Activation of indistinguishability-based quantum coherence for enhanced metrological applications with particle statistics imprint

Quantum coherence, an essential feature of quantum mechanics allowing quantum superposition of states, is a resource for quantum information processing. Coherence emerges in a fundamentally different way for nonidentical and identical particles. For the latter, a unique contribution exists linked to indistinguishability that cannot occur for nonidentical particles. Here we experimentally demonstrate this additional contribution to quantum coherence with an optical setup, showing that its amount directly depends on the degree of indistinguishability and exploiting it in a quantum phase discrimination protocol. Furthermore, the designed setup allows for simulating fermionic particles with photons, thus assessing the role of exchange statistics in coherence generation and utilization. Our experiment proves that independent indistinguishable particles can offer a controllable resource of coherence and entanglement for quantum-enhanced metrology.

A quantum system can reside in coherent superpositions of states, which have a role in the interpretation of quantum mechanics (1–4), lead to nonclassicality (5, 6), and imply the intrinsically probabilistic nature of predictions in the quantum realm (7, 8). Besides this fundamental role, quantum coherence is also at the basis of quantum algorithms (9–14) and, from a modern information-theoretic perspective, constitutes a paradigmatic basis-dependent quantum resource (15–17), providing a quantifiable advantage in certain quantum information protocols.For a single quantum particle, coherence manifests itself when the particle is found in a superposition of a reference basis, for instance, the computational basis of the Hilbert space. Formally, any quantum state whose density matrix contains nonzero diagonal elements when expressed in the reference basis is said to display quantum coherence (16). This is the definition of quantum coherence employed in our work. For multiparticle compound systems, the physics underlying the emergence of quantum coherence is richer and strictly connected to the nature of the particles, with fundamental differences for nonidentical and identical particles. A particularly intriguing observation is that the states of identical particle systems can manifest coherence even when no particle resides in superposition states, provided that the wave functions of the particles overlap (18–20). In general, a special contribution to quantum coherence arises thanks to the spatial indistinguishability of identical particles, which cannot exist for nonidentical (or distinguishable) particles (18). Recently, it has been found that the spatial indistinguishability of identical particles can be exploited for entanglement generation (21), applicable even for spacelike-separated quanta (22) and against preparation and dynamical noises (23–26). The presence of entanglement is a signature that the bipartite system as a whole carries coherence even when the individual particles do not, the amount of this coherence being dependent on the degree of indistinguishability. We name this specific contribution to quantumness of compound systems “indistinguishability-based coherence,” in contrast to the more familiar “single-particle superposition-based coherence.” Indistinguishability-based coherence qualifies in principle as an exploitable resource for quantum metrology (18). However, it requires sophisticated control techniques to be harnessed, especially in view of its nonlocal nature. Moreover, a crucial property of identical particles is the exchange statistics, while its experimental study requiring operating both bosons and fermions in the same setup is generally challenging.In the present work, we investigate the operational contribution of quantum coherence stemming from the spatial indistinguishability of identical particles. The main aim of our experiment is to prove that elementary states of two independent spatially indistinguishable particles can give rise to exploitable quantum coherence, with a measurable effect due to particle statistics. By utilizing our recently developed photonic architecture capable of tuning the indistinguishability of two uncorrelated photons (27), we observe the direct connection between the degree of indistinguishability and the amount of generated coherence and show that indistinguishability-based coherence can be concurrent with single-particle superposition-based coherence. In particular, we demonstrate its operational implications, namely, providing a quantifiable advantage in a phase discrimination task (28, 29), as depicted in Fig. 1. Furthermore, we design a setup capable of testing the impact of particle statistics in coherence production and phase discrimination for both bosons and fermions; this is accomplished by compensating for the exchange phase during state preparation, simulating fermionic states with photons, which leads to statistics-dependent efficiency of the quantum task.Open in a separate windowFig. 1.Illustration of the indistinguishability-activated phase discrimination task. A resource state ρin that contains coherence in a computational basis is generated from spatial indistinguishability. The state then enters a black box which implements a phase unitary U^k=eiG^ϕk,k∈{1,…,n} on ρin. The goal is to determine the ϕk actually applied through the output state ρout: indistinguishability-based coherence provides an operational advantage in this task.     

Global phosphorus retention by river damming

More than 70,000 large dams have been built worldwide. With growing water stress and demand for energy, this number will continue to increase in the foreseeable future. Damming greatly modifies the ecological functioning of river systems. In particular, dam reservoirs sequester nutrient elements and, hence, reduce downstream transfer of nutrients to floodplains, lakes, wetlands, and coastal marine environments. Here, we quantify the global impact of dams on the riverine fluxes and speciation of the limiting nutrient phosphorus (P), using a mechanistic modeling approach that accounts for the in-reservoir biogeochemical transformations of P. According to the model calculations, the mass of total P (TP) trapped in reservoirs nearly doubled between 1970 and 2000, reaching 42 Gmol y⁻¹, or 12% of the global river TP load in 2000. Because of the current surge in dam building, we project that by 2030, about 17% of the global river TP load will be sequestered in reservoir sediments. The largest projected increases in TP and reactive P (RP) retention by damming will take place in Asia and South America, especially in the Yangtze, Mekong, and Amazon drainage basins. Despite the large P retention capacity of reservoirs, the export of RP from watersheds will continue to grow unless additional measures are taken to curb anthropogenic P emissions.The systematic damming of rivers began with the onset of the Industrial Revolution and peaked in the period from 1950 to 1980 (1, 2). After slowing down during the 1990s, the pace of dam building has recently risen again sharply (3). As a consequence, the number of hydroelectric dams with generating capacity >1 MW is expected to nearly double over the next two decades (2). The current surge in dam construction will increase the proportion of rivers that are moderately to severely impacted by flow regulation from about 50% at the end of the 20th century to over 90% by 2030 (3). Homogenization of river flow regimes resulting from damming is a growing, worldwide phenomenon and has been invoked as one of the reasons for the decline in freshwater biodiversity (4).Another major global driver of environmental change of river systems is enrichment by anthropogenic nutrients, in particular phosphorus (P) (5, 6). Fertilizer use, soil erosion, and the discharge of wastewater have more than doubled the global P load to watersheds compared with the inferred natural baseline (7–10). Because P limits or colimits primary productivity of many aquatic ecosystems, increased river fluxes of P have been identified as a main cause of eutrophication of surface water bodies, including lakes and coastal marine environments (6, 11, 12). River damming and P enrichment are interacting anthropogenic forcings, because sediments accumulating in reservoirs trap P and, thus, reduce the downstream transfer of P along the river continuum (13–15). This raises the question to what extent P retention by dams may offset anthropogenic P enrichment of rivers.The number of published studies from which P retention efficiencies in dam reservoirs can be obtained is small: an extensive literature search only yields useable data for 155 reservoirs (Dataset S1), that is, less than 0.2% of the ∼75,000 dam reservoirs larger than 0.1 km² (16). The existing data nonetheless clearly show that even a single dam can significantly alter the flow of P along a river. For example, dam-impounded Lake Kariba (Zambezi River), Lake Diefenbaker (South Saskatchewan River), and Lac d’Orient (Seine River) sequester ∼87%, 94%, and 71% of their total P inflows, respectively (17–19). For the 1 million km² Lake Winnipeg watershed, 28 reservoirs and lakes accumulate over 90% of the total P load (18). The global retention of P by dams, however, remains poorly constrained (20, 21). Previous estimations have simply applied a correction factor to river P loads to represent retention by dams (22–24). This approach does not distinguish between the various chemical forms of P, nor does it account for differences in reservoir hydraulics or provide information about uncertainties on retention estimates.Here, we follow a mass balance modeling approach developed previously to calculate the global retention of nutrient silicon by dams (25). The mass balance model represents the key biogeochemical processes controlling P cycling in reservoirs (Fig. 1). The model separates total P (TP) into the following pools: total dissolved P (TDP); particulate organic P (POP); exchangeable P (EP); and unreactive particulate P (UPP). UPP consists mostly of crystalline phosphate minerals that are inert on reservoir-relevant timescales (≤100 y); TDP comprises inorganic and organic forms of P, whereas EP includes orthophosphate and organic P molecules sorbed to or coprecipitated with oxides, clay minerals, and organic matter. Reactive P (RP) is defined as the sum of TDP, EP, and POP; RP represents the potentially bioavailable fraction of TP.Open in a separate windowFig. 1.Mass balance model used to estimate retention of P in reservoirs. F_in,i is the influx of the ith P pool into the reservoir, F_i,out is the corresponding efflux out of the reservoir, F₁₂ represents P fixation by primary productivity, F₂₁ represents mineralization of POP, F₁₃ and F₃₁ are the sorption and desorption rates of dissolved P, and F_i,bur is the permanent burial flux of the ith particulate P pool in the reservoir’s sediments.Global predictive relationships for the retention of TP and RP in reservoirs are derived from a Monte Carlo analysis of the model, which accounts for parameter variability within expected ranges. The relationships are applied to the reservoirs in the Global Reservoirs and Dams (GRanD) database (16), to estimate the sequestration of TP and RP by dams in each of the major river basins of the world. Throughout, P retention efficiencies in a reservoir are defined asRX=Xin−XoutXin,[1]where R_X is the fractional retention of TP or RP, and X_in and X_out are the input and output fluxes of TP or RP in units of mass per unit time. Annual amounts of TP and RP retained in a reservoir are then calculated by multiplying the R_X values with the corresponding TP and RP input fluxes from the dam’s upstream watershed. The latter are obtained from the Global-NEWS-HD model, which estimates emission yields for dissolved inorganic P (DIP), dissolved organic P (DOP), and particulate P (PP), of which 20% is assumed to be reactive (7, 26). The Global-NEWS-HD yield estimates are based on the biogeophysical characteristics, population density, socioeconomic status, land use, and climatic conditions within the drainage basin (20).Because the biogeochemical mass balance model explicitly represents the in-reservoir transformations between the different forms of P, it allows us to estimate how dams modify both the total and reactive fluxes of P along rivers. With the proposed approach, we reconstruct global TP and RP retentions by dams in 1970 and 2000 and make projections for 2030. For the latter, we apply the nutrient P loading trends developed for the four Millennium Ecosystem Assessment (MEA) scenarios (27). The results illustrate the evolving role of damming in the continental P cycle and, in particular, the ongoing geographical shift in P retention resulting from the current boom in dam construction.     

Using a generative model of affect to characterize affective variability and its response to treatment in bipolar disorder

The affective variability of bipolar disorder (BD) is thought to qualitatively differ from that of borderline personality disorder (BPD), with changes in affect persisting longer in BD. However, quantitative studies have not been able to confirm this distinction. It has therefore not been possible to accurately quantify how treatments like lithium influence affective variability in BD. We assessed the affective variability associated with BD and BPD as well as the effect of lithium using a computational model that defines two subtypes of variability: affective changes that persist (volatility) and changes that do not (noise). We hypothesized that affective volatility would be raised in the BD group, noise would be raised in the BPD group, and that lithium would impact affective volatility. Daily affect ratings were prospectively collected for up to 3 y from patients with BD or BPD and nonclinical controls. In a separate experimental medicine study, patients with BD were randomized to receive lithium or placebo, with affect ratings collected from week −2 to +4. We found a diagnostically specific pattern of affective variability. Affective volatility was raised in patients with BD, whereas affective noise was raised in patients with BPD. Rather than suppressing affective variability, lithium increased the volatility of positive affect in both studies. These results provide a quantitative measure of the affective variability associated with BD and BPD. They suggest a mechanism of action for lithium, whereby periods of persistently low or high affect are avoided by increasing the volatility of affective responses.

