Manifestation of axion electrodynamics through magnetic ordering on edges of a topological insulator

Because topological surface states of a single-crystal topological insulator can exist on all surfaces with different crystal orientations enclosing the crystal, mutual interactions among those states contiguous to each other through edges can lead to unique phenomena inconceivable in normal insulators. Here we show, based on a first-principles approach, that the difference in the work function between adjacent surfaces with different crystal-face orientations generates a built-in electric field around facet edges of a prototypical topological insulator such as Bi₂Se₃. Owing to the topological magnetoelectric coupling for a given broken time-reversal symmetry in the crystal, the electric field, in turn, forces effective magnetic dipoles to accumulate along the edges, realizing the facet-edge magnetic ordering. We demonstrate that the predicted magnetic ordering is in fact a manifestation of the axion electrodynamics in real solids.A topological insulator (TI) hosts topologically protected metallic surface states on its boundaries between inner insulating bulk and outer vacuum that can exist on all of the surfaces with different crystal orientations enclosing the crystal (1, 2). Typically, the protected surface state has the relativistic massless dispersion relation around the time-reversal invariant momenta in the surface Brillouin zone, although its detailed features depend on surface characteristics (3–7). For example, the well-known TIs with the rhombohedral crystal structure such as Bi₂Se₃, Bi₂Te₃, and Sb₂Te₃ (8–10) have stacked quintuple layers along the (111) direction and the low-energy surface state on the (111) surface is isotropic in momentum space (9), whereas other surfaces have quite anisotropic dispersions (3–7). Besides changes in its low-energy electronic dispersions, different facets in a single crystalline TI would have many different physical properties depending on their orientations, and the facet-dependent work function (11, 12) is one interesting example among them. In the TIs mentioned above, such effects will be amplified because of their layered structure— surface atomic and electronic densities vary a lot depending on whether the surface is terminated along the layer or not.Although the physical properties of topological states on a specific facet of 3D TIs have been studied intensively (1–10), mutual interactions among those contiguous to each other through edges have not yet been examined well. A trivial example is the coupling between two massless surface states on the opposite surfaces resulting in an energy gap in the surface energy band of the TI thin film (13). Even in a sufficiently large single 3D TI crystal where the interaction between opposite surfaces can be neglected, different massless surface states should meet and interact with each other at edges between two adjacent facets. In this work, we demonstrate that the combined effects both from the usual surface-dependent properties such as facet-dependent work function difference and from the topological surface properties for a given broken time-reversal symmetry produce a topological magnetoelectric coupling (TME) (14–16) described by the axion electrodynamics without external charge controls as considered before (15). The resulting magnetic ordering along the edges should be robust and strong enough to be measured.Our study of TME couplings (14–16) on edges of TIs is based on the ab initio pseudopotential density functional method (17). We examine Bi₂Se₃ as an example material for our investigation. For a rhombohedral crystal structure of Bi₂Se₃ (18), a surface with the (111) direction has a triangular lattice of Se atoms (typical cleavage surface) whereas one with the (1¯10) or the (1¯1¯2) direction perpendicular to the (111) direction has a tetragonal surface unitcell (Fig. 1). In a single crystal of Bi₂Se₃ grown along the (111) direction, the rectangular-shaped crystal has the (1¯10) and (1¯1¯2) surfaces as side walls whereas the hexagonal (19) or triangular (20) column-shaped one has the (1¯10) surfaces as side surfaces. We choose the (1¯10) surface as a side wall in our study (Fig. 1B). Then we solve the modified Maxwell’s equation of the axion electrodynamics (14, 15, 21) for a model geometry of the Bi₂Se₃ single crystal with boundary conditions obtained from the first-principles calculations.Open in a separate windowFig. 1.(A) Rectangular-shaped crystal of Bi₂Se₃ with the top (111), the front (1¯1¯2), and the side (1¯10) surfaces. (B) Hexagonal-shaped crystal with the top (111) surface and the (1¯10) sides. The dashed squares in A and B are cross-sections of the crystal to be considered in the model calculations. (C) Atomic structure of the (111) and (D) that of the (1¯10) surface. The black parallelogram indicates the unit cell of each surface; the area for the (111) surface is 14.83 Ų and that for the (1¯10) surface is 68.42 Ų.     

