron–hole pairs, plasmons, and acoustic phonons, is analyzed. The screened Coulomb interaction allows for the formation of Cooper pairs and superconductivity in a significant range of twist angles and fillings. The tendency toward superconductivity is enhanced by the coupling between longitudinal phonons and electron–hole pairs. Scattering processes involving large momentum transfers, Umklapp processes, play a crucial role in the formation of Cooper pairs. The magnitude of the superconducting gap changes among the different pockets of the Fermi surface.

Twisted bilayer graphene (TBG) shows a complex phase diagram which combines superconducting and insulating phases (1, 2) and resembles strongly correlated materials previously encountered in condensed matter physics (3–6). On the other hand, superconductivity seems more prevalent in TBG (7–11), while in other strongly correlated materials magnetic phases are dominant.The pairing interaction responsible for superconductivity in TBG has been intensively studied. Among other possible pairing mechanisms, the effect of phonons (12–19) (see also ref. 20), the proximity of the chemical potential to a van Hove singularity in the density of states (DOS) (21–25) and excitations of insulating phases (26–28) (see also refs. 29–31), and the role of electronic screening (32–35) have been considered.In the following, we analyze how the screened Coulomb interaction induces pairing in TBG. The calculation is based on the Kohn–Luttinger formalism (36) for the study of anisotropic superconductivity via repulsive interactions. The screening includes electron–hole pairs (37), plasmons (38), and phonons (note that acoustic phonons overlap with the electron–hole continuum in TBG). Our results show that the repulsive Coulomb interaction, screened by plasmons and electron–hole pairs only, leads to anisotropic superconductivity, although with critical temperatures of order T_c ∼ 10⁻³ to 10⁻² K. The inclusion of phonons in the screening function substantially enhances the critical temperature, to T_c ∼ 1 to 10 K.     

DNA self-organization controls valence in programmable colloid design

Just like atoms combine into molecules, colloids can self-organize into predetermined structures according to a set of design principles. Controlling valence—the number of interparticle bonds—is a prerequisite for the assembly of complex architectures. The assembly can be directed via solid “patchy” particles with prescribed geometries to make, for example, a colloidal diamond. We demonstrate here that the nanoscale ordering of individual molecular linkers can combine to program the structure of microscale assemblies. Specifically, we experimentally show that covering initially isotropic microdroplets with N mobile DNA linkers results in spontaneous and reversible self-organization of the DNA into Z(N) binding patches, selecting a predictable valence. We understand this valence thermodynamically, deriving a free energy functional for droplet–droplet adhesion that accurately predicts the equilibrium size of and molecular organization within patches, as well as the observed valence transitions with N. Thus, microscopic self-organization can be programmed by choosing the molecular properties and concentration of binders. These results are widely applicable to the assembly of any particle with mobile linkers, such as functionalized liposomes or protein interactions in cell–cell adhesion.

Building blocks encoded with assembly rules harness thermal energy to put themselves together in a process called self-assembly (1, 2). These elements can be proteins (3, 4), DNA (5–8), or colloids (8–12). Akin to atoms and molecules, colloidal particles with well-defined shapes and interactions self-organize into bulk crystalline phases that minimize the free energy (13–19). More-complex objects with nonrepeating structures, such as protein folds or aperiodic crystals, require a prescribed limit to particle valence (20, 21). A fundamental goal is to fabricate structures with important technological applications (22). For example, colloidal self-assembly into a diamond lattice (10) or a quasicrystal (23, 24) is expected to exhibit photonic band gaps due to the materials’ interaction with light (25, 26). At its most complex, self-assembly of biological cells is a crucial part of the development of a living organism (27).Experimentally, valence control can be achieved by designing anisotropic sticky particles with patches to create colloidal clusters (28–30) or DNA origami that specifies the bond orientation (31, 32). Mixing particles with a given size and number ratio can result in steric valence control (33). Other proposed methods include the self-organization of nematic shells on spheres (34, 35) or the arrested phase separation of lipids on droplet surfaces (36). These processes are complex to experimentally realize, feature slow assembly kinetics due to the necessity of patch-to-patch binding, and require extensive purification (28).Unlike solid particles, droplets (37–40), lipid vesicles (41–46), and biological cells (47–50) allow any sticky binders to freely diffuse at the interface and segregate into adhesions with their neighbors. If the particles are Brownian or mobile, they can rearrange even after binding to reach the most favorable valence and geometry, avoiding kinetic bottlenecks. Angioletti-Uberti et al. (51) theoretically proposed that mobile ligands coupled with an additional repulsive potential—such as a steric brush—could yield colloidal valence selection in the bulk. More generally, the mobility and reversibility of linker binding between particles allows the system to optimize its equilibrium structure according to the laws of statistical mechanics. Not only is this strategy more robust than directed irreversible assembly, but it enables colloidal design based on the properties of molecular binders.Here, we derive and experimentally validate the free energy functional for droplet–droplet adhesion and predict the consequent thermodynamically stable valence for given control parameters. Moreover, we show that droplets recover their equilibrium valence in a matter of minutes after their bonds are broken. Our results are applicable to any functionalized particles with mobile binders, showing that molecular properties and concentration are sufficient to predetermine valence. Emulsions serve as a template for programmable solid materials because the droplets can be readily polymerized at any stage of the self-assembly process (52, 53).     

