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.     

Optimized river diversion scenarios promote sustainability of urbanized deltas

Socioeconomic viability of fluvial-deltaic systems is limited by natural processes of these dynamic landforms. An especially impactful occurrence is avulsion, whereby channels unpredictably shift course. We construct a numerical model to simulate artificial diversions, which are engineered to prevent channel avulsion, and direct sediment-laden water to the coastline, thus mitigating land loss. We provide a framework that identifies the optimal balance between river diversion cost and civil disruption by flooding. Diversions near the river outlet are not sustainable, because they neither reduce avulsion frequency nor effectively deliver sediment to the coast; alternatively, diversions located halfway to the delta apex maximize landscape stability while minimizing costs. We determine that delta urbanization generates a positive feedback: infrastructure development justifies sustainability and enhanced landform preservation vis-à-vis diversions.

Deltaic environments are critical for societal wellbeing because these landscapes provide an abundance of natural resources that promote human welfare (1, 2). However, the sustainability of deltas is uncertain due to sea-level rise (3, 4), sediment supply reduction (4–6), and land subsidence (7, 8). Additionally, river avulsion, the process of sudden channel relocation (9, 10), presents a dichotomy to delta sustainability: the unanticipated civil disruption associated with flooding brought by channel displacement is at odds with society’s desire for landscape stability, yet channel relocation is needed to deliver nutrients and sediment to various locations along the deltaic coastline (11, 12). Indeed, for many of the world’s megadeltas, channel engineering practices have sought to restrict channel mobility and limit floodplain connectivity (13, 14), which in turn prevents sediment dispersal that is necessary to sustain deltas; as a consequence, land loss has ensued (15). Despite providing near-term stability (13–15), engineering of deltaic channels is a long-term detrimental practice (11, 15–17).To maximize societal benefit, measures that promote delta sustainability must balance engineering infrastructure cost and impact on delta morphology with benefits afforded by maintaining and developing deltaic landscapes (1, 2, 11, 12, 16–19). For example, channel diversions, costing millions to billions of dollars (20–22), are now planned worldwide to both prevent unintended avulsions and ensure coastal sustainability through enhanced sediment delivery (e.g., Fig. 1A) (20, 21, 23–26).Open in a separate windowFig. 1.(A) Satellite image of Yellow River delta (Landsat, 1978) showing coastline response to a diversion in 1976 at the open circle, which changed the channel course from the north (Diaokou lobe) to the east (Qingshuigou lobe) and produced flooding over the stripe-hatched area (30). (B and C) Planform view (B) and along-channel cross-section view (C) of conceptual model for numerical simulations and societal benefit formulation. In the diagrams, a diversion at LD≈0.8Lb floods an area (af) defined by Lf and θ, diverting sediment away from the deltaic lobe (with length Ll). Aggradation of the former channel bed (dashed line) is variable; hence, diversion length influences the propensity for subsequent avulsion setup.In this article, we consider the benefits and costs of such engineered river diversions and determine how these practices most effectively sustain deltaic landscapes, by assessing optimal placement and timing for river diversions. Addressing these points requires combining two modeling frameworks: a morphodynamic approach—evolving the landscape over time and space by evaluating the interactions of river fluid flow and sediment transport—and a decision-making framework (21, 22, 27, 28). The former simulates deltaic channel diversions by assessing the nonlinear relationships between channel diversion length (LD) and the frequency (timing) of avulsions (TA), while the latter incorporates a societal benefit model that approximates urbanization by considering the cost of flooding a landscape that would otherwise generate revenue. The aim is to optimize timing and placement of channel diversions, by giving consideration to morphodynamic operations and societal wellbeing. Interestingly, optimal societal benefit indicates that urbanization justifies enhanced sustainability measures, which contradicts existing paradigms that label development and sustainability mutually exclusive (3, 7, 12). Ultimately, the societal benefit model should be an integrated component in decision-making frameworks. This will help locate diversions and promote sustainable and equitable decisions considering historical, ethical, and environmental contexts for river management decisions (29).     

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.     

Sharp thresholds limit the benefit of defector avoidance in cooperation on networks

Consider a cooperation game on a spatial network of habitat patches, where players can relocate between patches if they judge the local conditions to be unfavorable. In time, the relocation events may lead to a homogeneous state where all patches harbor the same relative densities of cooperators and defectors, or they may lead to self-organized patterns, where some patches become safe havens that maintain an elevated cooperator density. Here we analyze the transition between these states mathematically. We show that safe havens form once a certain threshold in connectivity is crossed. This threshold can be analytically linked to the structure of the patch network and specifically to certain network motifs. Surprisingly, a forgiving defector avoidance strategy may be most favorable for cooperators. Our results demonstrate that the analysis of cooperation games in ecological metacommunity models is mathematically tractable and has the potential to link topics such as macroecological patterns, behavioral evolution, and network topology.

Cooperation, behavior that leads to benefits for others at a cost to oneself, is widespread across biological systems, ranging from cells cooperating to form organisms, to cooperation among individuals in populations and among microbiotic and macrobiotic taxa in ecosystems. In many cases the costs of cooperation are high. Hence, how cooperative behavior persists in a population represents a fundamental question in biology (1–8). In general, cooperation is most likely to evolve and persist if there are mechanisms that directly or indirectly benefit cooperators’ reproductive success. Examples include kin selection, punishment of defectors who forgo the cooperative investment, or a direct self-benefit such as in cases of investment into a common good (4).Among the most general mechanisms that can favor cooperation is the notion of network or spatial reciprocity (1, 9–11). In classical examples of reciprocity, cooperation creates favorable conditions for other proximal cooperators (4). A result is the emergence of cooperative havens, where the rewards generated by mutual cooperation have enriched some physical or topological neighborhoods. The formation of cooperative neighborhoods in structured populations, where individuals interact with only a limited subset of the population, has traditionally been studied on networks, where each node represents an individual agent and an edge means that the two connected individuals play against each other (1, 10, 12–19). By assuming weak selection and treating space implicitly, the resulting systems can often be analyzed mathematically. Although this framework has become a powerful tool for conceptual understanding, it represents a strong abstraction from real-world ecology where interactions, and hence cooperative behaviors, occur often randomly within a location that is itself embedded in a larger spatial context (20–23). By focusing on spatially explicit models of cooperation, we gain the opportunity to understand feedbacks between the rules of the game, movement strategies, and long-term persistence of cooperation at larger scales (10, 20, 23–27).Here we study a model of cooperation in spatially structured populations inspired by ecological metacommunities (21–23, 28), where network nodes—instead of individuals—represent habitat patches containing many interacting individuals, and edges mean that two patches are connected by dispersal of those individuals (Fig. 1A). Each patch is a location where games are played, harboring cooperator and defector subpopulations which grow and shrink in time due to internal interactions and movement among locations. Metacommunity models allow one to represent the effects of physical spatial structure directly and explicitly. Moreover, they can be analyzed using master stability functions, which can be used to untangle the impacts of local dynamics and network structure (28–30). We use this ability to explore how different movement strategies impact the outcomes of a cooperation game as a function of network structure.Open in a separate windowFig. 1.Emergence of a heterogeneous stationary state on a two-patch network. (A) Schematic of the spatial game, showing local payoff (Π) relationships among cooperators and defectors occupying the same patch (gray circles) and the dispersal route between them. (B) Difference in equilibrium densities of both types in patches 1 and 2 as link strength is varied. Arrows refer to the example time series shown in C and D. Initial conditions were uniformly drawn from [10−4,10−3], and the patch with the largest initial cooperator density is patch 1. (C) The homogeneous steady state, with the same equilibrium densities of C and D across locations. (Inset) Network showing the proportions of each type in each patch. (D) The same game but with faster diffusion (larger δ), showing emergence of a heterogeneous steady state with higher cooperator densities in patch 1. Parameters are R = 3, S=2, T = 5, P=0.2, μ = 1, and α=3.     

Stagnation points control chaotic fluctuations in viscoelastic porous media flow

Viscoelastic flows through porous media become unstable and chaotic beyond critical flow conditions, impacting widespread industrial and biological processes such as enhanced oil recovery and drug delivery. Understanding the influence of the pore structure or geometry on the onset of flow instability can lead to fundamental insights into these processes and, potentially, to their optimization. Recently, for viscoelastic flows through porous media modeled by arrays of microscopic posts, Walkama et al. [D. M. Walkama, N. Waisbord, J. S. Guasto, Phys. Rev. Lett. 124, 164501 (2020)] demonstrated that geometric disorder greatly suppressed the strength of the chaotic fluctuations that arose as the flow rate was increased. However, in that work, disorder was only applied to one originally ordered configuration of posts. Here, we demonstrate experimentally that, given a slightly modified ordered array of posts, introducing disorder can also promote chaotic fluctuations. We provide a unifying explanation for these contrasting results by considering the effect of disorder on the occurrence of stagnation points exposed to the flow field, which depends on the nature of the originally ordered post array. This work provides a general understanding of how pore geometry affects the stability of viscoelastic porous media flows.