Excessive affective variability, sometimes called affective instability, characterizes psychiatric diagnoses such as bipolar disorder (BD) and borderline personality disorder (BPD) (1–4), and is associated with adverse outcomes across diagnoses (5, 6). It has been suggested that affective instability may be an important treatment target across a range of psychiatric presentations (3, 7, 8).Different types of affective variability are thought to exist; when asked to retrospectively describe their experiences, patients with BD report longer periods of raised or lowered affect, whereas patients with BPD report a higher frequency variation of affect (4). Consistent with this difference, mood stabilizing medications such as lithium, which reduce the occurrence of mania and depression (i.e., particularly prolonged periods of extreme affect) in BD (9), have not been found to be effective in patients diagnosed with BPD (10).Affective variability may be directly estimated from prospectively collected affect ratings, with a variety of different metrics of variability described (11–14). However, the different measures of variability tend to be highly correlated with one another (14) and to date do not clearly capture the qualitative differences in duration of affective changes described by patients. That is, previous work with prospectively collected data has not shown longer-lasting changes of affect in BD and shorter-lived changes in BPD. Rather, the same measures of affective variability that are raised in BPD (11, 15–18) are generally also raised, to a somewhat lesser degree, in bipolar disorder (11), posttraumatic stress disorder, and bulimia nervosa (16). Existing measures of variability of affect ratings therefore lack diagnostic specificity and cannot account for differences in treatment response between diagnoses.An alternative approach to conceptualizing and measuring the variability of an outcome is to construct a generative model of how that outcome is produced and then to invert the model using Bayes’ rule (19, 20). A generative model formally describes the assumed causal processes that produce an outcome (Fig. 1); inversion of the model creates a “Bayesian filter” (19–22), which allows one to start with the observations and then to estimate distinct, model-defined causes of variability within a single, overarching framework.Open in a separate windowFig. 1.A Bayesian filter to estimate types of affective variability. (A) A graphical illustration of the generative model that describes how affect ratings (represented by yt) are produced at each time point. The hypothesized causal processes leading to the production of the ratings is controlled by the nodes mut, SDt, vmut,kmu, and vSD, which are described in the main text. (B) An illustration of the types of variability in the generative model. Circles represent individual affect ratings, sequentially generated from top to bottom. The color of the circle indicates the distribution from which it was drawn. One type of variability, volatility (vmut, red arrow), arises from a shift in the distribution (from brown to pink), leading to a change in all subsequent ratings. A second type of variability, noise (SDt, blue arrow), arises from the sampling of the ratings from the distributions and leads to independent changes in each rating. (C) Behavior of the Bayesian filter using synthetic data. The black line illustrates a time series of synthetic data drawn from the range 0–1. The data contains periods in which volatility is high (time 1–120 and 301–360) and others in which it is low (time 121–300). Similarly, it contains periods in which noise is high (time points 61–120 and 241–360) and low (time 1–60 and 121–240). The green line illustrates the Bayesian filter''s belief about the mean of the generative process, mut, at each time point. As can be seen, the filter changes its estimate of the mean when it thinks variability in the data is caused by volatility (e.g., time 1–60) and does not alter its estimate of the mean when it thinks variability is caused by noise (e.g., time 260–300). It is able to adapt to changes in the level of volatility and noise, although it occasionally misattributes the cause (e.g., when the noise increases at time 240, the filter initially believes this is caused by an increase in volatility before correctly attributing it to noise by time 260). (D) The filter''s estimate of volatility (red line) and noise (blue line) from the same synthetic data as (C). Panels C and D are adapted from ref. 20.In this paper, we inverted a simple generative model of affect, as measured using ratings of momentary affect (Fig. 1), to estimate two different causes of affective variability, captured as changes in the affective ratings over time: volatility, which leads to persistent change in affect, and noise, which leads to transient change. We applied this approach to prospectively collected affect ratings of patients with BD and BPD as well as control subjects to assess whether it was able to capture the qualitative differences in affective variability between these diagnostic groups. We then used the model to characterize the causal effects of lithium on affective variability in an experimental medicine study of patients with BD. We hypothesized that BD would be associated with increased affective volatility and BPD with increased affective noise, and that lithium would impact affective volatility.     

A physical model of mantis shrimp for exploring the dynamics of ultrafast systems

Efficient and effective generation of high-acceleration movement in biology requires a process to control energy flow and amplify mechanical power from power density–limited muscle. Until recently, this ability was exclusive to ultrafast, small organisms, and this process was largely ascribed to the high mechanical power density of small elastic recoil mechanisms. In several ultrafast organisms, linkages suddenly initiate rotation when they overcenter and reverse torque; this process mediates the release of stored elastic energy and enhances the mechanical power output of extremely fast, spring-actuated systems. Here we report the discovery of linkage dynamics and geometric latching that reveals how organisms and synthetic systems generate extremely high-acceleration, short-duration movements. Through synergistic analyses of mantis shrimp strikes, a synthetic mantis shrimp robot, and a dynamic mathematical model, we discover that linkages can exhibit distinct dynamic phases that control energy transfer from stored elastic energy to ultrafast movement. These design principles are embodied in a 1.5-g mantis shrimp scale mechanism capable of striking velocities over 26 m s−1 in air and 5 m s−1 in water. The physical, mathematical, and biological datasets establish latching mechanics with four temporal phases and identify a nondimensional performance metric to analyze potential energy transfer. These temporal phases enable control of an extreme cascade of mechanical power amplification. Linkage dynamics and temporal phase characteristics are easily adjusted through linkage design in robotic and mathematical systems and provide a framework to understand the function of linkages and latches in biological systems.