Programmable droplet manipulation and wetting with soft magnetic carpets

The ability to regulate interfacial and wetting properties is highly demanded in anti-icing, anti-biofouling, and medical and energy applications. Recent work on liquid-infused systems achieved switching wetting properties, which allow us to turn between slip and pin states. However, patterning the wetting of surfaces in a dynamic fashion still remains a challenge. In this work, we use programmable wetting to activate and propel droplets over large distances. We achieve this with liquid-infused soft magnetic carpets (SMCs) that consist of pillars that are responsive to external magnetic stimuli. Liquid-infused SMCs, which are sticky for a water droplet, become slippery upon application of a magnetic field. Application of a patterned magnetic field results in a patterned wetting on the SMC. A traveling magnetic field wave translates the patterned wetting on the substrate, which allows droplet manipulation. The droplet speed increases with an increased contact angle and with the droplet size, which offers a potential method to sort and separate droplets with respect to their contact angle or size. Furthermore, programmable control of the droplet allows us to conduct reactions by combining droplets loaded with reagents. Such an ability of conducting small-scale reactions on SMCs has the potential to be used for automated analytical testing, diagnostics, and screening, with a potential to reduce the chemical waste.

Controlling surface-wetting properties is of interest in anti-icing (1), anti-biofouling (2–4), marine (5), and environmental (6–8) applications. Liquid-infused surfaces recently received significant attention because of their success in achieving such desired wetting properties (9, 10). Additionally, surfaces with switchable wetting properties are especially sought after because they offer two or more desired states serving different functions. Recent advances demonstrated examples of switchable wetting upon optical (11), acoustic (12, 13), electrical (14, 15), mechanical (16, 17), and magnetic (18–21) stimuli. Among these options, magnetic fields offer the advantage of untethered, simple, and strong actuation. However, these demonstrations usually lack the ability to pattern the wetting of the surface in a dynamic manner and were limited in spatial control. Although previous work has successfully demonstrated a patterned wetting surface, this has only been achieved via the microfabrication of static patterns (22, 23). Furthermore, the ability to reversibly locate and manipulate multiple droplets over large distances has been challenging (10, 24, 25) because of the static nature of the manipulation designs (26, 27). Some of the methods based on magnetic fields suffered from contamination in the used magnetic particles, requiring a purification step after transportation (28, 29). The possibility of water droplet transport on magnetically responsive surfaces has also been demonstrated (30, 31). However, this system could not be easily scaled up, the droplet motion was unidirectional (especially in the board-like structures) and limited to the transport of relatively small (1 to 6 µL) droplets. Here, we suggest that external field stimuli can be used to dynamically pattern the substrate wetting. Moreover, a strategy to locally move this stimulus on the substrate can potentially lead to droplet motion. We explore this strategy by creating “soft magnetic carpets” (SMCs) through a scalable self-assembly procedure that is based on the Rosensweig instability. Recently, we used similar SMCs with no infusion layer to transport solid and liquid cargos (32). In the current work, while the carpets are infused with a liquid, they also contain soft magnetic pillars that align with magnetic fields. By placing a patterned magnetic field underneath the carpet, the alignment response of the pillars induces a wetting pattern of pin and slip states, in which the pillars are straight or bent, respectively. While the straight pillars pin the droplets that are placed on the substrate, the bent ones allow droplets to move. Furthermore, by translating this patterned magnetic field, the effect of a magnetic wave is created, leading to the spatial control of the pinned droplets on the substrate and a method that transports large droplets without having contamination. Next, we showcase that the spatial control of multiple droplets allows us to conduct reactions by transporting and sequentially merging droplets loaded with chemicals and biological specimens. The ability of conducting small-scale reactions on a soft carpet can be potentially used to automatize analytical testing and diagnostics at an increased rate and reduced costs due to the limited use of the ingredients.     