Unlike viscous Newtonian liquids (e.g., water), many fluids exhibit an elastic response to an applied strain. Such “viscoelastic” fluids are widespread in biology (blood, mucus, synovial fluid) and industry (paints, coatings, fracking fluids). The elasticity is imparted by the presence of a microstructure (formed by, e.g., polymers, proteins, or self-assemblies of lipids or surfactants) that relaxes after deformation (1). The strength of the elastic response of the fluid to an imposed deformation (or flow) is quantified by the Weissenberg number Wi=τγ˙, with τ the fluid relaxation time and γ˙ the rate of strain. While flows of Newtonian fluids become unstable and turbulent due to the onset of inertial effects at high Reynolds number, Re≫1, viscoelastic flows can become unstable and exhibit so-called “elastic turbulence” even for Re≪1, purely due to elastic effects that arise at high Wi (2–7).Viscoelastic porous media flow occurs in diverse processes ranging from enhanced oil recovery (EOR) and filtration to drug delivery (8, 9). Porous media flow subjects a fluid to a complex cycle of deformation with high shear rates through the pore throats or between obstacles and high elongational rates at points of constriction or at stagnation points, leading to stretching of the fluid microstructure if Wi≳1 (10, 11). Stagnation points (which occur at the front and rear poles of obstacles in a flow) are particularly effective at causing high stretching and large tensile stresses due to the combination of zero flow velocity and finite velocity gradient that exists in such regions (10–15). Elastic tensile stresses due to stretching on curvilinear streamlines (as through porous media) are conditions well established to lead to linear instabilities in viscoelastic fluids (16–19), which can be precursors to elastic turbulence as Wi is further increased (7, 20–23). The chaotic fluctuations that result are expected to greatly enhance the pressure loss and the dispersion in porous media, with positive impacts on, for example, removing oil ganglia from the pore space in EOR or improving the distribution of drugs throughout a tumor (24–27).There have been various recent advances in modeling viscoelastic porous media flows both experimentally and numerically (14, 27–36). However, the complexity of the problem has limited numerical simulations to extremely simplified regular geometries (32, 36) and/or small computational domains and/or regimes of low Wi (31). Experimentally, Browne and coworkers (27, 33) have achieved the detailed characterization of the pore-scale dynamics in model porous media formed by three-dimensional (3D) random packings of spherical glass particles, correlating a global increase in the pressure drop across the media with the onset of elastic turbulence in the pores. Importantly, due to the complexity of the random sphere packings of Browne and coworkers (27, 33), fluid arriving at each pore experiences a unique flow history, and the flow through different pores becomes unstable at different values of the nominal Wi (computed based on macroscopic flow conditions). Fundamental questions remain over how the details of the pore-space geometry affect the onset and strength of the chaotic fluctuations that arise.While randomly packed beds of polydisperse spheres provide a good model for the complex pore geometries that arise in real media such as sandstone or carbonate rock (37, 38), ordered and regular geometries enable investigation of the role of different packing structures and hence, pore shape (29, 39, 40). This is most conveniently achieved by arrangements of posts forming either linear models of the interconnecting capillary network through the pore space (e.g., refs. 36, 41, and 42) or two-dimensional (2D) arrays that represent the tortuous flow paths around closely spaced grains (e.g., refs. 14, 24, 25, 28, 30, 35, 43, and 44).An outstanding open question concerns how the chaotic dynamics of viscoelastic flows are affected when geometric disorder (inherent in real heterogeneous systems) is introduced to a regular model porous medium. In a recent attempt to address this issue, Walkama et al. (28) performed experiments in a series of 2D microfluidic post arrays using shear thinning viscoelastic polymeric test solutions. They examined how the introduction of increasing random disorder to a hexagonal post array (arranged as shown in Fig. 1A) affected the onset and strength of the chaotic fluctuations observed for Wi≳1. Their results led to the broad general conclusion that “disorder suppresses chaos in viscoelastic flows.” However, other works have shown that instabilities and fluctuations in viscoelastic flows through 2D ordered post arrays strongly depend on the orientation of the array relative to the flow direction (30). Thus, different behavior might be anticipated from an ordered array of posts that are staggered along the flow direction (Fig. 1A) (as employed in ref. 28) than from an identical array rotated by 30° such that the posts become aligned (Fig. 1B). Indeed, as shown in Fig. 1 C and ​andD,D, even the low-Re flow of a simple Newtonian fluid shows qualitatively different flow patterns in the two contrasting post arrangements. Notably, in Fig. 1C, it is clear that each post presents both an upstream point and a downstream stagnation point that are accessible to the flow field. However, in the rotated arrangement in Fig. 1D, the flow is concentrated between the aligned rows of posts, largely bypassing the stagnation points. Given the known role of stagnation point regions in driving the onset of instabilities and fluctuations in viscoelastic flows (e.g., refs. 15, 17, and 45–49), we question the generality of the conclusions drawn by Walkama et al. (28), based on modifications made to a single-ordered geometry like in Fig. 1 A and ​andCC.Open in a separate windowFig. 1.(A and B) Unit cell representations of two contrasting ordered hexagonal arrays of posts used in the flow experiments. In A, the posts are staggered along the x direction in which the flow is imposed. The post radius is R, and lattice spacing is S. Rotating the array by 30° aligns the posts in the flow direction (B). Disordered aligned arrays are generated by the random displacement of each post within a hexagon of circumradius βS, as described in ref. 28. (C and D) Streamlines determined by flow velocimetry (Materials and Methods) with a Newtonian fluid in the staggered (C) and aligned (D) arrays at Re≈10−3. The red crossed circles in C and D indicate the locations of the leading and trailing-edge stagnation points on one of the circular posts.Here, we show by microfluidic experiments with a viscoelastic wormlike micelle (WLM) solution that a rotation of the hexagonal post array in Fig. 1 A and ​andCC in order to align the posts with the flow direction (Fig. 1 B and ​andD)D) strongly suppresses the chaotic fluctuations for a range of Wi≳1, consistent with our expectation based on the removal of stagnation points. Subsequently, following the methods of Walkama et al. (28), we introduce random disorder to the aligned array of posts (Fig. 1B). In this case, contrary to Walkama et al. (28), disorder does not further suppress but rather, promotes chaotic fluctuations over a wide range of Wi. Although our results appear to contradict those recently reported in Walkama et al. (28), both are simply explained by considering how disorder affects the prominence of stagnation points in the flow field (which is opposite, depending on the originally ordered geometric arrangement). Furthermore, we significantly extend the range of imposed Wi beyond that studied by Walkama et al. (28), showing that at sufficiently high Wi, the nature of the flow fluctuations becomes essentially geometry independent. Our work reaches an intuitive and general understanding of the role of geometry (specifically the importance of stagnation points) in controlling the onset and strength of chaotic fluctuations in viscoelastic porous media flows.     

Nonlinear rotational spectroscopy reveals many-body interactions in water molecules

Because of their central importance in chemistry and biology, water molecules have been the subject of decades of intense spectroscopic investigations. Rotational spectroscopy of water vapor has yielded detailed information about the structure and dynamics of isolated water molecules, as well as water dimers and clusters. Nonlinear rotational spectroscopy in the terahertz regime has been developed recently to investigate the rotational dynamics of linear and symmetric-top molecules whose rotational energy levels are regularly spaced. However, it has not been applied to water or other lower-symmetry molecules with irregularly spaced levels. We report the use of recently developed two-dimensional (2D) terahertz rotational spectroscopy to observe high-order rotational coherences and correlations between rotational transitions that were previously unobservable. The results include two-quantum (2Q) peaks at frequencies that are shifted slightly from the sums of distinct rotational transitions on two different molecules. These results directly reveal the presence of previously unseen metastable water complexes with lifetimes of 100 ps or longer. Several such peaks observed at distinct 2Q frequencies indicate that the complexes have multiple preferred bimolecular geometries. Our results demonstrate the sensitivity of rotational correlations measured in 2D terahertz spectroscopy to molecular interactions and complexation in the gas phase.