Latch-mediated spring actuation (LaMSA) is a class of mechanisms that enable small organisms to achieve extremely high accelerations (1–5). Small organisms generate fast movements by storing elastic energy and mediating its release through latching. LaMSA mechanisms are found across the tree of life, including fungi, plants, and animals, with such iconic movements as found in trap-jaw ant mandibles, frog legs, chameleon tongue projection, fungal ballistospores, and exploding plant seeds (4–8). While the use of materials for elastic energy storage and release has been examined to some extent (9–11), the principles of how latches enable storage of elastic energy and mediate its release have only recently begun to be explored (12, 13). Indeed, even after half a century of investigation, one of the most extensively studied and impressive LaMSA systems, the mantis shrimp (Stomatopoda), uses a latch mechanism that is not yet fully understood.In recent years, robots have grown in their importance as physical models for studying the mechanics and dynamics of organisms and their behaviors (14–18). Such models can be manipulated—both at design time and at run time—in ways that natural systems cannot, thus providing tools for the study of organism functional morphology, neuroethology, and operation in different environments. Here, based on previous studies of mantis shrimp biomechanics, we develop physical and analytical models to elucidate the latch-based control of energy flow during mantis shrimp strikes and, more broadly, to establish the design principles for repeated use, extreme mechanical power amplification in small engineered devices.Mantis shrimp use a LaMSA mechanism to achieve among the fastest predatory strikes in the animal kingdom, reaching extreme accelerations with their raptorial appendages on the order of 106 rad s−2 in water. These strikes are so fast that they create cavitation bubbles and break hard molluscan shells—an impressive feat given their small size (19–22). Even the largest species, the peacock mantis shrimp (Odontodactylus scyllarus), has a striking appendage (carpus, propodus, and dactyl segments of the raptorial appendage, colored in purple in Fig. 1C) length of only 2.65 cm. Mantis shrimp store potential energy through deformation of an elastic mechanism in the merus segment which is composed of a saddle-shaped piece of the exoskeleton (the “saddle”) and another stiff yet deformable region of the exoskeleton (called the “meral-V”) (23–27); see the blue segments in Fig. 1C. These components are part of a four-bar linkage mechanism that transforms stored elastic energy into the rapid rotation of the extremely fast strikes (28, 29). Biologists have long known about two small structures, called sclerites, which are embedded in the apodemes (tendons) of the flexor muscles that release the strikes (28, 30, 31). These tiny structures brace against the interior of the merus segment and oppose the forces of the large, antagonistic extensor muscles that load the elastic mechanism. When the extensor muscles contract to load potential energy, the sclerites serve as a contact latch to prevent the rotation of the striking appendages. Then the flexor muscles release the sclerites to allow the striking appendage to rotate. Once the contact latch is released, the extensor muscle remains contracted while the elastic mechanism recoils to actuate the rotation of the striking body. The locked position of the sclerites and subsequent release are shown in SI Appendix, Fig. S13. The exact locations of the sclerites, apodemes of the flexor muscle, and meres segment in mantis shrimp can be found in figure 3 in ref. 25. A representative striking motion of a mantis shrimp can be found in Movie S5.Open in a separate windowFig. 1.An overview of biologically inspired physical models that generate extreme accelerations. (A) A diagram illustrating high acceleration within biological and synthetic LaMSA systems. From left to right, two synthetic systems, water strider-inspired robot (44) and flea-inspired robot (69), and two biological systems, flea (70) and snipefish (36, 71), are shown. A survey of more acceleration data of biological and synthetic LaMSA systems can be found in table 1 of ref. 4. Water strider–inspired robot image from ref. 69. Reprinted with permission from American Association for the Advancement of Science. Flea-inspired robot image ©2012 Institute of Electrical and Electronics Engineers; reprinted, with permission, from ref. 43. Flea image credit: CanStockPhoto/ottoflick. Snipefish image credit: Wikimedia Commons/Tony Ayling. (B) Photograph of our mantis shrimp–inspired mechanism and photograph of a peacock mantis shrimp by Roy Caldwell. The proposed mantis shrimp robot generates 104 m s−2 for striking the arm, and the mantis shrimp generates 2.5×105 m s−2 for striking the appendage (19). Photographs adjusted for contrast with background removed. Adapted with permission from ref. 28. (C) (Right) The four-bar linkage in the mantis shrimp appendage is labeled (a to d). Adapted with permission from ref. 28. The striking arm has three tightly coupled components (dactyl, propodus, and carpus), which are colored purple. Two exoskeleton elastic components are colored blue. Last, the extensor muscle, which actuates the striking motion, is colored red. (Middle) A geometric abstraction of the four-bar linkage with two rigid bodies, the arm and the body. (Left) The synthetic realization of the proposed four-bar linkage with one variable-length link. The body is highlighted orange, and the arm is purple. Flexures which allow articulation are shown in yellow. The mechanism is secured to a 3D printed base using two screws. A tendon, shown in red, is used to actuate the mechanism. A series of holes in the base allow the tendon pulling angle to be adjusted between experiments. Potential energy is stored in a torsion spring (blue).In general, after loading the potential energy in the spring, the role of the contact latch (sclerites) is to lock the system in this loaded configuration. For a typical spring loaded mechanism with a contact latch, and once the physical latch is removed, the spring would immediately begin to release the stored energy. However, analyses of the temporal sequence of loading and release of the strikes reveal a substantial time delay between release of these small latches and the onset of rotation of the appendage (20, 28, 32, 33). Therefore, biologists have hypothesized, but not tested, that while the sclerites initiate unlatching, a second, geometric latch mediates the actuation of the appendage by the recoiling elastic mechanism (5, 33, 34).Latches can be classified into three types—fluidic, contact, and geometric (4, 5)—and contact latches (e.g., the sclerites shown in SI Appendix, Fig. S13) have previously been studied and assumed to be a primary latch mechanism in mantis shrimp. Contact latches are dependent on a physical structure blocking motion, while geometric latches are based on kinematic linkage mechanisms. Ninjabot uses a contact latch, and is, to our knowledge, the only other physical model of the mantis shrimp striking appendage (35). Ninjabot’s striking arm is part of a large assembly with a hand-cranked ratchet and pawl mechanism. It was designed to emulate the speed and acceleration of mantis shrimp strikes and to characterize the fluid dynamics of the striking motion but not to emulate the linkage or latch mechanics.Four-bar linkages can function as geometric latches if they mediate a sudden directional change of rotational motion (36–39). One type of geometric latch is a torque-reversal latch that consists of an n-bar linkage (most often a four-bar) where the kinematics of the linkage admits at least one point in the configuration space such that an infinitesimal motion of a configuration variable results in an instantaneous change in the sign of the torque around one or more joints (5). A four-bar–based geometric latch is depicted in Fig. 2 A and B in which the torque reversal is achieved when the system passes through a linkage overlap. Typically, the linkage overlap condition within a four-bar mechanism is denoted as an overcentering configuration. In engineered devices, the overcentering property of four-bar linkages is frequently used. For example, a four-bar linkage has been used to design a robust aircraft landing gear (40, 41). The spring attached within the four-bar linkage provides bistability of the downlocked and uplocked positions of the landing gear, which also reduces the load on the actuator. The primary design goal for this simple example lies in the stability of the two extreme configurations, whereas we focus our study on the rapid acceleration experienced when crossing the overcentering configuration.Open in a separate windowFig. 2.A planar model for the four-bar linkage of the mantis shrimp. (A) Dimensions and inertial components of two rotating bodies composed with the four-bar links (L0,L1,L2,lt). Arm and body are shown. The arm rotates away from the body (θ2) as the spring recoils (θ1). An external force, Ft, acts on the tendon, and a torsional spring, with spring coefficient ks, is attached between the body and ground (shown here as a linear spring for convenience; a torsional spring is used in the physical system). The two generalized coordinates are θ1 and θ2. (B) Configurations before and after overcentering are shown. The tendon links, lt, for both configurations are colinear and thus overlap in this drawing. (C) Direction of the generalized constraint torque, τ, between the arm and body when in contact. The constraint torque is a reaction force which is nonzero only when the arm is in contact with the body. In our physical model, there is an offset contact angle, denoted as ϕ, between the arm and the body when they are in contact.Geometric latches have been proposed in fleas, snapping shrimp, and mantis shrimp (36, 38, 39, 42) and designed into synthetic systems, such as a flea-inspired insect-scale jumping robot (43). A more recent design, demonstrated in a water strider inspired robot (44), uses a symmetric four-bar torque reversal linkage (45). A four-bar linkage in snipefish feeding strikes causes a rapid rotational direction change, as inferred from functional morphology and micro-CT scans (36). Rotation reversal is initiated via a separate triggering muscle, and the four-bar linkage exhibits a singular overcentering configuration. This causes the linkage to rotate in the reverse direction after overcentering.Until now, the mantis shrimp four-bar linkage mechanism has been analyzed solely as a mechanical pathway to transfer energy from their elastic mechanism to the rotation of their appendages (19, 28, 29, 46–49); however, through the additional lens of a hypothesized geometric latch, previous biological analyses of the linkage mechanism may need to be revisited. The four-bar linkage in a mantis shrimp’s raptorial appendage is composed of four links and pivots (Fig. 1C) (28). The link connecting the carpus and merus is formed by contracted muscles (c–d in Fig. 1C) as also occurs in other biological linkage and lever mechanisms that operate as LaMSA systems only during configurations determined by muscle activation (50–53). In mantis shrimp, the merus extensor muscles contract during spring loading and remain contracted during unlatching and spring recoil (30, 33); therefore, the link formed by the contracted extensor muscles is shorter during the operation of the LaMSA mechanism than when it is not being used (i.e., when the extensor muscles are not contracted to load the elastic mechanism) (28). The change in the extensor muscle length reduces by 10% relative to its relaxed position while loading energy in the saddle and meral-V (28).An accurate dynamic model can allow us to explore the initiation and switching between spring loading and spring actuation phases which are crucial for control of energy flow and reducing abrupt changes that cause damage (1, 54). A previous analytical derivation of latch release dynamics for a contact-based latch model (13) was possible because the contact latch component was in contact with the projectile: the unlatched condition occurs when the latch and projectile are no longer in contact. In contrast, mathematically defining latch release for a geometric latch is challenging due to the absence of a physical component serving as a latch. Nevertheless, inspired by the fact that the mantis shrimp’s striking body (carpus, propodus, and dactyl) and the meral-V are in contact while extensor muscles load the elastic components, the latching (and latched) phase can be identified by the constraint force holding the striking body and the meral-V together. As we will demonstrate in this study, a dynamic model for switching between phases can be properly defined using constrained Lagrangian mechanics (55). A dynamic mathematical model of four-bar latch dynamics has the potential to reveal previously hidden geometric latching control in four-bar systems, which is especially likely in systems with a contractile link. Thus, inspired by the controllable link length in the mantis shrimp’s raptorial appendage, we construct mathematical and physical models of a mantis shrimp–inspired four-bar mechanism with three rigid links and one variable-length link (red) at c–d shown in Fig. 1C (akin to muscle activation control).We take a three-pronged approach to establishing the general principles of latching dynamics in LaMSA systems and specifically the geometric latch hypothesized to control mantis shrimp striking. We first present our physical model inspired by mantis shrimp LaMSA and linkage mechanics. This physical model includes multiple degrees of freedom (DoFs) and flexure-based flexible joints and uses a linear spring for potential energy storage. In parallel, we develop a dynamic mathematical model composed of multiple rigid bodies and assume linear models for the stiffness and damping at each joint. We reanalyze and incorporate a previously published dataset of mantis shrimp kinematics to revisit the linkage dynamics and incorporate the hypothesized geometric latching process. Finally, we conduct a series of experiments on the physical model in both air and water to test how latch release can be controlled with various conditions of tendon control, fluidic loading, and mechanism design.     

Empirical social triad statistics can be explained with dyadic homophylic interactions

The remarkable robustness of many social systems has been associated with a peculiar triangular structure in the underlying social networks. Triples of people that have three positive relations (e.g., friendship) between each other are strongly overrepresented. Triples with two negative relations (e.g., enmity) and one positive relation are also overrepresented, and triples with one or three negative relations are drastically suppressed. For almost a century, the mechanism behind these very specific (“balanced”) triad statistics remained elusive. Here, we propose a simple realistic adaptive network model, where agents tend to minimize social tension that arises from dyadic interactions. Both opinions of agents and their signed links (positive or negative relations) are updated in the dynamics. The key aspect of the model resides in the fact that agents only need information about their local neighbors in the network and do not require (often unrealistic) higher-order network information for their relation and opinion updates. We demonstrate the quality of the model on detailed temporal relation data of a society of thousands of players of a massive multiplayer online game where we can observe triangle formation directly. It not only successfully predicts the distribution of triangle types but also explains empirical group size distributions, which are essential for social cohesion. We discuss the details of the phase diagrams behind the model and their parameter dependence, and we comment on to what extent the results might apply universally in societies.

Recognizing the fundamental role of triadic interactions in shaping social structures, Heider (1) introduced the notion of balanced and unbalanced triads. A triad (triangle) of individuals is balanced if it includes zero or two negative links; otherwise, it is unbalanced. Heider (1) hypothesized that social networks have a tendency to reduce the number of unbalanced triangles over time such that balanced triads would dominate in a stationary situation. This theory of “social balance” has been confirmed empirically in many different contexts, such as schools (2), monasteries (3), social media (4), or computer games (5). Social balance theory and its generalizations (6–8) have been studied extensively for more than a half century for their importance in understanding polarization of societies (9), global organization of social networks (10), evolution of the network of international relations (11), opinion formation (12, 13), epidemic spreading (14, 15), government formation (16), and decision-making processes (17).Following Heider’s intuition (18–41), current approaches toward social balance often account for the effect of triangles on social network formation in one way or another. For example, the models in refs. 22 and 23 consider a reduction of the number of unbalanced triads either in the neighborhood of a node or in the whole network. The latter process sometimes leads to imbalance due to the existence of so-called jammed states (42). In order to reach social balance, individuals can also update their links according to their relations to common neighbors (18–21) or adjust link weights via opinion updates (24, 25) or via a minimization of social stress based on triadic interactions (37–44). These works not only ignore the difficulty of individuals to know the social interactions beyond their direct neighbors in reality, so far, they also have not considered the detailed statistical properties of the over- or underrepresentation of the different types of triads, such as those reported in refs. 4 and 5, with the exception of refs. 43 and 44.It is generally believed that the similarity of individuals plays a crucial role in the formation of social ties in social networks, something that has been called homophily (45–48). This means that to form a positive or negative tie with another person, people compare only pairwise overlaps in their individual opinions (dyadic interaction). It has also been argued that social link formation takes into account a tendency in people to balance their local interaction networks in the sense that they introduce friends to each other, that they do give up friendships if two mutual friends have negative attitudes toward each other, and that they tend to avoid situations where everyone feels negatively about the others. This is the essence of social balance theory (1). Obviously, link formation following social balance is cognitively much more challenging than homophily-based link formation since in the former, one has to keep in mind the many mutual relations between all your neighbors in a social network. While social balance–driven link formation certainly occurs in the context of close friendships, it is less realistic to assume that this mechanism is at work in social link formation in general. In Fig. 1, we schematically show the situation in a portion of a social network. It is generally hard for node i to know all the relations between his neighbors j, k, and l.Open in a separate windowFig. 1.Schematic view of opinion and link updates in a society. Every individual has an opinion vector whose components represent (binary) opinions on G=5 different subjects. Red (blue) links denote positive (negative) relationships. The question marks denote unknown relationships between i’s neighbors. As an agent i flips one of its opinions (red circle), si1, from 1 to –1, i can either decrease or increase its individual stress, H(i), depending on the value of the parameter α (Eq. 1). For instance, H(i) would increase if α=1 but would decrease for α=0. For high “rationality” values of individuals w.r.t. social stress, as quantified by β, the latter is more likely to be accepted, resulting in a reduction of the number of unbalanced triads in i’s neighborhood.Here, assuming that it is generally unrealistic for individuals to know their social networks at the triadic level, we aim to understand the emergence and the concrete statistics of balanced triads on the basis of dyadic or one-to-one interactions. Therefore, we use a classic homophily rule (45, 46) to define a “stress level” between any pair of individuals based on the similarity (or overlap) of their individual opinions. Here, the opinions of an individual i are represented by a vector with G components, si, that we show in Fig. 1. Homophily implies that i and j tend to become friends if the overlap (e.g., scalar product of their opinion vectors) is positive, and they become enemies if the overlap is negative. Such a specification of homophily is often referred to as an attraction–repulsion or assimilation–differentiation rule (49, 50). Assuming that, generally, social relations rearrange such as to minimize individual social stress on average, we will show that balanced triads naturally emerge from purely dyadic homophilic interactions without any explicit selection mechanisms for specific triads. We formulate the opinion link dynamics leading to social balance within a transparent physics-inspired framework. In particular, we observe a dynamic transition between two different types of balanced steady states that correspond to different compositions of balanced triads.Explaining the empirical statistics of triangles in social systems is a challenge. Early works considered groups of a few monks in a monastery (3) or a few students in classrooms (51). The studies suffered from limited data and small network sizes. Large-scale studies were first performed in online platforms (4) and in the society of players of the massive multiplayer online game (MMOG) Pardus. Players in Pardus engage in a form of economic life, such as trade and mining, and in social activities, such as communication on a number of channels, forming friendships and enmities (details are in refs. 5, 52, and 53). In the social networks of this game, balanced triads were once more confirmed to be overrepresented compared with what is expected by chance. Similar patterns of triad statistics were also observed in Epinion, Slashdot, and Wikipedia (4). More details on the Pardus society are in Materials and Methods. This dataset gives us the unique possibility to validate the model and compare the predictions with actual triangle statistics and formation of positively connected groups that are foundational to social cohesion.     