Minimal model for collective kinetochore–microtubule dynamics

Chromosome segregation during cell division depends on interactions of kinetochores with dynamic microtubules (MTs). In many eukaryotes, each kinetochore binds multiple MTs, but the collective behavior of these coupled MTs is not well understood. We present a minimal model for collective kinetochore–MT dynamics, based on in vitro measurements of individual MTs and their dependence on force and kinetochore phosphorylation by Aurora B kinase. For a system of multiple MTs connected to the same kinetochore, the force–velocity relation has a bistable regime with two possible steady-state velocities: rapid shortening or slow growth. Bistability, combined with the difference between the growing and shrinking speeds, leads to center-of-mass and breathing oscillations in bioriented sister kinetochore pairs. Kinetochore phosphorylation shifts the bistable region to higher tensions, so that only the rapidly shortening state is stable at low tension. Thus, phosphorylation leads to error correction for kinetochores that are not under tension. We challenged the model with new experiments, using chemically induced dimerization to enhance Aurora B activity at metaphase kinetochores. The model suggests that the experimentally observed disordering of the metaphase plate occurs because phosphorylation increases kinetochore speeds by biasing MTs to shrink. Our minimal model qualitatively captures certain characteristic features of kinetochore dynamics, illustrates how biochemical signals such as phosphorylation may regulate the dynamics, and provides a theoretical framework for understanding other factors that control the dynamics in vivo.Microtubule (MT) dynamics are critical for cell division. Plus ends of spindle MTs interact with kinetochores, protein complexes that assemble at the centromere of each chromosome, and these dynamic MTs exert forces to move chromosomes. Individual MTs are “dynamically unstable,” spontaneously switching between a polymerizing state and a depolymerizing state (1) with growth, shortening, and switching rates that are regulated by the forces exerted at the MT tips (2–6). For many eukaryotes, however, multiple MTs are connected to each kinetochore, giving rise to collective MT behavior that is not well understood and can be entirely different from the behavior of individual MTs. Here, we develop a model of collective MT dynamics based on the measured force-dependent dynamics of individual MTs.Accurate chromosome segregation depends on correctly biorienting the kinetochore pairs by attaching sister kinetochores to opposite spindle poles. Properly attached kinetochores undergo center-of-mass (CM) and breathing oscillations that are regulated by collective MT dynamics (7–12). Incorrect attachments—such as syntelic attachment of both kinetochores to the same pole—must be corrected (13–17). Tension may cue this process because bioriented kinetochore pairs are under tension while syntelically attached kinetochores are not (7, 9, 15, 17, 18). Error correction is also mediated by Aurora B kinase phosphorylating MT-binding kinetochore proteins (13–17, 19–21). A consistent theory of metaphase kinetochore–MT dynamics should capture CM and breathing oscillations for correctly attached pairs and elucidate the contributions of tension and phosphorylation to syntelic error correction.Several models suggest that chromosome oscillations result from competition between poleward MT-based pulling and antipoleward “polar ejection” forces (22–24). Another model proposes that oscillations occur via a general mechanobiochemical feedback (25). Models of force-dependent MTs interacting with the same object also exhibit cooperative behavior (5, 26–29). However, these models do not explain error correction dynamics. Thus, the underlying physical mechanisms coordinating metaphase chromosome motions are unclear.We address these issues by developing a minimal model for collective MT dynamics based on in vitro measurements of single MTs interacting dynamically with kinetochore proteins (4, 6, 20, 21). In the model, MT polymerization and rescue are promoted by tension and inhibited by compression, whereas depolymerization and catastrophe are enhanced by compression and reduced by tension. With just these features, we find a robust and versatile mechanism by which force-dependent MTs coupled to the same kinetochore may drive metaphase chromosome motions. The force–velocity relation for a MT bundle is fundamentally different from that of a single dynamically unstable MT, exhibiting bistable behavior. Bistability gives rise to kinetochore oscillations and is shifted by phosphorylation to produce error correction. The model qualitatively predicts kinetochore motions in our experiments in which Aurora B is hyperactivated in bioriented kinetochore pairs. Thus, we find that many characteristics of metaphase kinetochore dynamics emerge simply from the force coupling of many MTs to the same kinetochore, and chemical signals such as phosphorylation can regulate this physical mechanism.     

The spontaneous emergence of conventions: An experimental study of cultural evolution