Water has attracted extensive spectroscopic interest because of its critical implications for theoretical and applied sciences (1, 2). Water shows anomalous properties because of complicated fluxional hydrogen-bonded networks and has been investigated by Raman and infrared spectroscopy (3, 4), sum frequency spectroscopy (5), optical Kerr effect spectroscopy (6), vibration-rotation-tunneling spectroscopy (7), and recently by two-dimensional (2D) infrared spectroscopy (8, 9) and 2D Raman-terahertz (THz) spectroscopy (10). In the gas phase, water is of utmost importance for atmospheric science, astrophysics, combustion research, and fundamental chemistry and physics (1, 11, 12). Although the pure rotation spectrum of water vapor has been well known for decades (13, 14), nonlinear THz spectroscopy of water rotational dynamics has not been previously reported. Nonlinear rotational spectroscopy in the microwave spectral range is well established (15), but because of the small moments of inertia of water, most of its rotational transition frequencies lie in the THz frequency range (Fig. 1). Nonlinear THz rotational spectroscopy was reported only recently (16, 17), and 2D THz rotational spectroscopy (10, 18, 19) more recently still. As in 2D spectroscopy of vibrational, electronic, and other degrees of freedom (9, 20–25), 2D rotational spectroscopy can reveal correlations between rotational states, many-body effects, and distinct multiple-field interactions that cannot be observed by linear spectroscopy (26). The large dipole moment of water, manifest in strong atmospheric absorption in the THz window (27–31), and the existence of water dimers and larger clusters with complex structures and dynamics (7, 32, 33), suggest that 2D spectroscopy of water could generate previously elusive insights (34–37).Open in a separate windowFig. 1.Overview of the experiment. (A) Water molecule in the laboratory frame, showing the dipole moment μ at an angle θ from the Z axis (THz polarization direction). (B) Water molecule in the molecule-fixed frame with the three moments of inertia I_a, I_b, and I_c along the corresponding axes. (C) Relative population distribution as a function of the J rotational quantum number. All relevant K_a and K_c components are included in the population distribution. (Inset) The relative population distribution within the state J = 2. (D) Rotational energy levels of para-H₂O and ortho-H₂O molecules. Red arrows illustrate rotational transitions and transition frequencies involved in this work. (E) Measured THz FID (Top) and Fourier transform (Bottom) showing rotational transitions (marked by dashed vertical lines) of water vapor in ambient air. (F) Schematic illustration of the 2D THz experimental setup. Linear THz spectra (example in E) are measured with only one THz pump pulse.Two-dimensional THz rotational spectroscopy has not been extended previously to water or any asymmetric-top molecules, although such molecules, whose rotational spectra are complicated because all three of their moments of inertia are unequal, are the majority of naturally occurring molecular species. Unlike a linear or symmetric-top molecule, in which the spectroscopic transitions between successive total rotational angular momentum levels denoted by the quantum number J are spaced by even-integer multiples of a common factor, the rotational constant B, the asymmetric-top nature of water molecules leads to irregularly spaced rotational energy levels. These levels are described approximately by quantum numbers J, K_a, and K_c that indicate the total angular momentum and its symmetry-axis projections (1, 2). The spectrum of water vapor consists of many transitions, with ΔJ=−1,0,+1 (P, Q, and R branches) all allowed and, for each, changes ΔKa=±1,ΔKc=±1 (1, 2). The large centrifugal distortion of water and the distinct sets of rotational states occupied by its nuclear spin isomers (even symmetry for para, odd symmetry for ortho) further complicate its rotational spectrum (1, 2, 38). A typical THz time-domain free-induction decay (FID) signal from water vapor at ambient conditions, induced by a weak single-cycle THz pulse, is shown in Fig. 1E. The irregular oscillations arise from more than 15 transitions (Fig. 1D) that contribute significantly to the water vapor absorption spectrum in the 0.1- to 2-THz region.     

Electrochemical borylation of carboxylic acids

A simple electrochemically mediated method for the conversion of alkyl carboxylic acids to their borylated congeners is presented. This protocol features an undivided cell setup with inexpensive carbon-based electrodes and exhibits a broad substrate scope and scalability in both flow and batch reactors. The use of this method in challenging contexts is exemplified with a modular formal synthesis of jawsamycin, a natural product harboring five cyclopropane rings.

Boronic acids are among the most malleable functional groups in organic chemistry as they can be converted into almost any other functionality (1–3). Aside from these versatile interconversions, their use in the pharmaceutical industry is gaining traction, resulting in approved drugs such as Velcade, Ninlaro, and Vabomere (4). It has been shown that boronic acids can be rapidly installed from simple alkyl halides (5–19) or alkyl carboxylic acids through the intermediacy of redox-active esters (RAEs) (Fig. 1A) (20–24). Our laboratory has shown that both Ni (20) and Cu (21) can facilitate this reaction. Conversely, Aggarwal and coworkers (22) and Li and coworkers (23) demonstrated photochemical variations of the same transformation. While these state-of-the-art approaches provide complementary access to alkyl boronic acids, each one poses certain challenges. For example, the requirement of excess boron source and pyrophoric MeLi under Ni catalysis is not ideal. Although more cost-effective and operationally simple, Cu-catalyzed borylation conditions can be challenging on scale due to the heterogeneity resulting from the large excess of LiOH•H₂O required. In addition to its limited scope, Li and coworkers’ protocol requires 4 equivalence of B₂pin₂ and an expensive Ir photocatalyst. The simplicity of Aggarwal and coworkers’ approach is appealing in this regard and represents an important precedent for the current study.Open in a separate windowFig. 1.(A) Prior approaches to access alkyl boronic esters from activated acids. (B) Inspiration for initiating SET events electrochemically to achieve borylation. (C) Summary of this work.At the heart of each method described above, the underlying mechanism relies on a single electron transfer (SET) event to promote decarboxylation and form an alkyl radical species. In parallel, the related borylation of aryl halides via a highly reactive aryl radical can also be promoted by SET. While numerous methods have demonstrated that light can trigger this mechanism (Fig. 1B) (16, 25–31), simple electrochemical cathodic reduction can elicit the same outcome (32–35). It was postulated that similar electrochemically driven reactivity could be translated to alkyl RAEs. The development of such a transformation would be highly enabling, as synthetic organic electrochemistry allows the direct addition or removal of electrons to a reaction, representing an incredibly efficient way to forge new bonds (36–40). This disclosure reports a mild, scalable, and operationally simple electrochemical decarboxylative borylation (Fig. 1C) not reliant on transition metals or stoichiometric reductants. In addition to mechanistic studies of this interesting transformation, applications to a variety of alkyl RAEs, comparison to known decarboxylative borylation methods, and a formal synthesis of the polycyclopropane natural product jawsamycin [(–)-FR-900848] are presented.     

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.     

Chlorination of arenes via the degradation of toxic chlorophenols

Aryl chlorides are among the most versatile synthetic precursors, and yet inexpensive and benign chlorination techniques to produce them are underdeveloped. We propose a process to generate aryl chlorides by chloro-group transfer from chlorophenol pollutants to arenes during their mineralization, catalyzed by Cu(NO₃)₂/NaNO₃ under aerobic conditions. A wide range of arene substrates have been chlorinated using this process. Mechanistic studies show that the Cu catalyst acts in cooperation with NO_x species generated from the decomposition of NaNO₃ to regulate the formation of chlorine radicals that mediate the chlorination of arenes together with the mineralization of chlorophenol. The selective formation of aryl chlorides with the concomitant degradation of toxic chlorophenol pollutants represents a new approach in environmental pollutant detoxication. A reduction in the use of traditional chlorination reagents provides another (indirect) benefit of this procedure.

Chlorophenols are widely encountered moieties present in herbicides, drugs, and pesticides (1). Owing to the high dissociation energies of carbon‒chloride bonds, chlorophenols biodegrade very slowly, and their prolonged exposure leads to severe ecological and environmental problems (Fig. 1A) (2–4). Several well-established technologies have been developed for the treating of chlorophenols, including catalytic oxidation (5–11), biodegradation (12–15), solvent extraction (16, 17), and adsorption (18–20) Among these methods, adsorption is the most versatile and widely used method due to its high removal efficiency and simple operation, but the resulting products are of no value, and consequently, these processes are not viable.Open in a separate windowFig. 1.Background and reaction design. (A) Examples of chlorophenol pollutants. (B) Examples of aryl chlorides. (C) The chlorination process reported herein was based on chloro-group transfer from chlorophenol pollutants.With the extensive application of substitution reactions (21, 22), transfunctionalizations (23, 24), and cross-coupling reactions (25, 26), aryl chlorides are regarded as one of the most important building blocks widely used in the manufacture of polymers, pharmaceuticals, and other types of chemicals and materials (Fig. 1B) (27–31). Chlorination of arenes is usually carried out with toxic and corrosive reagents (32–34). Less toxic and more selective chlorination reagents tend to be expensive [e.g., chloroamides (35, 36)] and are not atom economic (37–39). Consequently, from the perspective of sustainability, the ability to transfer a chloro group from unwanted chlorophenols to other substrates would be advantageous.Catalytic isofunctional reactions, including transfer hydrogenation and alkene metathesis, have been widely exploited in organic synthesis. We hypothesized that chlorination of arenes also could be achieved by chloro-group transfer, and since stockpiles of chlorophenols tend to be destroyed by mineralization and chlorophenol pollutants may be concentrated by adsorption (18–20), they could be valorized as chlorination reagents via transfer of the chloro group to arene substrates during their mineralization, thereby adding value to the destruction process (Fig. 1C). Although chlorophenol pollutants are not benign, their application as chlorination reagents, with their concomitant destruction to harmless compounds, may be considered as not only meeting the criteria of green chemistry but also potentially surpassing it. Herein, we describe a robust strategy to realize chloro-group transfer from chlorophenol pollutants to arenes and afford a wide range of value-added aryl chlorides.     