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.     

Decoupling between Shockley partials and stacking faults strengthens multiprincipal element alloys

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

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

Photon gating in four-dimensional ultrafast electron microscopy

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

Mechanisms of hematin crystallization and inhibition by the antimalarial drug chloroquine

Hematin crystallization is the primary mechanism of heme detoxification in malaria parasites and the target of the quinoline class of antimalarials. Despite numerous studies of malaria pathophysiology, fundamental questions regarding hematin growth and inhibition remain. Among them are the identity of the crystallization medium in vivo, aqueous or organic; the mechanism of crystallization, classical or nonclassical; and whether quinoline antimalarials inhibit crystallization by sequestering hematin in the solution, or by blocking surface sites crucial for growth. Here we use time-resolved in situ atomic force microscopy (AFM) and show that the lipid subphase in the parasite may be a preferred growth medium. We provide, to our knowledge, the first evidence of the molecular mechanisms of hematin crystallization and inhibition by chloroquine, a common quinoline antimalarial drug. AFM observations demonstrate that crystallization strictly follows a classical mechanism wherein new crystal layers are generated by 2D nucleation and grow by the attachment of solute molecules. We identify four classes of surface sites available for binding of potential drugs and propose respective mechanisms of drug action. Further studies reveal that chloroquine inhibits hematin crystallization by binding to molecularly flat {100} surfaces. A 2-μM concentration of chloroquine fully arrests layer generation and step advancement, which is ∼10⁴× less than hematin’s physiological concentration. Our results suggest that adsorption at specific growth sites may be a general mode of hemozoin growth inhibition for the quinoline antimalarials. Because the atomic structures of the identified sites are known, this insight could advance the future design and/or optimization of new antimalarials.Whereas significant public health initiatives have eradicated malaria from North America, Europe, and other developed regions of the world (1), the disease remains endemic in the equatorial regions of Africa, South America, Southeast Asia, and Oceania (2). Approximately 40% of the global population is at risk for malaria infection, predominantly from the protozoan parasite Plasmodium falciparum (2). Very disturbingly, a resurgence of the disease throughout the world has occurred since the 1960s due to the emergence and spread of Plasmodium parasites resistant to chloroquine combination treatments (2, 3). Delayed parasite clearance has been recorded for even the most recent artemisinin-based therapies (4). The weak responses to the common antimalarial drugs underscore the urgent need for research into the critical processes of malaria parasite physiology.Malaria parasites residing in the erythrocytes catabolize hemoglobin and release Fe(II) heme (5). The released heme rapidly oxidizes to toxic Fe(III) hematin, which is sequestered as crystalline hemozoin (6, 7). The traditional Western treatment for malaria, quinine, and its synthetic homologs (chloroquine, mefloquine, and others) (8–11) putatively works by blocking hematin crystallization (12). Available evidence suggests that artemisinin, another antimalarial drug, binds to heme (2, 13). The sequestration of heme into hemozoin is a suitable target for new antimalarials. Hence, an understanding of the mechanisms of hematin crystallization and its inhibition by antimalarials may prove to be influential for drug development (14). Despite many years of effort (7, 9, 12, 15–18), fundamental questions regarding the mechanism of hematin crystallization and its inhibition remain elusive. Among them are (i) What is the nature of the environment within the parasite where hemozoin crystals recruit hematin and grow? The two likely candidates are the aqueous phase in the parasite digestive vacuole (DV) (18, 19) and the lipid subphase that has been reported to reside either in the DV bulk (9, 16) or along the DV membrane (18–20). (ii) What is the mechanism of hematin crystallization?—classical, i.e., addition of molecules to growth sites (21–23), or nonclassical, i.e., association of precursors (24–26)? (iii) What is the mechanism of action of the inhibitor species? It is possible that the inhibitors either reduce the concentration and activity of hematin in the growth medium through complexation (27, 28), or interfere with crystallization by binding to the crystal surface(s) and restricting solute addition (23).The answers to these questions offer an improved understanding of malaria parasite physiology and may potentially lead to the rational design of hematin crystallization inhibitors that could serve as effective antimalarial drugs. As a model of hematin (Fig. 1A) crystallization we use the growth of β-hematin, the synthetic form of hemozoin. β-Hematin has a crystal structure (P1¯ symmetry) and habit identical to its natural analog (7), with predominant growth along its c→ direction, (Fig. 1B). Both natural and synthetic hematin crystals assemble as high-aspect-ratio parallelogram-shaped platelets, with basal {100} faces and sides defined by {010}, (01¯1¯), and (001) surfaces (17, 29).Open in a separate windowFig. 1.β-Hematin crystals. (A) Structure of hematin. (B) AFM image of a β-hematin crystal on a glass substrate reveals a morphology similar to hemozoin crystals isolated from P. falciparum. (Scale bar, 2 μm.) (C) A 3D AFM height image of a (1¯00) face reveals the presence of unfinished layers. The step height h = 1.17 ± 0.07 nm was determined by averaging measurements from multiple images. (D) Molecular model of β-hematin using the software package Diamond illustrates an unfinished layer (C atoms in white) on a (1¯00) face (C atoms in blue).     