How do shared conventions emerge in complex decentralized social systems? This question engages fields as diverse as linguistics, sociology, and cognitive science. Previous empirical attempts to solve this puzzle all presuppose that formal or informal institutions, such as incentives for global agreement, coordinated leadership, or aggregated information about the population, are needed to facilitate a solution. Evolutionary theories of social conventions, by contrast, hypothesize that such institutions are not necessary in order for social conventions to form. However, empirical tests of this hypothesis have been hindered by the difficulties of evaluating the real-time creation of new collective behaviors in large decentralized populations. Here, we present experimental results—replicated at several scales—that demonstrate the spontaneous creation of universally adopted social conventions and show how simple changes in a population’s network structure can direct the dynamics of norm formation, driving human populations with no ambition for large scale coordination to rapidly evolve shared social conventions.Social conventions are the foundation for social and economic life (1–7), However, it remains a central question in the social, behavioral, and cognitive sciences to understand how these patterns of collective behavior can emerge from seemingly arbitrary initial conditions (2–4, 8, 9). Large populations frequently manage to coordinate on shared conventions despite a continuously evolving stream of alternatives to choose from and no a priori differences in the expected value of the options (1, 3, 4, 10). For instance, populations are able to produce linguistic conventions on accepted names for children and pets (11), on common names for colors (12), and on popular terms for novel cultural artifacts, such as referring to junk email as “SPAM” (13, 14). Similarly, economic conventions, such as bartering systems (2), beliefs about fairness (3), and consensus regarding the exchangeability of goods and services (15), emerge with clear and widespread agreement within economic communities yet vary broadly across them (3, 16).Prominent theories of social conventions suggest that institutional mechanisms—such as centralized authority (14), incentives for collective agreement (15), social leadership (16), or aggregated information (17)—can explain global coordination. However, these theories do not explain whether, or how, it is possible for conventions to emerge when social institutions are not already in place to guide the process. A compelling alternative approach comes from theories of social evolution (2, 18–20). Social evolutionary theories maintain that networks of locally interacting individuals can spontaneously self-organize to produce global coordination (21, 22). Although there is widespread interest in this approach to social norms (6, 7, 14, 18, 23–26), the complexity of the social process has prevented systematic empirical insight into the thesis that these local dynamics are sufficient to explain universally adopted conventions (27, 28).Several difficulties have limited prior empirical research in this area. The most notable of these limitations is scale. Although compelling experiments have successfully shown the creation of new social conventions in dyadic and small group interactions (29–31), the results in small group settings can be qualitatively different from the dynamics in larger groups (Model), indicating that small group experiments are insufficient for demonstrating whether or how new conventions endogenously form in larger populations (32, 33). Important progress on this issue has been made using network-based laboratory experiments on larger groups (15, 24). However, this research has been restricted to studying coordination among players presented with two or three options with known payoffs. Natural convention formation, by contrast, is significantly complicated by the capacity of individuals to continuously innovate, which endogenously expands the “ecology” of alternatives under evaluation (23, 29, 31). Moreover, prior experimental studies have typically assumed the existence of either an explicit reward for universal coordination (15) or a mechanism that aggregates and reports the collective state of the population (17, 24), which has made it impossible to evaluate the hypothesis that global coordination is the result of purely local incentives.More recently, data science approaches to studying norms have addressed many of these issues by analyzing behavior change in large online networks (34). However, these observational studies are limited by familiar problems of identification that arise from the inability to eliminate the confounding influences of institutional mechanisms. As a result, previous empirical research has been unable to identify the collective dynamics through which social conventions can spontaneously emerge (8, 34–36).We addressed these issues by adopting a web-based experimental approach. We studied the effects of social network structure on the spontaneous evolution of social conventions in populations without any resources to facilitate global coordination (9, 37). Participants in our study were rewarded for coordinating locally, however they had neither incentives nor information for achieving large scale agreement. Further, to eliminate any preexisting bias in the evolutionary process, we studied the emergence of arbitrary linguistic conventions, in which none of the options had any a priori value or advantage over the others (3, 23). In particular, we considered the prototypical problem of whether purely local interactions can trigger the emergence of a universal naming convention (38, 39).     

Engineering hydrogels with homogeneous mechanical properties for controlling stem cell lineage specification

The extracellular matrix (ECM) is mechanically inhomogeneous due to the presence of a wide spectrum of biomacromolecules and hierarchically assembled structures at the nanoscale. Mechanical inhomogeneity can be even more pronounced under pathological conditions due to injury, fibrogenesis, or tumorigenesis. Although considerable progress has been devoted to engineering synthetic hydrogels to mimic the ECM, the effect of the mechanical inhomogeneity of hydrogels has been widely overlooked. Here, we develop a method based on host–guest chemistry to control the homogeneity of maleimide–thiol cross-linked poly(ethylene glycol) hydrogels. We show that mechanical homogeneity plays an important role in controlling the differentiation or stemness maintenance of human embryonic stem cells. Inhomogeneous hydrogels disrupt actin assembly and lead to reduced YAP activation levels, while homogeneous hydrogels promote mechanotransduction. Thus, the method we developed to minimize the mechanical inhomogeneity of hydrogels may have broad applications in cell culture and tissue engineering.