From the Cover: Stretchable origami robotic arm with omnidirectional bending and twisting

Inspired by the embodied intelligence observed in octopus arms, we introduce magnetically controlled origami robotic arms based on Kresling patterns for multimodal deformations, including stretching, folding, omnidirectional bending, and twisting. The highly integrated motion of the robotic arms is attributed to inherent features of the reconfigurable Kresling unit, whose controllable bistable deploying/folding and omnidirectional bending are achieved through precise magnetic actuation. We investigate single- and multiple-unit robotic systems, the latter exhibiting higher biomimetic resemblance to octopus’ arms. We start from the single Kresling unit to delineate the working mechanism of the magnetic actuation for deploying/folding and bending. The two-unit Kresling assembly demonstrates the basic integrated motion that combines omnidirectional bending with deploying. The four-unit Kresling assembly constitutes a robotic arm with a larger omnidirectional bending angle and stretchability. With the foundation of the basic integrated motion, scalability of Kresling assemblies is demonstrated through distributed magnetic actuation of double-digit number of units, which enables robotic arms with sophisticated motions, such as continuous stretching and contracting, reconfigurable bending, and multiaxis twisting. Such complex motions allow for functions mimicking octopus arms that grasp and manipulate objects. The Kresling robotic arm with noncontact actuation provides a distinctive mechanism for applications that require synergistic robotic motions for navigation, sensing, and interaction with objects in environments with limited or constrained access. Based on small-scale Kresling robotic arms, miniaturized medical devices, such as tubes and catheters, can be developed in conjunction with endoscopy, intubation, and catheterization procedures using functionalities of object manipulation and motion under remote control.

Compared to traditional robotic arms, where rigid links are connected by joints to provide rotational and translational degrees of freedom (DOFs), the soft counterparts in cephalopods—for example, octopus arms—exhibit intriguing features such as large and continuous deformations, adjustable compliance, and agile motions for moving and preying (1). Inspired by such biosystems, compliant mechanisms like foldable origami have been explored, as they allow reshaping of planar materials or structures into intricate three-dimensional (3D) architectures in various scales for robotic motions (2, 3) that can be applied to engineering fields including morphing structures (4–7), biomedical devices (8, 9), aerospace (10, 11), and electronics (12–14). Different origami mechanisms for robotic arms have been studied to achieve motions such as contraction (15, 16), deployment (17–19), bending (20, 21), and twisting (22, 23). These motions have been demonstrated for various functions—for instance, object grasping and biopsy (24–28). However, most existing origami robotic arms’ motions are hindered by limited DOFs, such as contraction/deployment-only (29), single-directional bending (30), and bidirectional bending (31). Although some systems have been developed to have limited integrated motions with multiple DOFs, they generally rely on multiple bulky actuators and/or wired driving forces—for example, motors (22, 23, 32) and pneumatic pumps (33)—which significantly limit the operation flexibility and versatility of the robotic arm in harsh environments with limited human and machine access. Motivated by these existing problems, a remotely actuated origami mechanism that can provide agile multi-DOF deformation for integrated large contraction/deployment, omnidirectional bending, and twisting is highly desired.Kresling origami, created from buckling of thin shell cylinders (34, 35), is an ideal building block for the origami robotic arm due to its inherent capability of multimodal deformation that provides deploying/folding and bending. As shown in Fig. 1A, the folding/deploying is induced by an in-plane torque Ti, and the bending is induced by an out-of-plane torque To. In-plane and out-of-plane are defined with respect to the plane of the undeformed hexagonal plane. The bistable Kresling origami with the stable folded state [0] and the stable deployed state [1] is achieved by geometrical design (36) (SI Appendix, Fig. S1). Under application of a positive in-plane torque (counterclockwise direction), the folded unit (stable state [0]) gradually deploys with the increased torque and snaps to the stable state [1] after it overcomes the energy barrier (Fig. 1B). Similarly, the deployed unit can fold back to the stable state [0] under a negative torque (SI Appendix, Fig. S2). When an out-of-plane torque is applied to the top hexagon of the Kresling unit, it bends with an angle of θ, defined as the angle between the horizontal direction and the top hexagon (Fig. 1C and SI Appendix, Fig. S3). The bending angle increases with the applied out-of-plane torque and has a maximum value due to the geometric constraints of the pattern. As discussed above, the direction and plane of the applied torque together determine the Kresling origami’s deformation mode: folding/deploying or bending. To realize fast-switchable deformation modes, we introduce magnetic actuation (37–40) to effectively and remotely control the instantaneous shift of the torque direction and torque plane for highly integrated complex motions, which haven’t been achieved by conventional actuation strategies (31, 32). With delicate designs of the magnetic Kresling structures and precise controls of the applied magnetic field, origami robotic arms with integrated multimodal deformations for large contraction/deployment, omnidirectional bending, and twisting are demonstrated in the following sections. Meanwhile, magnetic actuation enables small-scale robotic arms with the capability of flexible omnidirectional bending and integrated motions, allowing for the development of miniaturized medical devices in confined biomedical environments, such as stomach, intestine, trachea, and bronchi.Open in a separate windowFig. 1.Actuation mechanisms of magnetic Kresling unit for folding/deploying, bidirectional bending, and omnidirectional bending. (A) Folding/deploying and bending deformation modes of Kresling origami induced by in-plane and out-of-plane torques, respectively. (B) Mechanical characterization of the folding and deploying processes. Images show the folded unit (stable state [0]) and deployed unit (stable state [1]). (C) Mechanical characterization of the bending behavior. Dots are from experimental measurements, fitted by a polynomial function. C, Insets are images of a unit with different bending angles. (D) Magnetic Kresling with designed inclined magnetization (60°) for both folding/deploying and omnidirectional bending. (E) Actuation mechanism of folding/deploying induced by the in-plane magnetization Mi and in-plane magnetic field B. (F) Phase diagram showing the magnetic field conditions for switching the Kresling unit with inclined magnetization from the folded state (stable state [0]) to the deployed state (stable state [1]). Dots are from experimental measurements, fitted by a polynomial function. (G) Actuation mechanism of bidirectional bending induced by the in-plane magnetization Mi and out-of-plane magnetic field B. (H) Actuation mechanism of omnidirectional bending induced by the out-of-plane magnetization Mo and in-plane magnetic field B. (I) Polar plot and experimental images showing the bending angles in all directions. The applied magnetic field is perpendicular to the axial direction of the undeformed unit with inclined magnetization. The gray area denotes the conditions when the folded unit deploys.     

Decoupling between Shockley partials and stacking faults strengthens multiprincipal element alloys

Mechanical properties are fundamental to structural materials, where dislocations play a decisive role in describing their mechanical behavior. Although the high-yield stresses of multiprincipal element alloys (MPEAs) have received extensive attention in the last decade, the relation between their mechanistic origins remains elusive. Our multiscale study of density functional theory, atomistic simulations, and high-resolution microscopy shows that the excellent mechanical properties of MPEAs have diverse origins. The strengthening effects through Shockley partials and stacking faults can be decoupled in MPEAs, breaking the conventional wisdom that low stacking fault energies are coupled with wide partial dislocations. This study clarifies the mechanistic origins for the strengthening effects, laying the foundation for physics-informed predictive models for materials design.

Multiprincipal element alloys (MPEAs) have triggered ever-increasing interest from the physics and materials science community due to their huge unexplored compositional space and superior physical, mechanical, and functional properties (1–12). They also provide an ideal platform to study fundamental physical mechanisms (6, 9, 13, 14). With the rise of MPEAs, understanding their mechanical properties has become a central topic in materials science in the last decade. In face-centered cubic (fcc) MPEAs, the motion of partial dislocations (Shockley partials) and their associated stacking faults (SF) defines their mechanical properties. Alloys with low SF energies (SFEs) have more extended SFs, which are generally believed to have more strength and ductility through twinning-induced plasticity (TWIP) and transformation-induced plasticity (TRIP) mechanisms (15–17).Although extensive endeavors have been made, the commonalities in the origins of high-yield stresses shared by many MPEAs remain elusive. Among the most common intrinsic contributions of yield stresses are the lattice friction (or Peierls stress) and solute solution strengthening (18–22). Since the birth of MPEAs, it has been a controversy about the relative importance of Peierls stress among the other contributions of yield stress, including the solid-solution strengthening effect (18, 21–23). Many researchers assume small Peierls stresses based on the common wisdom of conventional alloys and pure metals (24, 25) and the low SFEs in MPEAs. Low SFEs usually accompany small Peierls stresses. Overall, this controversy originates from the lack of accurate dislocation geometry in MPEAs, which allows for a direct, critical evaluation of the Peierls stress. There are reports on the dislocation geometry in MPEAs, but almost all of them focused on the widths of SFs (26–28). In contrast, the core widths of Shockley partials are rarely reported for MPEAs, partly due to the difficulty in measurements and partly due to unawareness of its importance. To address this issue, we need very accurate determination of the core width of the Shockley partials. It is an important input parameter for mechanical simulations and various theories and models (21, 29–31). Here, we adopt three of the most extensively studied MPEAs, NiCoCr, VCoNi, and CoCrFeNiMn, and their only common fcc element, Ni, to address the above issues.The commonalities in the origins of high-yield stresses shared by the MPEAs can be indicated by the minimum energy profile along the dislocation motion path, i.e., the increased energies introduced by generalized SFEs (GSFEs; Fig. 1A). The local minima of the curves are SFEs, and the maxima are the theoretical energy barriers for pure shearing, which is a good indicator of the changes of Peierls stresses. Assisted by the accurate density functional theory (DFT), we compute GSFE curves for several representative MPEAs and their common fcc component Ni. This identifies a surprising fact: One of the representative MPEAs, NiCoCr, has a decoupled strengthening effect, i.e., it has a narrower dislocation core of Shockley partial than pure Ni, although its SF is much wider than Ni. Usually, in fcc alloys, when SFE is lower, its unstable SFE (USFE) (maximal GSFE) is also lower, which is coupled. Examples include the two other MPEAs, VCoNi and CoCrFeNiMn, and many Mg alloys (basal plane dislocations) (25) and Al alloys (32). However, NiCoCr does not follow this convention. The understanding from multiscale simulations, atomistic simulations, and the high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) images rationalizes the narrow core of Shockley partials. These results clearly reveal the diverse and decoupled mechanistic origins for the strengthening effects in the MPEAs with excellent mechanical properties.Open in a separate windowFig. 1.GSFEs of three representative MPEAs and pure Ni. (A) The schematic for the generation of GSFs along the slip direction. The displacement 0.75 is equivalent to –0.25 due to the adopted periodic boundary condition. (B) The atom models at two representative displacements for GSFs. (C) The dashed lines are the fitting of the data points to equation γ=γ0sin 2(πx)+(γu−γ0/2)sin 2(2πx) (64, 65). (D) The GSFEs in C are along the path indicated by the white arrows on the gamma surface, i.e., the minimum energy projected along the path denoted by the orange arrow. The GSFE curves reveal the origin for the wide SF and smaller half-width of Shockley partial of NiCoCr than Ni. We need to decrease SFE, while increasing γ_u, in order to optimize the mechanical properties.     