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.     

Topological liquid crystal superstructures as structured light lasers

Liquid crystals (LCs) form an extremely rich range of self-assembled topological structures with artificially or naturally created topological defects. Some of the main applications of LCs are various optical and photonic devices, where compared to their solid-state counterparts, soft photonic systems are fundamentally different in terms of unique properties such as self-assembly, self-healing, large tunability, sensitivity to external stimuli, and biocompatibility. Here we show that complex tunable microlasers emitting structured light can be generated from self-assembled topological LC superstructures containing topological defects inserted into a thin Fabry–Pérot microcavity. The topology and geometry of the LC superstructure determine the structuring of the emitted light by providing complex three-dimensionally varying optical axis and order parameter singularities, also affecting the topology of the light polarization. The microlaser can be switched between modes by an electric field, and its wavelength can be tuned with temperature. The proposed soft matter microlaser approach opens directions in soft matter photonics research, where structured light with specifically tailored intensity and polarization fields could be designed and implemented.

The long-range order and the fluid nature of liquid crystals (LCs) enable them to have some very unique properties not present in any other material. The large number of liquid crystalline phases in combination with inclusions and various boundary conditions results in a very wide variety of topological structures (1), which have been extensively studied in the last decades. Some of them form spontaneously, such as, for example, helices in cholesterics, three-dimensional (3D) periodic structures in blue phases, and focal conic domains in smectics, or are induced from outside, for example, torons in frustrated cholesterics (2). By introduction of colloidal particles into the LCs (3) or by confining LCs, even more complex structures arise, including ordered colloidal crystals (4, 5), topological colloids (6), knotted structures (7), and complex director orientations in LC droplets and shells (8). Active colloids (9) in LCs have also attracted great interest recently. Further, light–matter interaction can create, for example, optical solitons (10).Despite this richness of the LC structures, only very few of them have been used inside a laser cavity till now. In most studies, light is passed through an LC structure and in combination with other optical elements changes the light intensity, polarization, and/or phase. A light field with custom designable intensity, polarization, and phase fields is referred to as structured light (11). Structured light is highly relevant today, with applications ranging from imaging, metrology, optical trapping, ultracold atoms, to communications and memory (12–15). Special cases of structured light are optical vortex beams (16, 17), which carry orbital angular momentum and vector (18, 19) beams with a spatially varying direction of polarization.Structured light is mostly created by passing a simple Gaussian beam through a phase plate, or q plate, or by reflecting it from a metasurface, plasmonic nanostructure or spatial light modulator (11, 16). For example, structured light can be generated by passing Gaussian light through an LC layer with a single topological defect of charge q (20, 21), through a nematic LC droplet with a + 1 topological defect in its center (22), through LC disclinations with charge ranging from −3/2 to +3/2 (23), and even through more complex structures such as torons (24).Structured light can be also generated directly in the laser cavity (25, 26), which can be advantageous to achieve better mode purity and higher output powers. However, a controllable and easy to manufacture