In tissues, cells reside in a complex extracellular microenvironment whose mechanical properties often vary both in space and in time during regular tissue homeostasis or disease development (1). Growing evidence suggests that changes in local mechanical properties can have a considerable impact on cell fate (2–6, 7–13). For example, the intricate local mechanical environment can strongly affect wound healing and tissue regeneration (14, 15). In synthetic biomaterials (e.g., hydrogels) that are used for cell culture and tissue engineering, the mechanical heterogeneity is also ubiquitous although, in many cases, undesirable (10, 16–22). For hydrogels prepared by the polymerization of monomers, variations in local monomer concentrations and the heat released from the chemical reactions can lead to various defects in the hydrogel network. For hydrogels prepared by the chemical crosslinking of polymers, the broad distribution of the molecular weight of the polymers and their nonuniform mixing before gelation can also cause dramatic variation in the local mechanical properties. Although the effect of the overall mechanical properties of hydrogels on cell behaviors has been widely explored, how mechanical heterogeneity at the nanoscale affects cell behaviors remains poorly understood.A major obstacle in addressing this question is the synthesis of hydrogels with uniformly distributed mechanical properties. By coupling four-armed poly(ethylene glycol) (PEG) macromers with narrowly distributed molecular weights, Sakai and coworkers have shown that it is possible to prepare hydrogels with minimal structural defects (23). The chemical reactions that are widely used for gelation include click chemistry (24, 25), amine-active ester reactions (26), maleimide–thiol conjugation (27, 28), and thiol-ene reactions (29, 30). The maleimide–thiol reaction is of special interest because it takes place under mild conditions, requires no catalysis, and does not generate small-molecule byproducts (27, 31–34). The hydrogels prepared by maleimide–thiol reaction have been widely used for organoid generation (35), protein and cell delivery (36), and controlled release (37). However, this reaction is too fast to allow adequate mixing of the macromer solution, leading to heterogeneous gelation. Because of variation in the crosslinking density, hydrogels often contain microdomains with distinct mechanical properties (38, 39). A few methods have been developed to minimize hydrogel heterogeneity by slowing this reaction, including lowering the gelation pH, changing the local pK_a of thiol, or adding thiol-binding metal ions (38, 40–43). However, these methods often require nonphysiological gelation conditions or lead to only limited improvement.In this work, we introduced host–guest chemistry to slow down the maleimide–thiol reaction for hydrogel preparation. We discovered that maleimide can form a complex with β-cyclodextrin (β-CD), lowering the free maleimide concentrations in the gelation system. We showed that the four-armed PEG hydrogels prepared using this approach possessed fewer network defects and more uniform mechanical properties. Moreover, we revealed that mechanical homogeneity can considerably affect the lineage specification of human embryonic stem cells (hESCs). We proposed that this effect can be attributed to the disruption of the assembly of actin fibers and the subsequent mechanotransduction pathways. We anticipate that this method can greatly improve the mechanical homogeneity of many cell culture systems to better regulate stem cell lineage specification.     

From the Cover: Chiral symmetry breaking and surface faceting in chromonic liquid crystal droplets with giant elastic anisotropy