Conjugated polymers based on metalla-aromatic building blocks

Conjugated polymers usually require strategies to expand the range of wavelengths absorbed and increase solubility. Developing effective strategies to enhance both properties remains challenging. Herein, we report syntheses of conjugated polymers based on a family of metalla-aromatic building blocks via a polymerization method involving consecutive carbyne shuttling processes. The involvement of metal d orbitals in aromatic systems efficiently reduces band gaps and enriches the electron transition pathways of the chromogenic repeat unit. These enable metalla-aromatic conjugated polymers to exhibit broad and strong ultraviolet–visible (UV–Vis) absorption bands. Bulky ligands on the metal suppress π–π stacking of polymer chains and thus increase solubility. These conjugated polymers show robust stability toward light, heat, water, and air. Kinetic studies using NMR experiments and UV–Vis spectroscopy, coupled with the isolation of well-defined model oligomers, revealed the polymerization mechanism.

Conjugated polymers are macromolecules usually featuring a backbone chain with alternating double and single bonds (1–3). These characteristics allow the overlapping p-orbitals to form a system with highly delocalized π-electrons, thereby giving rise to intriguing chemical and physical properties (4–6). They have exhibited many applications in organic light-emitting diodes, organic thin film transistors, organic photovoltaic cells, chemical sensors, bioimaging and therapies, photocatalysis, and other technologies (7–10). To facilitate the use of solar energy, tremendous efforts have been devoted in recent decades to developing previously unidentified conjugated polymers exhibiting broad and strong absorption bands (11–13). The common strategies for increasing absorption involve extending π-conjugation by incorporating conjugated cyclic moieties, especially fused rings; modulating the strength of intramolecular charge transfer between donor and acceptor units (D–A effect); increasing the coplanarity of π conjugation through weak intramolecular interactions (e.g., hydrogen bonds); and introducing heteroatoms or heavy atoms into the repeat units of conjugated polymers (11–16). Additionally, appropriate solubility is a prerequisite for processing and using polymers and is usually achieved with the aid of long alkyl or alkoxy side chains (12, 17).Aromatic rings are among the most important building blocks for conjugated polymers. In addition to aromatic hydrocarbons, a variety of aromatic heterocycles composed of main-group elements have been used as fundamental components. These heteroatom-containing conjugated polymers show unique optical and electronic properties (4–10). However, while metalla-aromatic systems bearing a transition metal have been known since 1979 due to the pioneering work by Thorn and Hoffmann (18), none of them have been used as building blocks for conjugated polymers. The HOMO–LUMO gaps (E_g) of metalla-aromatics are generally narrower (Fig. 1) than those of their organic counterparts (19–22). We reasoned that this feature should broaden the absorption window if polymers stemming from metalla-aromatics are achievable.Open in a separate windowFig. 1.Comparison of traditional organic skeletons with metalla-aromatic building blocks (the computed energies are in eV). (A) HOMO–LUMO gaps of classic aromatic skeletons. (B) Carbolong frameworks as potential building blocks for novel conjugated polymers with broad absorption bands and improved solubility.In recent years, we have reported a series of readily accessible metal-bridged bicyclic/polycyclic aromatics, namely carbolong complexes, which are stable in air and moisture (23–25). The addition of osmium carbynes (in carbolong complexes) and alkynes gave rise to an intriguing family of d_π–p_π conjugated systems, which function as excellent electron transport layer materials in organic solar cells (26, 27). These observations raised the following question: Can this efficient addition reaction be used to access metalla-aromatic conjugated polymers? It is noteworthy that incorporation of metalla-aromatic units into conjugated polymers is hitherto unknown. In this contribution, we disclose a polymerization reaction involving M≡C analogs of C≡C bonds, which involves a unique carbyne shuttling strategy (Fig. 2A). This led to examples of metalla-aromatic conjugated polymers (polycarbolongs) featuring metal carbyne units in the main chain. On the other hand, the development of polymerization reactions plays a crucial role in involving certain building blocks in conjugated polymers (28–32). These efficient, specific, and feasible polymerizations could open an avenue for the synthesis of conjugated polymers.Open in a separate windowFig. 2.Design of polymers and synthesis of monomers. (A) Schematic illustration of the polymerization strategy. (B) Preparation of carbolong monomers. Insert: X-ray molecular structure for the cations of complex 3. Ellipsoids are shown at the 50% probability level; phenyl groups in PPh₃ are omitted for clarity.     

Diffusion and distal linkages govern interchromosomal dynamics during meiotic prophase

The pairing of homologous chromosomes (homologs) in meiosis is essential for distributing the correct numbers of chromosomes into haploid gametes. In budding yeast, pairing depends on the formation of 150 to 200 Spo11-mediated double-strand breaks (DSBs) that are distributed among 16 homolog pairs, but it is not known if all, or only a subset, of these DSBs contribute to the close juxtaposition of homologs. Having established a system to measure the position of fluorescently tagged chromosomal loci in three-dimensional space over time, we analyzed locus trajectories to determine how frequently and how long loci spend colocalized or apart. Continuous imaging revealed highly heterogeneous cell-to-cell behavior of foci, with the majority of cells exhibiting a “mixed” phenotype where foci move into and out of proximity, even at late stages of prophase, suggesting that the axial structures of the synaptonemal complex may be more dynamic than anticipated. The observed plateaus of the mean-square change in distance (MSCD) between foci informed the development of a biophysical model of two diffusing polymers that captures the loss of centromere linkages as cells enter meiosis, nuclear confinement, and the formation of Spo11-dependent linkages. The predicted number of linkages per chromosome in our theoretical model closely approximates the small number (approximately two to four) of estimated synapsis-initiation sites, suggesting that excess DSBs have negligible effects on the overall juxtaposition of homologs. These insights into the dynamic interchromosomal behavior displayed during homolog pairing demonstrate the power of combining time-resolved in vivo analysis with modeling at the granular level.