Photon gating in four-dimensional ultrafast electron microscopy

Ultrafast electron microscopy (UEM) is a pivotal tool for imaging of nanoscale structural dynamics with subparticle resolution on the time scale of atomic motion. Photon-induced near-field electron microscopy (PINEM), a key UEM technique, involves the detection of electrons that have gained energy from a femtosecond optical pulse via photon–electron coupling on nanostructures. PINEM has been applied in various fields of study, from materials science to biological imaging, exploiting the unique spatial, energy, and temporal characteristics of the PINEM electrons gained by interaction with a “single” light pulse. The further potential of photon-gated PINEM electrons in probing ultrafast dynamics of matter and the optical gating of electrons by invoking a “second” optical pulse has previously been proposed and examined theoretically in our group. Here, we experimentally demonstrate this photon-gating technique, and, through diffraction, visualize the phase transition dynamics in vanadium dioxide nanoparticles. With optical gating of PINEM electrons, imaging temporal resolution was improved by a factor of 3 or better, being limited only by the optical pulse widths. This work enables the combination of the high spatial resolution of electron microscopy and the ultrafast temporal response of the optical pulses, which provides a promising approach to attain the resolution of few femtoseconds and attoseconds in UEM.In ultrafast electron microscopy (UEM) (1–3), electrons generated by photoemission at the cathode of a transmission electron microscope are accelerated down the microscope column to probe the dynamic evolution of a specimen initiated by an ultrafast light pulse. The use of femtosecond lasers to generate the electron probe and excite the specimen has made it possible to achieve temporal resolution on the femtosecond time scale, as determined by the cross-correlation of the optical and electron pulses. One important method in the UEM repertoire is photon-induced near-field electron microscopy (PINEM) (4, 5), in which the dynamic response detected by the electron probe is the pump-induced charge density redistribution in nanoscale specimens (6).Photon–electron coupling is the basic building block of PINEM, which takes place in the presence of nanostructures when the energy-momentum conservation condition is satisfied (4, 5). This coupling leads to inelastic gain/loss of photon quanta by electrons in the electron packet, which can be resolved in the electron energy spectrum (5, 7, 8). This spectrum consists of discrete peaks, spectrally separated by multiples of the photon energy (n?ω), on the higher and lower energy sides of the zero loss peak (ZLP) (4) (Fig. 1). The development of PINEM enables the visualization of the spatiotemporal dielectric response of nanostructures (9), visualization of plasmonic fields (4, 5) and their spatial interferences (10), imaging of low atomic number nanoscale materials (11), characterization of ultrashort electron packets (12, 13), and imaging of different biological structures (14).Open in a separate windowFig. 1.Concept of photon gating in 4D electron microscopy. (A) The microscope column with one electron (dark blue) and two optical (red) pulses focused onto the specimen. The wavefunctions of the three pulses are schematically shown at the top. One optical pulse is coincident with the electron pulse at the specimen to generate a PINEM signal. The resulting light blue PINEM pulse is sliced out from other electrons for detection as an energy spectrum, an image, or a diffraction signal (see the text). The second optical pulse initiates the dynamics to be probed. (B) Electron energy spectrum generated at the specimen plane when optical and electron pulses arrive simultaneously. The gain energy range is shaded light blue. (C) Illustration for the temporal pulse sequence, two optical and one electron pulse for ultrafast time-resolved PINEM measurements.As shown by Park et al. (5), the PINEM intensity (I_PINEM) is given by the square modulus of the field integral F˜0 (i.e., IPINEM∝|F˜0|2), in the weak interaction limit. The near field of a nanoparticle leads to the scattering of the electron packet, which can be treated rigorously using the Schrödinger equation/Mie scattering theory. It follows that PINEM images the object and displays its field characteristics depending on its shape, the polarization and wavelength of optical excitation, and the width of pulses used. For a spherical nanoparticle, the field integral at point (x, y) in the specimen plane is simplified to give (6)F˜0≈−iE˜0⁡cos⁡ϕχs 23 a3(Δk)2K[Δkb],[1]where E˜0 is the electric field amplitude of the incident light, ? the light polarization angle, a the particle radius, b=x2+y2 the impact parameter, K the modified Bessel function of the second type, Δk the momentum change of the electron, and χ_s = 3(ε ? 1)/(ε + 2), where χ_s is the material susceptibility and ε the dielectric function.In previous studies of the parameters in Eq. 1, only E˜0 was time dependent. The PINEM intensity, at a given point in space, was a function only of the time delay between the optical and electron pulses, providing, for the pulse lengths currently used, a cross-correlation profile when this delay was scanned across the time of temporal coincidence, or t = 0 (4, 5, 9, 13). Hitherto, PINEM has not been used to study the ultrafast dynamics of matter. Here, we follow the strategy of using the PINEM gain electrons generated by a first optical pulse, whose delay relative to the electron pulse is maintained at t = 0, to probe dynamics initiated by introduction of a second optical pulse on the specimen, as proposed theoretically in ref. 15. By this approach, we were able to optically gate the electron pulse (i.e., create an electron pulse that only lasts for the duration of the optical pulse) and achieve significant enhancement of the temporal resolution (see the second paragraph below).The concept of the experiment is illustrated by Fig. 1A, in which the electron pulse in blue and one optical pulse (P₁) in red are shown arriving at the specimen plane simultaneously. Interaction between photon and electron in the presence of the specimen “slices out” the light blue pulse of gain electrons, which are separated from all other electrons by energy dispersion or filtering to be detected according to microscope settings in spectroscopy, imaging, or diffraction mode, as illustrated schematically at the bottom of the column. Note, it is possible to obtain PINEM diffraction, but this is not the subject of this paper. A second, or pump, optical pulse (P₂) is shown below the specimen, having already triggered the dynamics of interest. A series of time axes is plotted in Fig. 1C showing examples of characteristic sequences of pulse arrival times at the specimen plane during the experiment, with the pump arrival defining the zero of time.A striking feature of this technique that was alluded to above is the potential for high temporal resolution, unlimited by the electron pulse duration, because the optical pulse acts as a temporal gate for a longer electron pulse. In the weak interaction limit, the duration of the pulse of PINEM electrons emulates that of the optical pulse that created it (15), as clearly shown in Fig. 1A. When these photon-gated electrons are used to probe dynamics triggered by a second ultrafast optical pulse, the time resolution is determined by the cross-correlation of the two optical pulses. This paves the way for the realization of attosecond electron microscopy, as done in all-optical spectroscopy (16) but with the spatial resolution being that of atomic motions. As suggested in Fig. 1A, we envisage the use of the photon-gated electron pulses, in imaging or in diffraction mode, for the study of a variety of optically initiated material processes, either of the nanostructure or of its surrounding media.The PINEM signal can be directly monitored to detect changes in any of the specimen optical or physical properties expressed in Eq. 1. Here, we demonstrate the use of the time-resolved PINEM technique where it is shown that the photoinduced dielectric response of VO₂—which is strongly related to the lattice symmetry (17)—manifests itself in a change in PINEM intensity. We relate the changes in optical properties of the polycrystalline VO₂ nanoparticles to the phase transition dynamics from initial (monoclinic) insulator phase to (tetragonal) metal phase, the subject of numerous previous studies.Vanadium dioxide has been discussed as an active metamaterial (18) and one of the best candidates for solid-state ultrafast optical switches in photonics applications (19, 20) due to its unique structural photoinduced phase transition behavior (21). This phase transition has been examined by investigating the change in the heat capacity through thermal excitation (22, 23), whereas its ultrafast dynamics has been studied by optical spectroscopy (24, 25), THz spectroscopy (26, 27), X-ray diffraction (28, 29), ultrafast electron crystallography (30), and electron microscopy (31).     

SOD1 aggregation in ALS mice shows simplistic test tube behavior

A longstanding challenge in studies of neurodegenerative disease has been that the pathologic protein aggregates in live tissue are not amenable to structural and kinetic analysis by conventional methods. The situation is put in focus by the current progress in demarcating protein aggregation in vitro, exposing new mechanistic details that are now calling for quantitative in vivo comparison. In this study, we bridge this gap by presenting a direct comparison of the aggregation kinetics of the ALS-associated protein superoxide dismutase 1 (SOD1) in vitro and in transgenic mice. The results based on tissue sampling by quantitative antibody assays show that the SOD1 fibrillation kinetics in vitro mirror with remarkable accuracy the spinal cord aggregate buildup and disease progression in transgenic mice. This similarity between in vitro and in vivo data suggests that, despite the complexity of live tissue, SOD1 aggregation follows robust and simplistic rules, providing new mechanistic insights into the ALS pathology and organism-level manifestation of protein aggregation phenomena in general.So far, the difficulty to experimentally measure protein aggregation in live tissue has focused many researchers to infer mechanistic details of neurodegenerative disease from molecular studies in vitro. An important outcome of this in vitro development is the establishment of rational protocols for quantitative assessment of protein aggregation data (1–4), which now start to consolidate our view of what is happening (5). Protein aggregation follows general and simplistic rules dictated by the amino acid sequence. However, the sheer number of competing aggregation sites within a typical protein chain (6) makes the process intrinsically malleable and dependent on experimental conditions (7). The nagging concern is then to what extent these already complex in vitro data are transferable to the even more complex situation in vivo? Here, we shed light on this question by comparing directly in vitro aggregation kinetics with corresponding data from transgenic mice using a recently developed in vivo quantification strategy based on antibodies (8). Our model system is the aggregation of superoxide dismutase 1 (SOD1) associated with the motor neuron disease ALS (8) (Fig. 1). A key feature of this system is that the immature apoSOD1 monomer, which is also implicated as a precursor in human pathology (9–12), needs to be globally unfolded to fibrillate in vitro (7) (Fig. 1). This simplistic behavior presents the experimental advantage that the fibrillation kinetics of apoSOD1 show simple dependence on structural stability (13, 14):ΔGD−N=−RTlnKD−N=−RTln[N][D],[1]where N is the soluble native structure, and D is the aggregation-competent unfolded state. Accordingly, it has been shown that the in vitro fibrillation of apoSOD1 displays the characteristic fingerprint of fragmentation-assisted growth (15) with a square root dependence on [D] (7), consistent with the requirement of sample agitation to expedite the reaction (1–4, 10). Analogous fibrillation behavior is found for β2-microglobulin (2), yeast prions Sup35 (16) and Ure2p (17), insulin (18), WW domain (19), TI 127 (20), and α-synuclein (21). The main difference between these proteins seems to be that some are intrinsically disordered and constantly aggregation-competent by lacking the ability to hide sticky sequence material by folding. In this study, we see that this simplistic in vitro behavior also translates to the more complex conditions in live tissue: the survival times of ALS mice expressing SOD1 variants of different stabilities are directly correlated with the in vivo levels of globally unfolded protein. Also, spinal cords of mice expressing the human SOD1 mutation G93A show exponential buildup of SOD1 aggregates with a square root dependence on log[D] indistinguishable from the fibrillation kinetics observed in agitated test tubes. The data raise fundamental questions about not only the striking resemblance between mouse and test tube aggregation but also, the apparent differences with human ALS pathology, which seems to have less ordered progression. Clues to the latter, however, are hinted in data from homozygous D90A mice showing two strains of structurally distinct SOD1 aggregates.Open in a separate windowFig. 1.SOD1 aggregation in vitro and in ALS mice. (A) Aggregation of SOD in test tubes yields fibrillar structures similar to those of other proteins (7). (B) Immunohistochemistry of the ventral horn in the terminal hSOD1^G93A mouse showing characteristics of aggresomes (44). (C) Competition between SOD1 folding and fibrillation in vitro, where elongation occurs by unfolded monomers through an encounter complex (7). The question that we ask is how do the in vitro and in vivo aggregations compare mechanistically. (D) Agitation-induced fibrillation in vitro with representative data from an SOD1 mutant in 0 (blue) and 5 M (red) urea with the associated statistics of τ_1/2 for repeated measures. To account for this statistical variation, we use the distribution average (Table S1). (E) Log plot of ν_max vs. τ_1/2 for all individual measures in this study showing uniform behavior of the various SOD1 mutants and a slope of one characteristic for exponential growth (1–4). ALS-associated SOD1 mutations examined in ALS mice (red) (Table S1), other ALS-associated mutations (blue) (Table S1), and SOD1 control mutations (black) (Table S1).     