microcavity that generates structured light on demand is still an open challenge. Examples include laser cavities with a spatial light modulator (27), q plate (26), metasurface (28) and microspheres (29) inside the laser cavity, and microring cavities with broken mirror symmetry (30). In most studies, polarization of the laser output has been controlled in a limited way, primarily focusing on cylindrical vector vortex beams. There are also several examples of LC microlasers (31–35) which usually exhibit high tunability of the lasing wavelength, but not much emphasis has been given to the tailoring of the intensity profile of the output beam.In this work we demonstrate emission of laser vector beams (VBs) with diverse and beyond standard intensity and polarization profiles generated from self-assembled LC superstructures with topological defects, confined into a Fabry–Pérot microcavity. The microcavity is made of two closely spaced dichroic mirrors. The cavity contains LC structures with a different topology, specifically the radial nematic microdroplets with a +1 point defect, nematic disinclination line defects, torons and cholesteric fingers in chiral nematic LC, colloidal chains, and microtori, suspended in a nematic LC. The LC is doped with a fluorescent dye, which provides optical gain when illuminated with an external nanosecond pulsed laser. Above the lasing threshold, the microcavity emits coherent light, which is sent to a camera and an imaging spectrometer (Fig. 1A). The topology of light is leadingly ascribed in the actual spatial profiles of the polarization of the emitted light modes. In Laser Emission from LC Droplets in a Cavity and Polarization Selection and Mode Switching, laser modes from nematic droplets in an isotropic media are described, including mode polarization selection by dye orientation and mode switching and tuning by electric field and temperature. In Generation of Modes from Chiral Nematic Structures, more complex optical modes are shown as generated by chiral structures, specifically torons and chiral fingers. In Generation of Complex VBs, VBs with more general polarization are demonstrated by employing various LC structures with topological defects.Open in a separate windowFig. 1.Scheme of optical setup and generation of laser VBs. (A) Optical setup consists of a 532-nm pulsed laser for optical pumping, optional infrared 1,064-nm laser tweezers for manipulating the LC structures, an imaging spectrometer, a camera, and an objective. The sample is composed of an LC structure, which is sandwiched in between two dichroic mirrors, forming a Fabry–Pérot microcavity. To analyze the optical modes, the LC laser output is sent through an imaging spectrometer with the slit wide-open. The image of the lasing emission pattern is spread in wavelength and imaged on a CCD sensor. The shape of each lasing mode is retained when passing through the spectrometer, and the center position of each mode on the sensor indicates its wavelength. (B) Schematic representation of nematic director field (black) in the equatorial plane of a radial nematic droplet. (C) Bright-field image of a radial LC droplet in the cavity. (D) The same droplet viewed under crossed polarizers. (E) The droplet emits light when optically pumped above the lasing threshold. (F) Spectral decomposition of the laser modes emitted from another, smaller 6.2- μm-diameter radial nematic droplet in a 25- μm cavity. Three transversal modes are supported: VB2radial, VB0radial, and TEM₀₀ (transverse electromagnetic, simple Gaussian beam), which repeat as different longitudinal modes. (G) A single isolated mode, which is emitted from the droplet depicted in C–E with a diameter of 21 μm in a 25 μm cavity and is identified as VB8radial. (H) A beam from a droplet analyzed with a wavefront sensor. The color of the pixels represents the intensity map, and the arrows represent displacements of focal spots generated by the lenslet array.     