During meiosis prophase I, homologous chromosomes undergo pairing, synapsis, and crossing over to ensure their proper segregation at meiosis I. An overarching question is how each chromosome identifies and pairs with its homolog partner within the complex nuclear environment that includes nonhomologous chromosomes (1–4). The general view is that pairing is achieved through homology-based mechanisms that can bring the axes of chromosome pairs into close juxtaposition such that discrete pairing interactions, in conjunction with the establishment of synapsis, are sufficient to align homologs end to end (5). While the intermediate steps leading to pairing are not well understood, the process itself is thought to be stochastic with heterogeneity from cell to cell.The budding yeast, Saccharomyces cerevisiae, is an important model for the study of homolog pairing as it has been used extensively for characterizing many of the other dynamic events that occur over the course of meiotic prophase I that are now known to be conserved across phyla. These include the transition from the Rabl (centromeres-clustered) to bouquet (telomeres-clustered) configurations; telomere-led chromosome movement driven by cytoskeletal motor proteins via the linker of nucleoskeleton and cytoskeleton complex; the formation and repair of Spo11-induced DNA double-strand breaks (DSBs); and the assembly and disassembly of the synaptonemal complex (SC), which is a ribbon-like structure that joins homologs together along their lengths (Fig. 1) (5–11). Several theoretical models of pairing in yeast have been developed that take into account chromosome size, linkage numbers, and the attachment and motion of telomeres at the nuclear envelope (12–16), yet no study to date has combined biophysical modeling together with empirical measurements of meiotic “pairing” dynamics in live cells.Open in a separate windowFig. 1.Overview of chromosome conformations in premeiotic cells (TM=T0) and in meiotic cells in midprophase (∼T3,T4) and late prophase (∼T5,T6). At T₀, cells are in the G0 stage prior to DNA replication, and chromosomes are arranged in the Rabl configuration with centromeres clustered at the nuclear periphery (59). Following transfer to sporulation media, the meiotic program begins with cells entering S phase, over which time the centromeres are dispersed and telomeres start to cluster in the bouquet (59–61, 74, 115). At early to midprophase, Spo11 initiates the formation of DSBs (116), shown as stars, of which the majority are repaired using the homologous chromosome as a substrate (9) (homologs are red and orange lines; note that each line in mid- and late prophase represents the pair of newly replicated sister chromatids). DSBs that go on to form class I or interfering COs, shown as the large stars, assemble the SIC (33, 41, 42), where the new SC is shown as blue lines. Concomitantly, telomeres are subject to motion driven by cytoskeletal motor proteins shown as gray arrows (7, 117). By late prophase, homologs are synapsed end to end and with CO intermediates maturing into CO products as shown.Homolog pairing in yeast has been studied using a number of different assays, including fluorescence in situ hybridization applied to spread chromosome preparations (17, 18), a “collision” assay based on Cre/loxP recombination measuring the relative position and accessibility of pairs of homologous loci (19), and a fluorescence reporter operator system (FROS) that enables specific chromosomal loci to be tagged and followed microscopically in live cells. When allelic loci on homologous chromosomes are tagged, this “one-spot, two-spot” assay has been used as a proxy for local homolog juxtaposition (Fig. 2) (2, 4, 20–26). However, with only a static snapshot, it is not possible to know if colocalization represents a true homolog pairing interaction: that is, if the foci remain colocalized until homologs are segregated at anaphase. While it has been proposed that homologs may undergo many transient interactions that become progressively stabilized throughout prophase (27), this has not yet been investigated.Open in a separate windowFig. 2.(A) A typical field of cells, highlighting example cells showing either two spots (Left) or one spot (Right). (B and C) Maximum intensity projections of the relative positions of fluorescent foci at 30-s intervals. In B, the vertical axis corresponds to a z stack (with step size 0.25 μm). For each x and y coordinate, the maximum value over all time points for that z stack is shown. In C, the vertical axis represents time (t; in seconds), and the projection is instead performed over z stacks. The positions of the loci and the distance between them are highlighted for select time points. (D–F) Kymographs showing the distance between the loci in a single cell over the 25-min imaging period. Each horizontal slice in the kymograph shows the fluorescence intensity along the line joining the centers of the two loci in a single frame. Example of cells where the loci are separated (D) or colocalize (F) for every frame. The mixed cell shown in E undergoes several transitions between the two states. (G) Fraction of cells in the mixed state vs. hours in SPM through meiosis for the URA3 and LYS2 loci in wild-type (WT) and spo11Δ cells. The plot was made from aggregating all available data for each meiotic stage. The error is the SEM with the sample count set to the number of trajectories. (H) Schematic representation of the genomic positions of the URA3 and LYS2 loci on chromosomes V and II, respectively.Although the mechanisms promoting homolog colocalization are not well understood, in yeast interhomolog linkages depend on the formation and repair of DSBs created by Spo11 and its partners during prophase I (9). For any given cell in meiosis, any sequence has the “potential” (albeit not all equally) to experience a DSB. While 150 to 200 DSBs are formed per cell, only ∼90 to 94 DSBs go on to form crossovers (COs). Another ∼66 are repaired using the homologous chromosome but do not lead to CO formation, called noncrossovers (NCOs), and the remaining ones are repaired with the sister chromatid (28–32). COs are divided into class I and class II. Class I COs account for ∼70% of total COs; their position and number are specified in midprophase by the ZMM proteins that make up the synapsis initiation complex (SIC), which functions to couple homologous recombination with the establishment of the SC (8, 33–43). Class II COs arise from an alternative repair process that does not involve the SIC and are “interference independent” (44–46). Thus, the following question arises. Are the excess DSBs necessary to mediate pairing, or is the smaller number that goes on to form COs (class I and/or class II) sufficient?Rather than the homolog pairing process being independent for each “paired” locus, several models relating meiotic homolog pairing to polymer theory predict that pairing at one locus will increase the probability that pairing at an adjacent site will occur (14–16, 47, 48). That is, a molecular linkage at one site on the chromosome is expected to restrict the diffusive properties of adjacent sites along that chromosome (49–51). However, this has not been explicitly evaluated experimentally in the case of meiotic homolog pairing. Furthermore, it is not known if the repair of Spo11 DSBs leads to any directed motion that could aid in bringing homolog axes into close juxtaposition, similar to the observed DSB-dependent directed motion that brings telomeres into proximity seen in ALT (alternative lengthening of telomeres) cells (52). For instance, it has been proposed that single-stranded DNA filaments, formed by resection of DSBs, might capture a locus of the homologous chromosome and processively “reel” the axis into alignment (53–55).To address these gaps in knowledge, we observed the behavior of FROS-tagged loci in three-dimensional (3D) space over time and show the highly dynamic behavior between loci on homologous chromosomes during meiosis prophase I. In contrast to static snapshots, continuous imaging revealed that the majority of cells show a “mixed” phenotype in which foci alternate between colocalized and separated states, indicating that once paired, homologous loci need not remain paired until anaphase. We then used our experimental measurements of the dynamic changes in distance between homologous loci to develop a theoretical model of interhomolog dynamics based on the presence of linkages and polymer diffusion in the viscoelastic medium of the nucleus. This modeling suggests that as chromosomes transition from an unlinked to a linked state, the chromosomes are subject to random fluctuations and not an active mechanism that progressively pulls or pushes them together. Moreover, the addition of a small number of linkages (between two and four) per chromosome pair, closely approximating the number of class I COs, accounts for the observed level of confinement, while the position of linkages and other factors account for the heterogeneous cell-to-cell behavior. These insights illustrate the utility of combining live imaging with biophysical modeling for the study of dynamic processes in living cells.     

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.     

Generalizing Bayesian phylogenetics to infer shared evolutionary events

Many processes of biological diversification can simultaneously affect multiple evolutionary lineages. Examples include multiple members of a gene family diverging when a region of a chromosome is duplicated, multiple viral strains diverging at a “super-spreading” event, and a geological event fragmenting whole communities of species. It is difficult to test for patterns of shared divergences predicted by such processes because all phylogenetic methods assume that lineages diverge independently. We introduce a Bayesian phylogenetic approach to relax the assumption of independent, bifurcating divergences by expanding the space of topologies to include trees with shared and multifurcating divergences. This allows us to jointly infer phylogenetic relationships, divergence times, and patterns of divergences predicted by processes of diversification that affect multiple evolutionary lineages simultaneously or lead to more than two descendant lineages. Using simulations, we find that the method accurately infers shared and multifurcating divergence events when they occur and performs as well as current phylogenetic methods when divergences are independent and bifurcating. We apply our approach to genomic data from two genera of geckos from across the Philippines to test if past changes to the islands’ landscape caused bursts of speciation. Unlike previous analyses restricted to only pairs of gecko populations, we find evidence for patterns of shared divergences. By generalizing the space of phylogenetic trees in a way that is independent from the likelihood model, our approach opens many avenues for future research into processes of diversification across the life sciences.

There are many processes of biological diversification that affect multiple evolutionary lineages, generating patterns of temporally clustered divergences across the tree of life. Understanding such processes of diversification has important implications across many fields and scales of biology. At the scale of genome evolution, the duplication of a chromosome segment harboring multiple members of a gene family causes multiple, simultaneous (or “shared”) divergences across the phylogenetic history of the gene family (1–4). In epidemiology, when a pathogen is spread by multiple infected individuals at a social gathering, this will create shared divergences across the pathogen’s “transmission tree” (5–7). If one of these individuals infects two or more others, this will create a multifurcation (a lineage diverging into three or more descendants) in the transmission tree. At regional or global scales, when biogeographic processes fragment communities, this can cause shared divergences across multiple affected species (8–13). If the landscape is fragmented into three or more regions, this can also cause multifurcations (14). For example, the repeated fragmentation of the Philippines by interglacial rises in sea level since the late Pliocene (15–19) has been an important model to help explain remarkably high levels of microendemism and biodiversity across the archipelago (20–30). This model predicts that recently diverged taxa across the islands should have (potentially multifurcating) divergence times clustered around the beginning of interglacial periods. We are limited in our ability to infer patterns of divergences predicted by such processes because phylogenetic methods assume that lineages diverge independently.To formalize this assumption of independent divergences and develop ways to relax it, it is instructive to view phylogenetic inference as an exercise of statistical model selection, where each topology is a separate model (31–33). Current methods for estimating rooted phylogenies with N tips only consider tree models with N−1 bifurcating divergences and assume that these divergences are independent, conditional on the topology (see ref. 34 for multifurcations in unrooted trees). If, in the history leading to the tips we are studying, diversification processes affected multiple lineages simultaneously or caused them to diverge into more than two descendants, the true tree could have shared or multifurcating divergences. This would make current phylogenetic models with N−1 independent divergence times overparameterized, introducing unnecessary error (Fig. 1). Even worse, with current methods, we lack an obvious way of using our data to test for patterns of shared or multifurcating divergences predicted by such processes.Open in a separate windowFig. 1.A hypothetical evolutionary history with shared divergences (Left) and the benefits of the generalizing tree space under such conditions (Right). Current methods are restricted to one class of tree models, where the tree is fully bifurcating and independent divergence-time parameters are estimated for all internal nodes (Center). Figure was made by using Gram [v4.0.0 (35)] and the P4 phylogenetic toolkit [v1.4 5742542 (36)]. Image credit for top and bottom lizard silhouettes: Phylopic/Steven Traver. Image credit for middle lizard silhouettes: Pixabay/No-longer-here.We relax the assumption of independent, bifurcating divergences by introducing a Bayesian approach to generalizing the space of tree models to allow for shared and multifurcating divergences. In our approach, we view trees with N−1 bifurcating divergences as only one class of tree models in a greater space of trees with anywhere from 1 to N−1 potentially shared and/or multifurcating divergences (SI Appendix, Fig. S1). We introduce reversible-jump Markov chain Monte Carlo (MCMC) algorithms (37–39) to sample this generalized space of trees, allowing us to jointly infer evolutionary relationships, shared and multifurcating divergences, and divergence times. We couple these algorithms with a likelihood model for directly calculating the probability of biallelic characters, given a population (or species) phylogeny, while analytically integrating over all possible gene trees under a coalescent model and all possible mutational histories under a finite-sites model of character evolution (40, 41). Using simulations, we find that the generalized tree model accurately infers shared and multifurcating divergences, while maintaining a low rate of falsely inferring such divergences. To test for patterns of shared and multifurcating divergences predicted by repeated fragmentation of the Philippines by interglacial rises in sea level (42–44), we apply the generalized tree model to genomic data from two genera of geckos codistributed across the islands.     