From hidden order to antiferromagnetism: Electronic structure changes in Fe-doped URu2Si2

In matter, any spontaneous symmetry breaking induces a phase transition characterized by an order parameter, such as the magnetization vector in ferromagnets, or a macroscopic many-electron wave function in superconductors. Phase transitions with unknown order parameter are rare but extremely appealing, as they may lead to novel physics. An emblematic and still unsolved example is the transition of the heavy fermion compound URu2Si2 (URS) into the so-called hidden-order (HO) phase when the temperature drops below T0=17.5 K. Here, we show that the interaction between the heavy fermion and the conduction band states near the Fermi level has a key role in the emergence of the HO phase. Using angle-resolved photoemission spectroscopy, we find that while the Fermi surfaces of the HO and of a neighboring antiferromagnetic (AFM) phase of well-defined order parameter have the same topography, they differ in the size of some, but not all, of their electron pockets. Such a nonrigid change of the electronic structure indicates that a change in the interaction strength between states near the Fermi level is a crucial ingredient for the HO to AFM phase transition.

The transition of URu2Si2 from a high-temperature paramagnetic (PM) phase to the hidden-order (HO) phase below T0 is accompanied by anomalies in specific heat (1–3), electrical resistivity (1, 3), thermal expansion (4), and magnetic susceptibility (2, 3) that are all typical of magnetic ordering. However, the small associated antiferromagnetic (AFM) moment (5) is insufficient to explain the large entropy loss and was shown to be of extrinsic origin (6). Inelastic neutron scattering (INS) experiments revealed gapped magnetic excitations below T0 at commensurate and incommensurate wave vectors (7–9), while an instability and partial gapping of the Fermi surface was observed by angle-resolved photoemission spectroscopy (ARPES) (10–16) and scanning tunneling microscopy/spectroscopy (17, 18). More recently, high-resolution, low-temperature ARPES experiments imaged the Fermi surface reconstruction across the HO transition, unveiling the nesting vectors between Fermi sheets associated with the gapped magnetic excitations seen in INS experiments (14, 19) and quantitatively explaining, from the changes in Fermi surface size and quasiparticle mass, the large entropy loss in the HO phase (19). Nonetheless, the nature of the HO parameter is still hotly debated (20–23).The HO phase is furthermore unstable above a temperature-dependent critical pressure of about 0.7 GPa at T=0, at which it undergoes a first-order transition into a large moment AFM phase where the value of the magnetic moment per U atom exhibits a sharp increase, by a factor of 10 to 50 (6, 24–30). When the system crosses the HO → AFM phase boundary, the characteristic magnetic excitations of the HO phase are either suppressed or modified (8, 31), while resistivity and specific heat measurements suggest that the partial gapping of the Fermi surface is enhanced (24, 27).As the AFM phase has a well-defined order parameter, studying the evolution of the electronic structure across the HO/AFM transition would help develop an understanding of the HO state. So far, the experimental determination of the Fermi surface by Shubnikov de Haas (SdH) oscillations only showed minor changes across the HO → AFM phase boundary (32). Here, we take advantage of the HO/AFM transition induced by chemical pressure in URu2Si2, through the partial substitution of Ru with Fe (33–37), to directly probe its electronic structure in the AFM phase using ARPES. As we shall see, our results reveal that changes in the Ru 4d–U 5f hybridization across the HO/AFM phase boundary seem essential for a better understanding of the HO state.     

Defined core–shell particles as the key to complex interfacial self-assembly

The two-dimensional self-assembly of colloidal particles serves as a model system for fundamental studies of structure formation and as a powerful tool to fabricate functional materials and surfaces. However, the prevalence of hexagonal symmetries in such self-assembling systems limits its structural versatility. More than two decades ago, Jagla demonstrated that core–shell particles with two interaction length scales can form complex, nonhexagonal minimum energy configurations. Based on such Jagla potentials, a wide variety of phases including cluster lattices, chains, and quasicrystals have been theoretically discovered. Despite the elegance of this approach, its experimental realization has remained largely elusive. Here, we capitalize on the distinct interfacial morphology of soft particles to design two-dimensional assemblies with structural complexity. We find that core–shell particles consisting of a silica core surface functionalized with a noncrosslinked polymer shell efficiently spread at a liquid interface to form a two-dimensional polymer corona surrounding the core. We controllably grow such shells by iniferter-type controlled radical polymerization. Upon interfacial compression, the resulting core–shell particles arrange in well-defined dimer, trimer, and tetramer lattices before transitioning into complex chain and cluster phases. The experimental phase behavior is accurately reproduced by Monte Carlo simulations and minimum energy calculations, suggesting that the interfacial assembly interacts via a pairwise-additive Jagla-type potential. By comparing theory, simulation, and experiment, we narrow the Jagla g-parameter of the system to between 0.9 and 2. The possibility to control the interaction potential via the interfacial morphology provides a framework to realize structural features with unprecedented complexity from a simple, one-component system.

Two-dimensional (2D) colloidal self-assembly enables fundamental studies of structure formation and has the potential to yield defined surface patterns from simple and inexpensive building blocks. The ideal template to experimentally study 2D colloidal self-assembly are liquid interfaces (1–3). Colloidal particles strongly adsorb to such liquid interfaces (4, 5) and are therefore inherently confined in two dimensions, yet retain the mobility required to form ordered arrangements. The interfacially assembled colloidal monolayer can be subsequently transferred to a solid substrate, providing nanoscale surface patterns with useful functionalities in a range of technologies (6, 7), including photonics (8, 9), phononics (10, 11), plasmonics (12, 13), solar cell engineering (14), cell-surface interactions (15, 16), or liquid repellency (17, 18).The structural motifs accessible to 2D colloidal assembly are typically determined by the shape of the particles via their most efficient packing. In particular, the general propensity of spherical particles to assemble into hexagonal lattices limits the versatility of using spherical building blocks to create complex structures. Surface patterns with increasing complexity have been achieved by multiple deposition steps (19, 20), deformation of preassembled lattices upon transfer to a solid substrate (21), or mechanical stretching of the underlying substrates (22). While these approaches can provide practical solutions, they do not alter the fundamental self-assembly process itself.An elegant solution to directly decouple particle shape from the resulting self-assembled phases has been theoretically proposed decades ago. In 1998, Jagla showed that a simple addition of a soft repulsive shell surrounding a hard sphere introduces a second length scale in the interaction potential, which allows for the creation of nonhexagonal minimum energy configurations (MECs) such as chains, squares, and rhombic phases (23). The formation of such counterintuitive phases results from the competition between the two length scales in the interaction: when the core–shell particles are compressed such that their shells begin to touch, the system can minimize its energy by fully overlapping neighboring shells in some directions in order to prevent the overlap of shells in other directions (24–26). Jagla further showed that the generic potential, shown in Fig. 1A and Eq. 1, provides flexibility to tune the resultant self-assembly behavior. In particular, the minimum energy phase in such core–shell systems is determined by three parameters: the ratio of the shell-to-core diameter (r1/r0), the shape of the soft repulsive potential, expressed by the parameter g, and the area fraction of the system (η), which determines the total amount of shell overlap (23, 27). Since this initial discovery, many theoretical reports have shown that dozens of different structures can originate from simple spherical particles interacting via such Jagla-like potentials, including honeycombs, or quasicrystals of various symmetries for relative small shell-to-core ratios (r1/r0≲2) (26–30), as well as defined particle clusters and complex chains phases at higher shell-to-core ratios (r1/r0≳2) (24, 31–35).Open in a separate windowFig. 1.Interfacial morphology of soft particle systems and hypothesized interaction potentials. (A) While a crosslinked shell retains a quasi–three-dimensional character at the interface (red), the noncrosslinked polymer shell of hairy particles can spread efficiently into a two-dimensional corona (blue). (B) Interaction potentials of the two different interfacial morphologies, calculated using a simple model where the repulsive potential is assumed to be proportional to the volume of shell overlap. A linear ramp Jagla potential (g=1) is also shown for comparison. (C) Reaction scheme to synthesize hairy particles with controllable shell thickness. A silica core is functionalized with an iniferter molecule, from which defined poly(2-dimethylaminoethyl) methacrylate (PDMAEMA) polymer chains are grafted in a controlled radical polymerization. (D) PDMAEMA@SiO2 core–shell particle and its dimensions in bulk and at the interface.In contrast to this theoretical understanding, the experimental progress of such systems has remained largely elusive. The fundamental bottleneck that has impeded the experimental realization of such complex assembly phases is the difficulty of engineering suitable interaction potentials. For a system to form Jagla phases, two stringent requirements need to be met. First, the particle interaction potential requires two distinct length scales as described earlier and, in particular, a soft repulsive shell with a nonconvex shape (23, 25, 26), meaning that the repulsion should have at least a linear ramp profile (i.e., the Jagla parameter g≳1). Second, the interaction potentials need to be strictly pairwise additive (i.e., many-body effects where the interaction between two core–shell particles is influenced by the presence of other neighboring particles need to be avoided).In principle, interaction potentials satisfying the two length-scale criteria can be implemented using core–shell particles consisting of a solid, incompressible core and a compressible shell. Microgels (36) are ideally suited as shell material because of their soft nature and their ability to deform under the influence of surface tension (3, 37–39). In particular, when adsorbed at a liquid interface, microgels with and without a solid core exhibit a pronounced, very thin corona at the periphery, which is formed by the interfacial spreading of dangling chains (5, 40–43). This corona acts as a compressible spacer between the cores, effectively introducing a repulsive shoulder to the interaction potential.However, despite their interfacial core–corona morphology, we note that for pure microgels (44, 45) and typical core–microgel shell systems (46–49), only an isostructural hexagonal non–close packed to hexagonal close-packed transition is observed. This behavior has been rationalized by the quasi–three-dimensional shape that these particle systems retain despite their deformation at the interface (Fig. 1A, Top). Due to their crosslinked nature, the shell protrudes significantly into the water subphase (38, 49, 50). This interfacial morphology causes a rapid increase in shell overlap upon compression. Assuming that that the energy penalty associated with the compression of the polymer shell scales with the overlap volume, this interfacial morphology therefore can be assumed to form a convex shape for the interaction potential (Fig. 1B and SI Appendix, Supplementary Discussion). In the terminology of the Jagla potential, the g parameter for the shell interaction is much smaller than 1, which is not sufficient for observing complex assembly phases (25–27). The ability to expand at a liquid interface is intimately connected to the molecular architecture of the microgel. Microgels with low or ultralow crosslinking densities can spread particularly well at the interface, as the individual chains are less hindered by mutual crosslinking points (44, 51). While such systems may exhibit a larger g parameter, they lack a hard core and therefore do not possess the required two length scales in the potential and do not form any unconventional phases (49). In contrast, the only reports of anisotropic chain phases to date were observed in interfacial systems with extremely flat coronae, formed by binary mixtures of polystyrene microspheres and very small microgels (25), and core–shell particles with a pronounced crosslinker gradient (49). These examples indicate that the ideal interfacial morphology to achieve Jagla-type interaction potentials with sufficiently large g-parameters is a core–shell system with an effectively 2D shell, where the overlap volume increases nearly linearly with compression. Again assuming that the overlap volume is proportional to the resultant energy penalty, this results in a near-linear ramp potential (i.e., g≈1) (Fig. 1A and SI Appendix, Supplementary Discussion). Even though they pinpoint at important structural requirements, both initial experimental systems are limited in their ability to probe the wealth of theoretically predicted Jagla phases because they lack proper control of the shell dimensions. In particular, an experimental realization of more complex chains and defined clusters, predicted for larger shells, remains elusive.The interconnected nature of a crosslinked microgel shell not only limits the interfacial spreading but also forces the polymer chains in the corona to react in a concomitant manner. This implies that upon compression, cross-linked shells are forced to distribute stress across the entire shell. As a consequence, a collapse of the shell with one neighboring particle also facilitates the collapse of the same shell with other neighboring contacts. It has been shown that such many-body interactions destabilize the formation of anisotropic Jagla phases and bias the system toward the conventionally observed isostructural phase transitions (49).Here, we circumvent the problems associated with conventional core–shell particles by using hairy particles consisting of an inorganic silica core functionalized with individual, noncrosslinked, and surface-active polymer chains (Fig. 1 C and D). As we will see, at a liquid interface, the polymer chains in these hairy particles spread very efficiently and form an effectively 2D corona, which we assume to translate into a near-linear repulsive potential. Using controlled radical polymerization to grow these polymer chains from the particle surface (Fig. 1C) (52–54), our method further provides uniform shell structures and control over their dimensions. By completely avoiding any crosslinking in the shell, we also ensure that mechanical stress, arising from a local shell collapse upon compression, is not translated throughout the entire microgel shell. This, in turn, facilitates the partial and anisotropic collapse of a single shell in the vicinity of a neighboring particle. In the Jagla terminology, this behavior reflects a pairwise-additive character of the interaction potential. Our experimental particle system thus fulfils both the stringent conditions required for the formation of Jagla phases. As we will show, upon compression these particles indeed form a series of complex 2D phases that are quantitatively reproduced by minimum energy calculations and Monte Carlo (MC) simulations based on the Jagla potential.     