Developmental constraints enforce altruism and avert the tragedy of the commons in a social microbe

Organisms often cooperate through the production of freely available public goods. This can greatly benefit the group but is vulnerable to the “tragedy of the commons” if individuals lack the motivation to make the necessary investment into public goods production. Relatedness to groupmates can motivate individual investment because group success ultimately benefits their genes’ own self-interests. However, systems often lack mechanisms that can reliably ensure that relatedness is high enough to promote cooperation. Consequently, groups face a persistent threat from the tragedy unless they have a mechanism to enforce investment when relatedness fails to provide adequate motivation. To understand the real threat posed by the tragedy and whether groups can avert its impact, we determine how the social amoeba Dictyostelium discoideum responds as relatedness decreases to levels that should induce the tragedy. We find that, while investment in public goods declines as overall within-group relatedness declines, groups avert the expected catastrophic collapse of the commons by continuing to invest, even when relatedness should be too low to incentivize any contribution. We show that this is due to a developmental buffering system that generates enforcement because insufficient cooperation perturbs the balance of a negative feedback system controlling multicellular development. This developmental constraint enforces investment under the conditions expected to be most tragic, allowing groups to avert a collapse in cooperation. These results help explain how mechanisms that suppress selfishness and enforce cooperation can arise inadvertently as a by-product of constraints imposed by selection on different traits.

Individuals often perform cooperative acts that are costly to the actor but benefit all members of their group, regardless of individual contributions (1, 2). While this type of cooperation through public goods can be hugely beneficial for the group, the self-sacrifice it requires may outweigh the incremental benefits that an individual’s own contribution adds to group success (3, 4). As a result, individuals will often lack motivation to contribute to public goods, which can lead to the tragedy of the commons (5), where selfish behaviors that maximize personal interests reduce the success of the whole group (4). The potential risk that the tragedy represents to societies has long been recognized in economics (6, 7), and its role in shaping the evolution of cooperation and group organization in nature has become increasingly recognized in biology (3, 8, 9). Despite this, we still have a limited understanding of the conditions under which groups actually suffer from the tragedy, the factors that determine how bad the outcome is, and the mechanisms that mitigate its impact and allow groups to avert the most catastrophic consequences where public goods are not produced at all.In biological systems, groups can decrease the threat of the tragedy by ensuring that relatedness is high enough to motivate public goods investment (3). Relatedness is a powerful motivator of group-beneficial behaviors at a genetic level because the benefits accrued by copies of the actor’s genes present in groupmates can more than offset the cost of the self-sacrifice by the actor (10). However, many systems lack mechanisms that can always reliably ensure high relatedness (11–13). Reduced relatedness can be problematic for groups because it can shift the balance of selection away from favoring individuals acting for the good of the group toward maximizing their selfish interests. However, under all relatedness conditions, selection should favor individuals who are able to contribute to public goods at the level that maximizes their inclusive fitness (given their relatedness), which can be accomplished by strategically adjusting contributions depending on their relatedness to the group (2, 14–18). The logic of such strategic cooperation is captured in the “Collective Investment” game (17, 18) in which the “players” are different genotypes interacting in groups and each player decides what fraction of their resources to invest into production of public goods. Group members benefit (at a rate given by b) from the total collective amount of public goods produced, while individuals pay a personal cost (at a rate of c per unit contributed) in terms of reduced direct reproduction or some other component of direct