INAUGURAL ARTICLE by a Recently Elected Academy Member:Chirality-matched catalyst-controlled macrocyclization reactions

Macrocycles, formally defined as compounds that contain a ring with 12 or more atoms, continue to attract great interest due to their important applications in physical, pharmacological, and environmental sciences. In syntheses of macrocyclic compounds, promoting intramolecular over intermolecular reactions in the ring-closing step is often a key challenge. Furthermore, syntheses of macrocycles with stereogenic elements confer an additional challenge, while access to such macrocycles are of great interest. Herein, we report the remarkable effect peptide-based catalysts can have in promoting efficient macrocyclization reactions. We show that the chirality of the catalyst is essential for promoting favorable, matched transition-state relationships that favor macrocyclization of substrates with preexisting stereogenic elements; curiously, the chirality of the catalyst is essential for successful reactions, even though no new static (i.e., not “dynamic”) stereogenic elements are created. Control experiments involving either achiral variants of the catalyst or the enantiomeric form of the catalyst fail to deliver the macrocycles in significant quantity in head-to-head comparisons. The generality of the phenomenon, demonstrated here with a number of substrates, stimulates analogies to enzymatic catalysts that produce naturally occurring macrocycles, presumably through related, catalyst-defined peripheral interactions with their acyclic substrates.

Macrocyclic compounds are known to perform a myriad of functions in the physical and biological sciences. From cyclodextrins that mediate analyte separations (1) to porphyrin cofactors that sit in enzyme active sites (2, 3) and to potent biologically active, macrocyclic natural products (4) and synthetic variants (5–7), these structures underpin a wide variety of molecular functions (Fig. 1A). In drug development, such compounds are highly coveted, as their conformationally restricted structures can lead to higher affinity for the desired target and often confer additional metabolic stability (8–13). Accordingly, there exists an entire synthetic chemistry enterprise focused on efficient formation and functionalization of macrocycles (14–18).Open in a separate windowFig. 1.(A) Examples of macrocyclic compounds with important applications. HCV, hepatitis C virus. (B) Use of chiral ligands in metal-catalyzed or mediated stereoselective macrocyclization reactions. (C) Remote desymmetrization using guanidinylated ligands via Ullmann coupling. (D) This work: use of copper/peptidyl complexes for macrocyclization and the exploration of matched and mismatched effect.In syntheses of macrocyclic compounds, the ring-closing step is often considered the most challenging step, as competing di- and oligomerization pathways must be overcome to favor the intramolecular reaction (14). High-dilution conditions are commonly employed to favor macrocyclization of linear precursors (19). Substrate preorganization can also play a key role in overcoming otherwise high entropic barriers associated with multiple conformational states that are not suited for ring formation. Such preorganization is most often achieved in synthetic chemistry through substrate design (14, 20–22). Catalyst or reagent controls that impose conformational benefits that favor ring formation are less well known. Yet, critical precedents include templating through metal-substrate complexation (23, 24), catalysis by foldamers (25) or enzymes (26–29), or, in rare instances, by small molecules (discussed below). Characterization of biosynthetic macrocyclization also points to related mechanistic issues and attributes for efficient macrocyclizations (30–34). Coupling macrocyclization reactions to the creation of stereogenic elements is also rare (35). Metal-mediated reactions have been applied toward stereoselective macrocyclizations wherein chiral ligands transmit stereochemical information to the products (Fig. 1B). For example, atroposelective ring closure via Heck coupling has been applied in the asymmetric total synthesis of isoplagiochin D by Speicher and coworkers (36–40). Similarly, atroposelective syntheses of (+)-galeon and other diarylether heptanoid natural products were achieved via Ullman coupling using N-methyl proline by Salih and Beaudry (41). Finally, Reddy and Corey reported the enantioselective syntheses of cyclic terpenes by In-catalyzed allylation utilizing a chiral prolinol-based ligand (42). While these examples collectively illustrate the utility of chiral ligands in stereoselective macrocyclizations, such examples remain limited.We envisioned a different role for chiral catalysts when addressing intrinsically disfavored macrocyclization reactions. When unfavorable macrocyclization reactions are confronted, we hypothesized that a catalyst–substrate interaction might provide transient conformational restriction that could promote macrocyclization. To address this question, we chose to explore whether or not a chiral catalyst-controlled macrocyclization might be possible with peptidyl copper complexes. In the context of the medicinally ubiquitous diarylmethane scaffold, we had previously demonstrated the capacity for remote asymmetric induction in a series of bimolecular desymmetrizations using bifunctional, tetramethylguanidinylated peptide ligands. For example, we showed that peptidyl copper complexes were able to differentiate between the two aryl bromides during C–C, C–O, and C–N cross-coupling reactions (Fig. 1C) (43–45). Moreover, in these intermolecular desymmetrizations, a correlation between enantioselectivity and conversion was observed, revealing the catalyst’s ability to perform not only enantiotopic group discrimination but also kinetic resolution on the monocoupled product as the reaction proceeds (44). This latter observation stimulated our speculation that if an internal nucleophile were present to undergo intramolecular cross-coupling to form a macrocycle, stereochemically sensitive interactions (so-called matched and mismatched effects) (46) could be observed (Fig. 1D). Ideally, we anticipated that transition state–stabilizing interactions might even prove decisive in matched cases, and the absence of catalyst–substrate stabilizing interactions might account for the absence of macrocyclization for these otherwise intrinsically unfavorable reactions. Herein, we disclose the explicit observation of these effects in chiral catalyst-controlled macrocyclization reactions.     

Using homology relations within a database markedly boosts protein sequence similarity search