Energy penalties enhance flexible receptor docking in a model cavity

Protein flexibility remains a major challenge in library docking because of difficulties in sampling conformational ensembles with accurate probabilities. Here, we use the model cavity site of T4 lysozyme L99A to test flexible receptor docking with energy penalties from molecular dynamics (MD) simulations. Crystallography with larger and smaller ligands indicates that this cavity can adopt three major conformations: open, intermediate, and closed. Since smaller ligands typically bind better to the cavity site, we anticipate an energy penalty for the cavity opening. To estimate its magnitude, we calculate conformational preferences from MD simulations. We find that including a penalty term is essential for retrospective ligand enrichment; otherwise, high-energy states dominate the docking. We then prospectively docked a library of over 900,000 compounds for new molecules binding to each conformational state. Absent a penalty term, the open conformation dominated the docking results; inclusion of this term led to a balanced sampling of ligands against each state. High ranked molecules were experimentally tested by T_m upshift and X-ray crystallography. From 33 selected molecules, we identified 18 ligands and determined 13 crystal structures. Most interesting were those bound to the open cavity, where the buried site opens to bulk solvent. Here, highly unusual ligands for this cavity had been predicted, including large ligands with polar tails; these were confirmed both by binding and by crystallography. In docking, incorporating protein flexibility with thermodynamic weightings may thus access new ligand chemotypes. The MD approach to accessing and, crucially, weighting such alternative states may find general applicability.

Proteins interchange between conformational states of varying probabilities (1). These rearrangements, naturally, also alter its physicochemical properties (2, 3). Exploiting these varying features can benefit ligand discovery (4–7) but also presents several challenges. Key among them is weighting the different states by their energies, which has been shown to be crucial for docking success (4, 8); without such weights, high-energy protein conformations, often better suited to ligand complementarity but harder to access, can dominate docking results, acting effectively as decoy conformations.Structural models of proteins in distinct conformational states can be obtained from experiments like X-ray crystallography, NMR, or cryoelectron microscopy. The choice of the single structure used for a docking campaign contributes to its likelihood of success and choosing any single conformation inevitably leads to false negatives, even in successful campaigns. A solution to this problem is to consider multiple protein conformations, often referred to as ensemble docking or flexible receptor docking (4, 9–15). Yet incorporating multiple protein conformations only increases accuracy in ligand discovery when they are weighted according to their ensemble probabilities (10, 16, 17). When such energies have been incorporated in docking campaigns, they have enabled the discovery of ligands that are inaccessible to single-state docking, often with high fidelity to the subsequent structure determination of ligand–protein complexes. However, incorporating these weights has relied on experimental observables, such as occupancies from high-resolution structures. This has both limited the range of states that may be used—since states higher in energy than a few kilocalories per mole above the ground state will not be observed experimentally—and cannot be generalized to the vast number of targets for which such information is unavailable. Even when alternative conformational states can be observed in complex with different ligands (4, 11, 18, 19), their thermodynamic weights in the apo ensemble are typically unknown. It would be useful to have a general method of sampling and energy-weighting conformational states that would enable their exploitation in ligand discovery, in general, and for molecular docking in particular.In principle, computationally modeled conformations, such as those derived from molecular dynamics (MD) simulations, can sample such states (9, 20, 21) and can estimate their thermodynamic weighting (22–24). Encouraging studies on how MD simulation can be leveraged to explore the flexibility of ligand binding sites include work from the Bowman group, in which exhaustive MD simulations aided the discovery of allosteric binders (6, 10). More recently, exascale simulations of proteins central to SARS-CoV-2 immune evasion were able to explain and predict cryptic binding sites (25, 26). In practice, however, challenges with many MD simulations include insufficient sampling and the difficulty in weighting states by relative energies. The free energy minima, representing conformational states of a protein, are often separated by high-energy barriers, which are rarely overcome on time scales covered by conventional MD (cMD) simulations (1). Enhanced sampling algorithms, such as accelerated MD (aMD) (27), introduce a bias potential to lower the barriers between individual conformational states. This makes the sampling of a diverse, conformational ensemble, including higher-energy conformational states, more efficient by increasing the sampling by up to three orders of magnitude (28–30). A core question is whether the assumptions and approximations made in aMD affect its ability to usefully weight the conformations sampled.Here, we test energetic weights from MD simulation for ligand discovery in the engineered cavity site of T4 lysozyme L99A (L99A). This hydrophobic cavity was first introduced by Eriksson, Morton, Baase, and Matthews (31–34), as a model system to explore ligand binding and thermodynamics. While binding to this site is not thought to affect the enzymes function (it is over 20 Å from the catalytic aspartate and does not overlap with the muramyl peptide binding site; SI Appendix, Fig. S7), it has important advantages for exploring terms in ligand binding and docking (here, protein flexibility). The cavity site is relatively small, only 150 ų in its apo state, and is completely enclosed from solvent in that conformation (Fig. 1A). Combined with its dominance by apolar interactions, this simplifies the determinants of ligand binding. Despite its small size, there are still many hundreds of likely ligands that are readily available and testable from within docking libraries, enabling prospective predictions to test new docking terms and methods (11, 32, 33, 35–37). Previous studies have revealed at least 68 ligands for this cavity, many of which have protein-bound crystal structures determined (31, 38), enabling detailed retrospective studies. Despite its simplicity, L99A has complexities that make it interesting and relevant as a model site, and its thermodynamics (34, 39–41), dynamics (28, 42–50), and ligand (un)binding (33, 36, 51–59) have been intensely studied.Open in a separate windowFig. 1.Three conformations of the L99A cavity binding site. (A) Crystal structures of T4 lysozyme L99A in its apo state show a small, buried, and entirely apolar cavity. (B) Structures of the protein in complex with ligands of increasing size show three major conformational states of the binding site: closed (purple), intermediate (blue), and open (green). (C) Workflow.Particularly germane to this study, the cavity undergoes a conformational change as larger and larger ligands bind to it, adopting three principal conformations termed closed (150 ų), intermediate (∼200 ų), and open (<300 ų) (35) (Fig. 1B). As larger ligands bind, the cavity opens owing to the unwinding of helix F from an α- to a 3 to 10-helix. In the most voluminous state of the cavity (twice that of the closed state), it opens to form a channel between bulk solvent and the hydrophobic cavity. Thus, despite being a simplified model system, L99A exhibits substantial structural rearrangements, making it a useful site to test flexible receptor docking (11, 60).For this study, we derive conformational state definitions from apo and holo crystal structures of L99A in its closed, intermediate, and open state (Fig. 1C). Removing the ligands, we perform aMD and cMD simulations for exhaustive and efficient sampling. We then construct a Markov state model (MSM) (61–64) to estimate the relative probability of each crystallographic conformational state in the apo ensemble. Converted into a conformational energy penalty Ep (Eq. 1), we incorporate the state probabilities into our flexible receptor docking scoring function (4).Ep=−m⋅kB⋅T⋅ln(p),[1]where k_B is the Boltzmann constant, T is the temperature in K, P is the population, and m is the weighting multiplier.The multiplier m weights the conformational penalty energy to bring it into balance with the other terms in the DOCK3.7 scoring function, which are typically higher in magnitude than true ligand-binding energies. As in earlier studies that used crystallographic occupancies to measure populations, this m value may need to be optimized for each system studied, at least for DOCK3.7 (4); for scoring functions whose energies are already aligned with experimental binding energies, this may not be necessary. While this is admittedly a weakness, we test the reliability of the applied penalties in retrospective screens based on the known ligands and their property-matched decoys, as we do with the normal scoring function (see Results). Thus, while this weighting may change from system to system, doing so fits with the retrospective control calculations that are already typical in docking.Crucially, we evaluate the ability of the approach to predict ligands with new chemotypes selective for each of the three relevant conformations of the cavity in a prospective docking screen. We consider the usefulness of this approach to the general problem of predicting weighted, conformational ensembles of proteins for docking and ligand discovery.     