fitness (see Materials and Methods for a brief presentation of the model). Given some benefits and costs of public goods production, the optimal level of investment for each player will depend on their relatedness to the group (r_i) (Fig. 1). When a player has a relatedness of 1 to the group (i.e., only one genotype is present in the group), they should invest at a level that maximizes the total fitness of the group (denoted by θ, which equals [b−c]/2bc). However, as relatedness declines from 1, motivation to invest in public goods declines, eventually reaching 0 when relatedness drops below the level where the costs outweigh the benefits (which occurs once r_i < c/b, following Hamilton’s rule) (10). The degree to which this will occur will depend on the level of relatedness within a group and the magnitude of benefits from public goods relative to their costs, which shapes motivation to invest across the range of relatedness (Fig. 1). Furthermore, the catastrophic collapsing tragedy is guaranteed to arise under conditions where no group member is motivated to invest, unless there is some form of enforcement. Indeed forms of enforcement have been reported in nature (3, 14, 19–23), but we still have a very limited mechanistic understanding of their evolution, their mode of action, the role they play in the face of strategic cooperation, and the extent to which they provide a solution to the tragedy of the commons.Open in a separate windowFig. 1.A player’s investment in public goods as a function of their relatedness to the group. The different lines correspond to different benefits relative to costs (b/c) (see inset legend). Each line corresponds to a value of 12(1c−1bri) whenever r_i > c/b, and a value of 0 otherwise. The y axis scales investment relative to that which optimizes group fitness (θ).To understand the threat posed by the tragedy of the commons in a natural system, and the potential for enforcement to avert its impact, we measured the pattern of relatedness-dependent public goods investment in groups containing multiple strains of Dictyostelium discoideum (replicated across several different sets of strains) and used these to estimate the parameters of the Collective Investment game. In this system, single-celled individuals aggregate to collectively form a fruiting body constructed of a stalk (the public good) that facilitates dispersal of spores (the benefit from public goods) (24–26). Data on the frequency of clonality/chimerism in nature indicate that both clonality and chimerism are relatively common (27). Clonality should provide strong selection for a system of canalization (28) that ensures adaptive fruiting body proportioning to optimize clonal group success. Similarly, the high frequency of chimerism in nature [with about a quarter of aggregations containing multiple genotypes (27)] provides ample opportunities for selection to shape adaptive responses to chimerism. Indeed, D. discoideum has been shown to exhibit strategic adjustment of contributions to the stalk in response to relatedness (17) and an allorecognition mechanism that can increase relatedness by causing partial segregation in chimeric aggregations (29–31). However, while segregation can potentially limit opportunities for selfishness to undermine group success, it does not allow strains to completely avoid the threat of the tragedy because the extent of segregation varies depending on the genotypes of the interacting strains and, even when high, it does not result in clonality (31). Instead, it simply increases the variance in relatedness across fruiting bodies, which allows some groups to escape the worst of the tragedy by ending up with one strain with high relatedness (which can ensure adequate stalk investment), although many other groups remain highly heterogeneous and potentially suffer the tragedy (31). Moreover, strains with low relatedness to their group show lower levels of segregation (17), which means that groups containing a large number of strains, each with low relatedness, are expected to show relatively low levels of segregation. These patterns of imperfect segregation mean that high relatedness cannot be ensured and, critically, strains can be trapped in the most tragic conditions, where no strain has high enough relatedness to be motivated to invest while strains are able to segregate away from the group. Under these conditions, natural selection could favor processes that enforce cooperation and limit selfish behavior to avert the catastrophic collapse of stalk production.     