Inference of homology from protein sequences provides an essential tool for analyzing protein structure, function, and evolution. Current sequence-based homology search methods are still unable to detect many similarities evident from protein spatial structures. In computer science a search engine can be improved by considering networks of known relationships within the search database. Here, we apply this idea to protein-sequence–based homology search and show that it dramatically enhances the search accuracy. Our new method, COMPADRE (COmparison of Multiple Protein sequence Alignments using Database RElationships) assesses the relationship between the query sequence and a hit in the database by considering the similarity between the query and hit’s known homologs. This approach increases detection quality, boosting the precision rate from 18% to 83% at half-coverage of all database homologs. The increased precision rate allows detection of a large fraction of protein structural relationships, thus providing structure and function predictions for previously uncharacterized proteins. Our results suggest that this general approach is applicable to a wide variety of methods for detection of biological similarities. The web server is available at prodata.swmed.edu/compadre.Prediction of protein structure and function by sequence homology is among the most important problems in computational biology of proteins, perhaps next after the grand problem of de novo protein folding. The existing gap between the number of known protein sequences and the number of experimentally determined 3D structures is bound to grow with more genomes sequenced by high-throughput technologies (1, 2). Currently, the most reliable and effective way to predict the structure of an uncharacterized protein is to find a sequence homolog with available structural information (3, 4). The chance of finding such a template for a given protein sequence is increasing as sequence space is becoming more extensively covered by 3D structures (5). However, there is, and will be for a long time, a significant fraction of proteins for which finding experimentally characterized sequence homologs is challenging or impossible. The structures of many such proteins, when solved, reveal their remote homology to previously known structures that are undetectable by current sequence-based homology search methods (6). Therefore, the quality of sequence-based homology search remains key for accurate structure prediction, as consistently confirmed by multiple rounds of the Critical Assessment of protein Structure Prediction (7).In the last several years, methods for sequence similarity search have been greatly improved by the analysis of sequence patterns reflecting evolutionary, structural, and functional constraints in protein families. Introduction of numerical profiles (3) and hidden Markov models (HMM) (8) has allowed comparing a sequence to a multiple sequence alignment (MSA) (8–10). Such work was later followed by methods for profile–profile (11–13) and HMM–HMM (14–16) comparison, aimed at detecting similarities between distant families. In addition to the residue substitution preferences at sequence positions, MSA can reveal highly informative patterns of interdependence between amino acid content at different positions, in the form of MSA motifs and secondary structure predictions (15, 17, 18).Is it possible to further improve sequence-based homology search by considering nonsequence information? In a typical homology search aimed at 3D structure prediction, a sequence or family of interest is compared with a database of proteins with known structures. This knowledge allows confident establishment of evolutionary links within the database. In computer science, networks of relationships between database subjects have been successfully used to improve the quality of search methods, most notably web searchers (19). Here, we show that knowledge of the protein database homology network dramatically increases the accuracy of sequence-based search.To capitalize on this idea, we modified PROCAIN (protein profile comparison with assisting information) (18), our sensitive method for sequence profile similarity search, by considering the template’s homologs within the database (Fig. 1). We designed the new similarity measure of COMPADRE (COmparison of Multiple Protein sequence Alignments using Database RElationships) as a linear combination of the original score for the given template with the scores for a set of its homologs identified by structure, function, and sequence. Consistent similarity of these homologs to the query elevates the original score, which can increase the significance of a marginal sequence-based similarity to a level above detection threshold. On the other hand, a favorable score for a spurious hit becomes less significant if the set of its homologs is consistently dissimilar from the query. Therefore, this measure improves both sensitivity and specificity of homology detection. The resulting method is implemented on a web server (prodata.swmed.edu/compadre) that allows submission of a query sequence for identifying homologs with available 3D structure.Open in a separate windowFig. 1.Context of template’s relationships within the database is used to modify the original score (S0T) for sequence-based similarity between query and template. The modified measure is a linear combination of S0T and scores (∑S0H) for the similarity between query and template’s homologs.     

An image-computable model of how endogenous and exogenous attention differentially alter visual perception

Attention alters perception across the visual field. Typically, endogenous (voluntary) and exogenous (involuntary) attention similarly improve performance in many visual tasks, but they have differential effects in some tasks. Extant models of visual attention assume that the effects of these two types of attention are identical and consequently do not explain differences between them. Here, we develop a model of spatial resolution and attention that distinguishes between endogenous and exogenous attention. We focus on texture-based segmentation as a model system because it has revealed a clear dissociation between both attention types. For a texture for which performance peaks at parafoveal locations, endogenous attention improves performance across eccentricity, whereas exogenous attention improves performance where the resolution is low (peripheral locations) but impairs it where the resolution is high (foveal locations) for the scale of the texture. Our model emulates sensory encoding to segment figures from their background and predict behavioral performance. To explain attentional effects, endogenous and exogenous attention require separate operating regimes across visual detail (spatial frequency). Our model reproduces behavioral performance across several experiments and simultaneously resolves three unexplained phenomena: 1) the parafoveal advantage in segmentation, 2) the uniform improvements across eccentricity by endogenous attention, and 3) the peripheral improvements and foveal impairments by exogenous attention. Overall, we unveil a computational dissociation between each attention type and provide a generalizable framework for predicting their effects on perception across the visual field.

Endogenous and exogenous spatial attention prioritize subsets of visual information and facilitate their processing without concurrent eye movements (1–3). Selection by endogenous attention is goal-driven and adapts to task demands, whereas exogenous attention transiently and automatically orients to salient stimuli (1–3). In most visual tasks, both types of attention typically improve visual perception similarly [e.g., acuity (4–6), visual search (7, 8), perceived contrast (9–11)]. Consequently, models of visual attention do not distinguish between endogenous and exogenous attention (e.g., refs. 12–19). However, stark differences also exist. Each attention type differentially modulates neural responses (20, 21) and fundamental properties of visual processing, including temporal resolution (22, 23), texture sensitivity (24), sensory tuning (25), contrast sensitivity (26), and spatial resolution (27–34).The effects of endogenous and exogenous attention are dissociable during texture segmentation, a visual task constrained by spatial resolution [reviews (1–3)]. Whereas endogenous attention optimizes spatial resolution to improve the detection of an attended texture (32–34), exogenous attention reflexively enhances resolution even when detrimental to perception (27–31, 34). Extant models of attention do not explain these well-established effects.Two main hypotheses have been proposed to explain how attention alters spatial resolution. Psychophysical studies ascribe attentional effects to modulations of spatial frequency (SF) sensitivity (30, 33). Neurophysiological (13, 35, 36) and neuroimaging (37, 38) studies bolster the idea that attention modifies spatial profiles of neural receptive fields (RFs) (2). Both hypotheses provide qualitative predictions of attentional effects but do not specify their underlying neural computations.Differences between endogenous and exogenous attention are well established in segmentation tasks and thus provide an ideal model system to uncover their separate roles in altering perception. Texture-based segmentation is a fundamental process of midlevel vision that isolates regions of local structure to extract figures from their background (39–41). Successful segmentation hinges on the overlap between the visual system’s spatial resolution and the levels of detail (i.e., SF) encompassed by the texture (39, 41, 42). Consequently, the ability to distinguish between adjacent textures varies as resolution declines toward the periphery (43–46). Each attention type differentially alters texture segmentation, demonstrating that their effects shape spatial resolution [reviews (1–3)].Current models of texture segmentation do not explain performance across eccentricity and the distinct modulations by attention. Conventional models treat segmentation as a feedforward process that encodes the elementary features of an image (e.g., SF and orientation), transforms them to reflect the local structure (e.g., regions of similarly oriented bars), and then pools across space to emphasize texture-defined contours (39, 41, 47). Few of these models account for variations in resolution across eccentricity (46, 48, 49) or endogenous (but not exogenous) attentional modulations (18, 50). All others postulate that segmentation is a “preattentive” (42) operation whose underlying neural processing is impervious to attention (39, 41, 46–49).Here, we develop a computational model in which feedforward processing and attentional gain contribute to segmentation performance. We augment a conventional model of texture processing (39, 41, 47). Our model varies with eccentricity and includes contextual modulation within local regions in the stimulus via normalization (51), a canonical neural computation (52). The defining characteristic of normalization is that an individual neuron is (divisively) suppressed by the summed activity of neighboring neurons responsive to different aspects of a stimulus. We model attention as multiplicative gains [attentional gain factors (15)] that vary with eccentricity and SF. Attention shifts sensitivity toward fine or coarse spatial scales depending on the range of SFs enhanced.Our model is image-computable, which allowed us to reproduce behavior directly from grayscale images used in psychophysical experiments (6, 26, 27, 29–33). The model explains three signatures of texture segmentation hitherto unexplained within a single computational framework (Fig. 1): 1) the central performance drop (CPD) (27–34, 43–46) (Fig. 1A), that is, the parafoveal advantage of segmentation over the fovea; 2) the improvements in the periphery and impairments at foveal locations induced by exogenous attention (27–32, 34) (Fig. 1B); and 3) the equivalent improvements across eccentricity by endogenous attention (32–34) (Fig. 1C).Open in a separate windowFig. 1.Signatures of texture segmentation. (A) CPD. Shaded region depicts the magnitude of the CPD. Identical axis labels are omitted in B and C. (B) Exogenous attention modulation. Exogenous attention improves segmentation performance in the periphery and impairs it near the fovea. (C) Endogenous attention modulation. Endogenous attention improves segmentation performance across eccentricity.Whereas our analyses focused on texture segmentation, our model is general and can be applied to other visual phenomena. We show that the model predicts the effects of attention on contrast sensitivity and acuity, i.e., in tasks in which both endogenous and exogenous attention have similar or differential effects on performance. To preview our results, model comparisons revealed that normalization is necessary to elicit the CPD and that separate profiles of gain enhancement across SF (26) generate the effects of exogenous and endogenous attention on texture segmentation. A preferential high-SF enhancement reproduces the impairments by exogenous attention due to a shift in visual sensitivity toward details too fine to distinguish the target at foveal locations. The transition from impairments to improvements in the periphery results from exogenous attentional gain gradually shifting to lower SFs that are more amenable for target detection. Improvements by endogenous attention result from a uniform enhancement of SFs that encompass the target, optimizing visual sensitivity for the attended stimulus across eccentricity.     