Confined liquid crystals (LC) provide a unique platform for technological applications and for the study of LC properties, such as bulk elasticity, surface anchoring, and topological defects. In this work, lyotropic chromonic liquid crystals (LCLCs) are confined in spherical droplets, and their director configurations are investigated as a function of mesogen concentration using bright-field and polarized optical microscopy. Because of the unusually small twist elastic modulus of the nematic phase of LCLCs, droplets of this phase exhibit a twisted bipolar configuration with remarkably large chiral symmetry breaking. Further, the hexagonal ordering of columns and the resultant strong suppression of twist and splay but not bend deformation in the columnar phase, cause droplets of this phase to adopt a concentric director configuration around a central bend disclination line and, at sufficiently high mesogen concentration, to exhibit surface faceting. Observations of director configurations are consistent with Jones matrix calculations and are understood theoretically to be a result of the giant elastic anisotropy of LCLCs.The director configurations of confined liquid crystals exhibit a rich phenomenology, the physics of which is determined by a delicate interplay of topology, elastic free energy, and anchoring conditions at the boundaries (1–12). Droplets present arguably the simplest and most symmetric confining container for liquid crystals. Droplets of thermotropic liquid crystals (TLCs) and the manipulation of their director configurations, for example, are actively studied, in part because of their demonstrated use as core materials in display technologies (3, 13) and their potential applications ranging from biosensors (14, 15) to microlasers (16). Indeed, significant fundamental and technological progress has been made with TLC droplets, because their bulk elasticity and surface anchoring phenomena are now well understood and easily controlled.Lyotropic chromonic liquid crystals (LCLCs) are composed of organic, charged, and plank-like mesogens that self-assemble in water into columnar aggregates via noncovalent electrostatic, excluded volume, hydrophobic, and pi–pi stacking interactions (17–20). The aggregates, in turn, assemble into nematic or columnar phases, depending on temperature and concentration. A variety of organic molecules such as dyes, drugs, and biomolecules form LCLCs (17–28). However, far less is known about the fundamental science and applications potential of LCLCs than the more-studied TLCs. Indeed, basic properties of LCLCs, including aggregate size distribution and formation dynamics, bulk elasticity, and surface anchoring are neither fully characterized nor understood and are the subject of exciting ongoing research. Only recently, for example, have measurements been made of fundamental properties, such as the Frank–Oseen elastic constants (28, 29), of any LCLC, and they have revealed unusual concentration and temperature dependences of the splay and bend moduli and a twist modulus that is unusually small compared with the other two.Here, we explore the behavior of aqueous LCLCs droplets suspended in a background oil phase. The droplets provide an excellent platform for the study of basic LCLC properties because of their highly symmetric finite-volume confining geometry and, usually, their uniform boundary conditions. Our study investigates droplets similar to those in “classic” thermotropic LCs for which bulk elasticity and anchoring are easily characterized. Further, droplet size is more easily controlled in the water-in-oil emulsions than in systems at nematic–isotropic coexistence studied in previous work (9, 30–32). In particular, the water-in-oil emulsion system permits independent control of the continuous background phase into which one can add chemicals such as surfactants and through which one can regulate LCLC concentration to create isotropic, nematic, and columnar LCLC phases within the same drop.Specifically, we investigate configurations of Sunset Yellow FCF (SSY) LCLCs in surfactant-stabilized spherical water droplets. The experiments reveal a variety of unusual droplet types arising from nematic LCLCs'' very small twist modulus, from their room-temperature columnar phase, and from the planar anchoring of their aggregates at an oil–water interface. In the nematic phase, the director adopts a chiral-symmetry-breaking, twisted-bipolar configuration with an extraordinarily large twist revealed by polarized optical microscopy (POM). These droplets provide an archetypical example of an exotic structure that can be produced by the combination of geometric frustration and giant elastic anisotropy. In droplets of the columnar phase, which occurs at higher mesogen concentration, columns wrap in concentric circles around a central director disclination line while retaining their lattice structure. Interestingly, the lattice structure causes surface faceting of the soft boundary as the mesogen concentration is further increased.     

A traveling-wave solution for bacterial chemotaxis with growth

Bacterial cells navigate their environment by directing their movement along chemical gradients. This process, known as chemotaxis, can promote the rapid expansion of bacterial populations into previously unoccupied territories. However, despite numerous experimental and theoretical studies on this classical topic, chemotaxis-driven population expansion is not understood in quantitative terms. Building on recent experimental progress, we here present a detailed analytical study that provides a quantitative understanding of how chemotaxis and cell growth lead to rapid and stable expansion of bacterial populations. We provide analytical relations that accurately describe the dependence of the expansion speed and density profile of the expanding population on important molecular, cellular, and environmental parameters. In particular, expansion speeds can be boosted by orders of magnitude when the environmental availability of chemicals relative to the cellular limits of chemical sensing is high. Analytical understanding of such complex spatiotemporal dynamic processes is rare. Our analytical results and the methods employed to attain them provide a mathematical framework for investigations of the roles of taxis in diverse ecological contexts across broad parameter regimes.