Carbon dioxide as a line active agent: Its impact on line tension and nucleation rate

By considering a water capillary bridge confined between two flat surfaces, we investigate the thermodynamics of the triple line delimiting this solid–liquid–vapor system when supplemented in carbon dioxide. In more detail, by means of atom-scale simulations, we show that carbon dioxide accumulates at the solid walls and, preferably, at the triple lines where it plays the role of a line active agent. The line tension of the triple line, which is quantitatively assessed using an original mechanical route, is shown to be driven by the line excess concentrations of the solute (carbon dioxide) and solvent (water). Solute accumulation at the lines decreases the negative line tension (i.e., more negative) while solvent depletion from the lines has the opposite effect. Such an unprecedented quantitative assessment of gas-induced line tension modifications shows that the absolute value of the negative line tension increases upon increasing the carbon dioxide partial pressure. As a striking example, for hydrophilic surfaces, the line tension is found to increase by more than an order of magnitude when the carbon dioxide pressure exceeds 3 MPa. By considering the coupling between line and surface effects induced by gaseous adsorption, we hypothesize from the observed gas concentration-dependent line tension a nontrivial impact on heterogeneous nucleation of nanometric critical nuclei.

Line tension, a concept introduced by Gibbs, is still mostly considered as an academic curiosity. Like excess quantities at an interface (e.g., surface tension), lines separating several interfaces may also be endowed with excess quantities. In particular, the excess free energy per unit length of such a line—the so-called line tension—can be seen as a force with the underlying picture of the tension acting in a molecularly thin thread. It has been long considered that such a force contributes only at the molecular or maybe the nanometer scale. Yet, line tension is now recognized as a crucial parameter even in physical, chemical, and biological systems where it was probably the least expected [e.g., phase separation within a lipid layer and nucleation of rafts within a biological membrane (1, 2)]. Line tension effects are also directly involved in heterogeneous nucleation due to the presence of a triple line between the nucleus and the preexisting phases (3). For instance, it has been shown theoretically that the line tension may contribute to water condensation on atmospheric aerosols and cloud formation (4) [various atmospheric aerosols can originate from multicomponent nucleation of trace condensable vapors—in particular, water, acids, bases, and organics (5, 6)].Despite its now broadly acknowledged role in both science and engineering fields, the accurate determination of line tension is still a matter of debate even for a triple line involving vapor/liquid equilibrium for a single fluid on a well-defined solid surface. Thermodynamically, the line tension can be positive or negative while preserving the coexistence of the adjacent phases (7). In the particular case of solid/liquid/vapor triple lines, a negative sign is mainly expected, except for a system close to the wetting transition, with magnitude of the order of a few piconewtons (8–16). For instance, for ordered hydrophobic nanopores of a few nanometers in diameter, it has been shown experimentally and confirmed numerically that large drying pressures of more than 200 bar are induced by a negative line tension. In fact, such a negative line tension favors the emergence of a gas nucleus at the origin of the drying process (12, 13). This example shows that the line tension, which balances with surface and bulk thermodynamic contributions, acts as a lever controlling the stability of confined fluids (17).In 1982, Rowlinson and Widom (7) envisioned theoretically adsorption at a triple line separating three phases and its impact on line tension. More recently, some authors have suggested that line tension could be lowered by using line active molecules—the so-called lineactants [namely surfactants that present specific affinity for the line in addition to their affinity for the interface (18)]. Such adsorption effects on three-phase coexistence are also central to the physics of oversolubility aspects, which refer to the large gas solubility increase in liquids confined in nanoporous solids (19–21). In this context, we stress that the thermodynamics of a mixture of water and noncondensable soluble gases near solid surfaces as well as the phase transition kinetics in such a mixture remain to be investigated. Among numerous examples, such aspects are related to important issues in the context of climate change and energy transition: CO2 geological capture in aquifers (22–25), formation and stability of gas clathrates [methane hydrate trapped in seafloor and rocks corresponds to critical amounts of greenhouse gases potentially harmful to the environment (26–28)], water electrolysis, and fuel cells [which involve a confined reactive zone with nucleating bubbles or droplets (29, 30)].Up to now, when addressing these specific topics and, more generally, the question of the state of a confined water/gas mixture [either for technological or for scientific problems (31)], the role of line tension has been often overlooked (9). A consensus has started to emerge concerning the line tension of a solid/liquid/vapor triple line involving a single fluid. However, the case of a fluid mixture with potential accumulation of one species at the triple line is still an open problem. While a few experiments suggest that dissolved gas may accumulate at solid interfaces and consequently impact nucleation (32–36), there are no quantitative data concerning their contribution to a triple line. Key questions relevant to this complex problem include the following: Does a gas solute behave as a line active agent at a triple line? Would such solute excess at the line impact heterogeneous nucleation rates? Here, we address these questions using molecular dynamics simulations for a liquid droplet confined between two surfaces and supplemented with a noncondensable gas. In more detail, this paper is focused on water/CO2 mixtures—a key system of interest for applied and basic sciences—in contact with either hydrophilic or hydrophobic surfaces. We aim at addressing the pivotal role of adsorption at the triple line and its coupling with adsorption at the solid surfaces. We do not consider any chemical reaction such as the formation of a small amount of carbonic acid from the dissolution of CO2 in water (which is known to occur in real systems). We believe that a confined CO2/water mixture is a prototypical example with results that should also pertain to many other common systems (corresponding to solute/solvent couples with a low solubility). Moreover, while the present work is limited to a specific mixture for feasibility purposes, in addition to varying the gas pressure in a large range, we tune the hydrophobicity/hydrophilicity of the solid surface to cover the diversity of situations that can be met experimentally. However, in any case, while we think that our model subclass is representative of a larger set of systems corresponding to weakly soluble gases, we recognize here that other systems could display a different behavior with additional complexity.In practice, we consider an infinite water liquid droplet confined between two flat solid surfaces—hence forming four straight triple lines that are the locus of specific molecular structuring (Fig. 1). The solid surfaces are formed using two structureless dispersive walls that interact with the fluid through an external 9–3 Lennard-Jones potential as detailed in Materials and Methods. The droplet, which is invariant by translation in the y direction, is modeled as a finite system confined in a fully periodic rectangular box. The system is made up of water molecules in the liquid state (solvent) and of CO2 molecules (solute) in the gas state and partly solubilized in water. This fluid mixture is considered at constant temperature, constant numbers of solvent and solute molecules, and constant volume defined by the rectangular box. Molecular simulations are performed using Large-scale Atomic/Molecular Massively Parallel Simulator software (37) with a Verlet integration algorithm coupled to a Nosé–Hoover thermostat. The two curved liquid–gas interfaces intersect the solid walls along the triple lines with a contact angle θY. The distance h between the walls is such that disjoining pressure effects are negligible (SI Appendix, section 5). As the triple line is straight, its tension does not contribute to the contact angle (15) so that θY corresponds to Young’s contact angle. The thermodynamic properties of the system—in particular, the line tension and line excess concentrations—are studied as a function of the solute partial pressure in the gas phase. To determine the line tension of the straight solid/liquid/gas triple lines, we use a recently introduced mechanical methodology that offers unprecedented sensitivity and reliability (15). The line tension is directly extracted from force measurements. More precisely, as detailed in Materials and Methods, the specific contribution of the line in the y direction is separated from the bulk and surface contributions determined using force measurements in the x and z directions as the line tension is not acting in these directions (15) (Fig. 1). The line excess concentrations are readily obtained by subtracting bulk and surface excess quantities from the total amount of fluid molecules for each species. The measurement approach is further detailed in Materials and Methods.Open in a separate windowFig. 1.Setup consisting of a liquid (dark blue) in contact with a partially soluble gas confined between two solid walls (perpendicular to the z direction). Solid/fluid and liquid–gas interfaces are separated by distances h and l, respectively. The dependence of the line tension τ on the adsorption of molecules at the straight contact lines (in red; Inset) is estimated from the forces Σx, Σy, and Σz exerted along x, y, and z.     

Low-Reynolds-number,biflagellated Quincke swimmers with multiple forms of motion

In the limit of zero Reynolds number (Re), swimmers propel themselves exploiting a series of nonreciprocal body motions. For an artificial swimmer, a proper selection of the power source is required to drive its motion, in cooperation with its geometric and mechanical properties. Although various external fields (magnetic, acoustic, optical, etc.) have been introduced, electric fields are rarely utilized to actuate such swimmers experimentally in unbounded space. Here we use uniform and static electric fields to demonstrate locomotion of a biflagellated sphere at low Re via Quincke rotation. These Quincke swimmers exhibit three different forms of motion, including a self-oscillatory state due to elastohydrodynamic–electrohydrodynamic interactions. Each form of motion follows a distinct trajectory in space. Our experiments and numerical results demonstrate a method to generate, and potentially control, the locomotion of artificial flagellated swimmers.

In a Newtonian fluid, locomotion of microswimmers requires nonreciprocal body motions (1–3). Bacteria or eukaryotic cells achieve this by beating or rotating their slender hair-like organelles, flagella (4, 5) or cilia (6), powered by molecular motors. Mimicking these organisms, artificial swimmers propelled by rotating helices (7, 8) or whipping filaments (9–12) have been fabricated. They are commonly driven by an external power source such as a magnetic field (7–9, 13, 14), sound (15), light (16, 17), and biological materials (12). However, there are very few electrically powered microswimmers (18–20), although electric fields have been exploited to drive other active systems (21–26) via a phenomenon called Quincke rotation (27).Quincke rotation originates from an electrohydrodynamic instability (28–30). Submerged in a liquid with permittivity εl and conductivity σl, a spherical particle with permittivity εs and electric conductivity σs is polarized under a uniform, steady electric field E→. When the particle is stationary, the induced dipole p→ due to the free charges is parallel or antiparallel to E→ (Fig. 1A): if the particle’s relaxation time τs=εs/σs is shorter than that of the ambient liquid, τl=εl/σl, p→ points in the same direction as E→; when τs>τl, p→ is opposite to E→, which generates an electric torque Γ→Q=p→×E→ that amplifies any angular perturbation. However, due to the resisting viscous torque Γ→μ, the system becomes unstable only when E=|E→| exceeds a threshold Ec. This instability causes the particle to rotate with a constant angular velocity ω:ω=1τEEc2−1,[1]where τ=εs+2εlσs+2σl is the relaxation time of the system (see SI Appendix, SI Text, or refs. 28, 29, 31 for derivation), and the rotational axis can be in any direction perpendicular to E→. During steady-state Quincke rotation, there is a constant angle between p→ and E→ (Fig. 1A), which results in a nonzero Γ→Q.Open in a separate windowFig. 1.Quincke rotation and the experimental setup. (A) Distribution of free charge and the corresponding dipole p→ on a sphere in a uniform, steady electric field E→. The sphere is (Left) stationary, (Middle) stationary, and (Right) rotating with a constant angular velocity ω. (B) A sketch of the biflagellated swimmer. Dashed lines show the roll axis (blue) and pitch axis (green). (C) A schematic illustration of the experimental setup.Recently, a flagellated swimmer in unbounded space driven by Quincke rotation has been proposed theoretically (32, 33). In light of the theory, we built a laboratory prototype, a biflagellated Quincke swimmer composed of a spherical particle and two attached elastic filaments, as shown in Fig. 1B, and systematically studied its behaviors at low Reynolds number (Re<0.3; Materials and Methods). Varying the electric field E→ and the angle between the two filaments, the Quincke swimmers exhibit three distinct forms of motion—two unidirectional rotations, which we call roll and pitch, and a self-oscillatory rotation, due to the balances between the electrical, elastic, and hydrodynamic torques, resulting in distinct trajectories in space. Surprisingly, it was recently reported (34) that spherical bacteria Magnetococcus marinus exhibit a similar pitch motion as our biflagellated artificial swimmers, which is rarely adopted by other microorganisms. Moreover, we found a threshold tail angle that separates the swimmers’ preferred forms of rotation, and within a small range close to this threshold angle, the three forms of motion coexist.