Self-assembly of amphiphilic Janus dendrimers into uniform onion-like dendrimersomes with predictable size and number of bilayers

A constitutional isomeric library synthesized by a modular approach has been used to discover six amphiphilic Janus dendrimer primary structures, which self-assemble into uniform onion-like vesicles with predictable dimensions and number of internal bilayers. These vesicles, denoted onion-like dendrimersomes, are assembled by simple injection of a solution of Janus dendrimer in a water-miscible solvent into water or buffer. These dendrimersomes provide mimics of double-bilayer and multibilayer biological membranes with dimensions and number of bilayers predicted by the Janus compound concentration in water. The simple injection method of preparation is accessible without any special equipment, generating uniform vesicles, and thus provides a promising tool for fundamental studies as well as technological applications in nanomedicine and other fields.Most living organisms contain single-bilayer membranes composed of lipids, glycolipids, cholesterol, transmembrane proteins, and glycoproteins (1). Gram-negative bacteria (2, 3) and the cell nucleus (4), however, exhibit a strikingly special envelope that consists of a concentric double-bilayer membrane. More complex membranes are also encountered in cells and their various organelles, such as multivesicular structures of eukaryotic cells (5) and endosomes (6), and multibilayer structures of endoplasmic reticulum (7, 8), myelin (9, 10), and multilamellar bodies (11, 12). This diversity of biological membranes inspired corresponding biological mimics. Liposomes (Fig. 1) self-assembled from phospholipids are the first mimics of single-bilayer biological membranes (13–16), but they are polydisperse, unstable, and permeable (14). Stealth liposomes coassembled from phospholipids, cholesterol, and phospholipids conjugated with poly(ethylene glycol) exhibit improved stability, permeability, and mechanical properties (17–20). Polymersomes (21–24) assembled from amphiphilic block copolymers exhibit better mechanical properties and permeability, but are not always biocompatible and are polydisperse. Dendrimersomes (25–28) self-assembled from amphiphilic Janus dendrimers and minidendrimers (26–28) have also been elaborated to mimic single-bilayer biological membranes. Amphiphilic Janus dendrimers take advantage of multivalency both in their hydrophobic and hydrophilic parts (23, 29–32). Dendrimersomes are assembled by simple injection (33) of a solution of an amphiphilic Janus dendrimer (26) in a water-soluble solvent into water or buffer and produce uniform (34), impermeable, and stable vesicles with excellent mechanical properties. In addition, their size and properties can be predicted by their primary structure (27). Amphiphilic Janus glycodendrimers self-assemble into glycodendrimersomes that mimic the glycan ligands of biological membranes (35). They have been demonstrated to be bioactive toward biomedically relevant bacterial, plant, and human lectins, and could have numerous applications in nanomedicine (20).Open in a separate windowFig. 1.Strategies for the preparation of single-bilayer vesicles and multibilayer onion-like vesicles.More complex and functional cell mimics such as multivesicular vesicles (36, 37) and multibilayer onion-like vesicles (38–40) have also been discovered. Multivesicular vesicles compartmentalize a larger vesicle (37) whereas multibilayer onion-like vesicles consist of concentric alternating bilayers (40). Currently multibilayer vesicles are obtained by very complex and time-consuming methods that do not control their size (39) and size distribution (40) in a precise way. Here we report the discovery of “single–single” (28) amphiphilic Janus dendrimer primary structures that self-assemble into uniform multibilayer onion-like dendrimersomes (Fig. 1) with predictable size and number of bilayers by simple injection of their solution into water or buffer.     

Sphericity and symmetry breaking in the formation of Frank–Kasper phases from one component materials

Frank–Kasper phases are tetrahedrally packed structures occurring in numerous materials, from elements to intermetallics to self-assembled soft materials. They exhibit complex manifolds of Wigner–Seitz cells with many-faceted polyhedra, forming an important bridge between the simple close-packed periodic and quasiperiodic crystals. The recent discovery of the Frank–Kasper σ-phase in diblock and tetrablock polymers stimulated the experiments reported here on a poly(isoprene-b-lactide) diblock copolymer melt. Analysis of small-angle X-ray scattering and mechanical spectroscopy exposes an undiscovered competition between the tendency to form self-assembled particles with spherical symmetry, and the necessity to fill space at uniform density within the framework imposed by the lattice. We thus deduce surprising analogies between the symmetry breaking at the body-centered cubic phase to σ-phase transition in diblock copolymers, mediated by exchange of mass, and the symmetry breaking in certain metals and alloys (such as the elements Mn and U), mediated by exchange of charge. Similar connections are made between the role of sphericity in real space for polymer systems, and the role of sphericity in reciprocal space for metallic systems such as intermetallic compounds and alloys. These findings establish new links between disparate materials classes, provide opportunities to improve the understanding of complex crystallization by building on synergies between hard and soft matter, and, perhaps most significantly, challenge the view that the symmetry breaking required to form reduced symmetry structures (possibly even quasiperiodic crystals) requires particles with multiple predetermined shapes and/or sizes.The discovery of materials with aperiodic order, often referred to as “quasicrystals,” 30 years ago (1, 2) heralded new and promising vistas for designing materials endowed with unique properties. In the 1950s Frank and Kasper (3, 4) recognized complex tetrahedral atomic- and molecular-packing geometries that bridge the familiar close-packed crystals [e.g., face-centered cubic (FCC), hexagonally close-packed (HCP), and body-centered cubic (BCC) structures] characterized by periodic order, and quasiperiodic crystals (QCs) that extend crystallography beyond the 230 space groups relevant to periodic crystals (5, 6). The scientific literature is replete with examples of Frank–Kasper phases in hard materials, particularly in the area of intermetallics (7–9), but also in a few complex elemental crystals, including manganese (10, 11) and uranium (12). Recently, this class of crystalline order has cropped up in a host of soft materials, including dendrimers (13), surfactant solutions (14), and block polymers (15, 16), often in close proximity to QC phases (17–19). To the best of our knowledge the principles underlying the formation of Frank–Kasper phases across both categories of materials have not been established, presenting enticing challenges to scientist and engineers bent on controllably arranging atoms and molecules for specific materials applications.Self-assembly of asymmetric diblock copolymers in excess solvent that selectively interacts with one of the blocks leads to the formation of spherical micelles (20, 21) with a core and corona structure as illustrated in Fig. 1. In the absence of solvent, and under conditions that favor segregation of the two blocks, these soft mesomorphic particles produce ordered structures with a lattice size that scales with the size of the particles, controlled by the overall length (degree of polymerization or molecular weight) of the constituent polymers (22). In this article we offer an analysis and interpretation of experimental data obtained from a short diblock copolymer reported earlier to form a Frank–Kasper σ-phase (23, 24). The compositionally asymmetric poly(isoprene-b-lactide) (PI-PLA; IL) diblock copolymer considered in this work (22% PLA by volume; Fig. 1A) is essentially a single-component system. Here we note that this statement is not rigorously correct because the material is made up of a collection of molecules that span a (relatively narrow) distribution in chain lengths and compositions. We argue that such small deviations from ideality do not interfere with or explain the phenomena reported herein. We find that competition between the preferred spherical particle shape and the need to uniformly fill space (i.e., to avoid thermodynamically costly density variations such as voids) results in a transition from a state with BCC structure (Im3¯m space group symmetry) to a tetragonal Frank–Kasper σ-phase (P4₂/mnm symmetry) upon cooling below the order–disorder transition temperature. This transition is mediated by exchange of mass (diblock copolymer chains), resulting in a redistribution of particle sizes and shapes from the single polyhedron associated with the BCC Wigner–Seitz cells to five discrete cells (30 in total per unit cell; ref. 23), which on average better approximate spherical symmetry.Open in a separate windowFig. 1.Schematic illustration of (A) the molecular structure of a poly(isoprene-b-lactide) diblock copolymer, and (B) an isolated self-assembled spherical micelle.Building on this result in soft systems we proceed to draw a number of analogies between the drive toward spherical symmetry in many-body diblock copolymers in real space and long-standing arguments for metals, alloys, and intermetallics regarding the role of sphericity in accommodating the shape of the Fermi surface subject to the constraints imposed by the crystal lattice. In essence we argue that the tendency of alloys and intermetallic compounds to transform to apparently low-symmetry structures, in an attempt to better reconcile the symmetry of the crystal with the spherical reciprocal space symmetry of their (nearly) free electrons, is analogous to the preference for real-space sphericity in the polymeric system studied here. We further highlight analogies between the mechanisms of symmetry breaking in these polymer- and metal-based systems, the former by exchange of mass, the latter by exchange of charge. It is suggested that these analogies provide potentially useful connections between complex crystalline structures in hard and soft matter.