As a fundamental part of their life cycle, bacteria spread by dispersing into and colonizing new habitats. Many species of bacteria navigate in these new habitats by sensing gradients of certain chemicals and biasing their flagellum-based swimming to move themselves along these gradients (1, 2). This process, known as chemotaxis, is among the most extensively investigated topics in molecular biology (1, 3–7) and was observed in diverse microbial habitats such as the gut (8); the soil (9); leaves (10, 11); and marine environments such as the phycosphere, sinking marine particles, and coral reefs (2, 12–14). Further, chemotaxis is employed by many eukaryotic cells such as the free-living Dictyostelium (15) and is an important element of many tissue-forming processes involved in embryogenesis (16), neuronal patterning (17), wound healing (18), and tumor metastasis (19).Beyond promoting the movements by individual cells, chemotaxis also drives the collective movement of cells leading to emergent patterns and behaviors at the population level (20, 21). Such collective dynamics have been best studied with bacteria in culture plates and microfluidic devices. For example, when Escherichia coli cells are inoculated at the center of a soft agar plate replete with nutrients, consumption of preferred chemicals (referred to as attractants) results in collective cell movement up self-generated attractant gradients (22), leading to the emergence of striking migrating bands that propagate radially outward from the inoculation site (23–25). These migrating bands typically comprise one or two peaks in population density, which stand in contrast to the predictions of canonical models of front propagation and population expansion (26–28); they also expand at much faster speeds than predicted by canonical models. These population-level changes can strongly shape fitness and ecological interactions as recent laboratory studies have shown (29–32).The first attempt to understand these migrating bands mathematically was made by Keller and Segel, who recovered a traveling-wave solution using a pair of reaction–diffusion–convection equations to describe the density of bacterial populations and the concentration of the attractant they consume (33). While being highly influential, the Keller–Segel (KS) model neglected cell growth, a substantial factor in the expansion process. It further required unrealistic assumptions on attractant sensing without which the migrating bands lose stability (34). Subsequent modeling efforts including cell growth managed to recover the stability of the bands, but their predictions did not match major experimental observations such as the sharply peaked density profiles and their rapid migration speeds (31, 35–38).Recent work by Cremer et al. (39) demonstrated that the major features of the migrating bands for E. coli in soft agar can be accurately captured using a model in which bacterial growth is independent of the attractant. Numerical solutions to their growth-expansion (GE) model quantitatively described not only the boosted speed of the migrating band but also the signature spatial profile of the bands and their dependence on molecular parameters (39). Their results established the role of attractants as an environmental cue exploited by bacteria independent of possible nutritional values to promote rapid expansion.The success of the GE model in describing E. coli in soft agar raises the possibility that the phenotype of rapid expansion and distinct density bands might also occur for chemotactic systems in the wild, in situations where growth, diffusion, and chemotaxis dominate. However, from the numerical work of Cremer et al. (39), it is not clear what aspects of their results are generalizable given that both bacterial and environmental characteristics can be vastly different in the wild. For example, bacteria living near sulphidic sediments move more than 30 times faster than E. coli (39, 40), while bacterial motility is significantly reduced by high viscosity in the gut (41, 42). Addressing the generalizability of the GE model requires a detailed mathematical analysis of the interplay of 1) growth, 2) diffusion, and 3) chemotaxis, preferably with analytical solutions. While growth and diffusion have been studied together in the canonical models of front propagation (26–28), as have diffusion and chemotaxis in the KS model (33, 36, 43–45), a sufficient understanding of the interplay of all three is still lacking.Toward obtaining such an understanding, we describe here a detailed analytical study of the GE model. Through a heuristic analysis, we derive analytic relations that describe the dependence of the expansion speed and density profile on important molecular, cellular, and environmental parameters, including the rate of cell growth, the diffusivity and availability of the attractants, the motility and sensitivity of the bacteria, carrying capacity, and the limit of attractant sensing. Our analysis reveals the key condition for the population to attain rapid expansion speed and suggests a very broad parameter regime for which rapid expansion can be expected.     

Active topolectrical circuits

The transfer of topological concepts from the quantum world to classical mechanical and electronic systems has opened fundamentally different approaches to protected information transmission and wave guidance. A particularly promising emergent technology is based on recently discovered topolectrical circuits that achieve robust electric signal transduction by mimicking edge currents in quantum Hall systems. In parallel, modern active matter research has shown how autonomous units driven by internal energy reservoirs can spontaneously self-organize into collective coherent dynamics. Here, we unify key ideas from these two previously disparate fields to develop design principles for active topolectrical circuits (ATCs) that can self-excite topologically protected global signal patterns. Realizing autonomous active units through nonlinear Chua diode circuits, we theoretically predict and experimentally confirm the emergence of self-organized protected edge oscillations in one- and two-dimensional ATCs. The close agreement between theory, simulations, and experiments implies that nonlinear ATCs provide a robust and versatile platform for developing high-dimensional autonomous electrical circuits with topologically protected functionalities.

Information transfer and storage in natural and man-made active systems, from sensory organs (1–3) to the internet, rely on the robust exchange of electrical signals between a large number of autonomous units that balance local energy uptake and dissipation (4, 5). Major advances in the understanding of photonic (6–9), acoustic (10–12), and mechanical (13–16) metamaterials have shown that topological protection (17–24) enables the stabilization and localization of signal propagation in passive and active (25–27) dynamical systems that violate time-reversal and/or other symmetries. Recent studies have successfully applied these ideas to realize topolectrical circuits (28) in the passive linear (29–34) and passive nonlinear (35, 36) regimes. However, despite substantial progress in the development of topological wave guides (37), lasers (38, 39), and transmission lines (40–43), the transfer of these concepts to active (44, 45) nonlinear circuits made from autonomously acting units still poses an unsolved challenge. From a broader perspective, not only does harnessing topological protection in nonlinear active circuits promise a new generation of autonomous devices, but also understanding their design and self-organization principles may offer insights into information storage and processing mechanisms in living systems, which integrate cellular activity, electrical signaling, and nonlinear feedback to coordinate essential biological functions (46, 47).Exploiting a mathematical analogy with active Brownian particle systems (26), we theoretically develop and experimentally demonstrate general design principles for active topolectrical circuits (ATCs) that achieve self-organized, self-sustained, topologically protected electric current patterns. The main building blocks of ATCs are nonlinear dissipative elements that exhibit an effectively negative resistance over a certain voltage range. Negative resistances can be realized using van der Pol (vdP) circuits (48), tunnel diodes, unijunction transistors, solid-state thyristors (49), or operational amplifiers set as negative impedance converters through current inversion (50), and the design principles described below are applicable to all these systems. Indeed, we expect them to apply to an even broader class of nonlinear systems, as similar dynamics also describe electromagnetic resonators with Kerr-type nonlinearities (51–53).     

Sensing surface morphology of biofibers by decorating spider silk and cellulosic filaments with nematic microdroplets

Probing the surface morphology of microthin fibers such as naturally occurring biofibers is essential for understanding their structural properties, biological function, and mechanical performance. The state-of-the-art methods for studying the surfaces of biofibers are atomic force microscopy imaging and scanning electron microscopy, which well characterize surface geometry of the fibers but provide little information on the local interaction potential of the fibers with the surrounding material. In contrast, complex nematic fluids respond very well to external fields and change their optical properties upon such stimuli. Here we demonstrate that liquid crystal droplets deposited on microthin biofibers—including spider silk and cellulosic fibers—reveal characteristics of the fibers’ surface, performing as simple but sensitive surface sensors. By combining experiments and numerical modeling, different types of fibers are identified through the fiber-to-nematic droplet interactions, including perpendicular and axial or helicoidal planar molecular alignment. Spider silks align nematic molecules parallel to fibers or perpendicular to them, whereas cellulose aligns the molecules unidirectionally or helicoidally along the fibers, indicating notably different surface interactions. The nematic droplets as sensors thus directly reveal chirality of cellulosic fibers. Different fiber entanglements can be identified by depositing droplets exactly at the fiber crossings. More generally, the presented method can be used as a simple but powerful approach for probing the surface properties of small-size bioobjects, opening a route to their precise characterization.Natural microfilaments produced by plants, insects, or spiders are fascinating materials not just because of their specific properties such as wear resistance, elasticity, tensile strength, and toughness (1–5) but also because of their microorganization (6–9). Their macroscopic properties can match properties of materials like kevlar but are at the same time biocompatible and biodegradable (10). These fascinating macroscopic properties actually originate from bulk and surface properties of the fibers (1). The chemical composition of the threads combined with their morphology determines the final properties of the material (11–13). The mechanical properties of the spider fibers are determined by the existence of a lyotropic liquid crystalline phase, from which the threads are drawn (14). Such silks are known to include nanoscale networks of defects and cavities that yield surface structures notably dependent on the spider species (3). These differences do not affect much the mechanical performance of the fibers (1, 3, 5). From a technological perspective, many attempts have been made to reproduce these natural bionetworks (15–17). In fact cellulose-based fibers with few micrometers of diameter, produced by electrospinning, can also acquire different morphologies depending upon the processing conditions, giving diverse features of the final threads and mats (18). Therefore, probing the surface structure of the microfibers is crucial for a complete understanding of their individual and interthreaded properties.From another perspective, nematic complex fluids are materials which are inherently responsive to diverse external stimuli, notably including diverse surface interactions which in the literature are known as the surface anchoring (19). Being effectively elastic materials, the orientational order of nematics responds on long, typically micrometer scales (20–22), which results in a spatially varying birefringence that can be optically detected (23). Recently, it was demonstrated that glass fibers induce numerous defects in a well-aligned nematic liquid crystal cell and thus provide a simple illustration of topological phenomena (24). It is also known that liquid crystal droplets can considerably change their structure by the action of otherwise imperceptibly small external stimuli (21). Pierced nematic and chiral nematic droplets develop defects that can be controlled by the liquid crystal elasticity, chirality, and surface boundary conditions (25, 26) indicating exceptional sensitivity. Therefore, to generalize, putting nematics into contact with diverse surfaces (18, 27) can be used as a simple but very powerful technique to detect the surface properties of microobjects such as biological fibers.In this paper we demonstrate the surface morphology sensing of biorelevant fibers, including spider silk and cellulosic microfibers, by nematic droplets that are sprayed onto the fibers. Specifically, we explore the chiral and achiral nature of the fiber’s surface and the in-plane or perpendicular alignment fields the fibers impose on the nematic. Droplets with degenerate in-plane and perpendicular alignment of the nematic at their free surfaces are explored, combining experiments and numerical modeling, to allow for tuning of the sensing precision. Further, the entanglement sites of the fiber webs are explored, with the droplets deposited at the sites clearly revealing contact, noncontact, and entangled morphologies.