Direct visualization of polaron formation in the thermoelectric SnSe

SnSe is a layered material that currently holds the record for bulk thermoelectric efficiency. The primary determinant of this high efficiency is thought to be the anomalously low thermal conductivity resulting from strong anharmonic coupling within the phonon system. Here we show that the nature of the carrier system in SnSe is also determined by strong coupling to phonons by directly visualizing polaron formation in the material. We employ ultrafast electron diffraction and diffuse scattering to track the response of phonons in both momentum and time to the photodoping of free carriers across the bandgap, observing the bimodal and anisotropic lattice distortions that drive carrier localization. Relatively large (18.7 Å), quasi-one-dimensional (1D) polarons are formed on the 300-fs timescale with smaller (4.2 Å) 3D polarons taking an order of magnitude longer (4 ps) to form. This difference appears to be a consequence of the profoundly anisotropic electron–phonon coupling in SnSe, with strong Fröhlich coupling only to zone-center polar optical phonons. These results demonstrate a high density of polarons in SnSe at optimal doping levels. Strong electron-phonon coupling is critical to the thermoelectric performance of this benchmark material and, potentially, high performance thermoelectrics more generally.

Thermoelectric materials convert a difference in temperature into an electrical potential (i.e., the thermoelectric effect) and promise to become increasingly important components of energy-harvesting devices and technologies (1–3). This could make a significant contribution to sustainability efforts by enabling electrical power generation from otherwise wasted heat. Unfortunately, the combination of thermal and electrical properties that leads to high thermoelectric performance is not found in naturally occurring materials (4); efficient thermoelectrics must be engineered. The figure of merit for thermoelectric efficiency is ZT=(S2σ/κ)T, where T is the absolute temperature, S is the Seebeck coefficient (induced voltage per temperature gradient), σ is the electrical conductivity, and κ is the thermal conductivity. Historically, increasing ZT has consisted in starting with compounds with a high Seebeck coefficient (e.g., selenides), and then selecting for good electrical conductivity and low thermal conductivity. In this sense, the ideal thermoelectric has been referred to as a “phonon glass–electron crystal” (5)—a concept that, interestingly, also seems to apply to lead halide perovskite light-harvesting materials (6). Nanostructuring has also been explored as a way to further reduce the thermal conductivity of thermoelectrics without significantly impacting electrical conductivity (7), but concerns regarding manufacturing and longevity favor the use of bulk materials (8). In practice, attempts to optimize the performance of bulk thermoelectric materials by favorably influencing a single parameter have not been a successful strategy, because the key properties are all interdependent (7). Thus, developing a more sophisticated understanding of the fundamental interdependencies between key material parameters (S, σ, and κ) is widely recognized as critical to the development of high-performance thermoelectrics.Recently, tin selenide (SnSe) has been shown to exhibit remarkable thermoelectric efficiency, while also being non–lead based and composed of earth-abundant elements (9–11). Its high performance owes to three factors: 1) an anomalously low lattice thermal conductivity ¡1 W·m−1 ·K⁻¹ (9) at room temperature that decreases even further at higher temperature, 2) an electrical conductivity that increases notably above 600 K, and 3) a high Seebeck coefficient. These factors combine to yield a profound enhancement in thermoelectric performance in SnSe above 600 K, from ZT≈0.1 to a maximum ZT > 2 at 800 K (9, 10). In the case of undoped SnSe, this enhancement is associated with a second-order Pnma→Cmcm phase transition (Fig. 1 A and B) of a displacive character (15) but, at a microscopic level, is related to changes in the character of the electron–phonon (16) and phonon–phonon (17) interactions that control electrical and thermal transport in the material.Open in a separate windowFig. 1.(A) SnSe has a layered orthorhombic structure in the Pnma phase at room temperature. (B) The Pnma structure is derived from 3D distortion of the higher-symmetry (distorted rock salt) Cmcm phase, which is stable above 750 K. Crystallographic directions are all given with respect to the low-temperature Pnma phase, and structures were rendered using Visualization for Electronic and Structural Analysis (VESTA) (12). (C) Diagram of the electronic structure of Pnma SnSe in the b⋆–c⋆ plane at 300 K. Three distinct valleys are present in both the valence and conduction bands: at Γ, 2/3 Y, and 3/4 Z (13). Photoexcitation at 800 nm (1.55 eV) photodopes electrons and holes into all three valleys. (D) Schematic (single valley) band structure diagram immediately following photoexcitation, which generates delocalized conduction band electrons (equivalent picture for holes not shown). (E) Schematic band structure diagram after carrier localization indicating a polaron peak below the Fermi energy E_F. (F) Configuration coordinate showing the free energy of the system as carriers self-localize via phonon dressing; that is, the generation of a local lattice distortion (14). The phonon wavevector dependence of this dressing process is probed directly through the UEDS experiments reported here.Unlike most previous studies, which have attempted to understand the enhancement of thermoelectric properties in SnSe in terms of lattice anharmonicity and the Pnma→Cmcm phase transition (17–20), in this work, we focus on the momentum dependence of electron–phonon coupling in the Pnma phase specifically (21). We seek to develop a full understanding of the carrier–lattice interactions that may also contribute to thermoelectric performance. To this end, we use ultrafast electron diffraction (UED) and ultrafast electron diffuse scattering (UEDS) (22–26) to directly probe electron–phonon interactions in momentum and time following the photodoping of carriers (Fig. 1C). A feature of these ultrafast measurements is that they freeze out changes in electronic and phonon band structure that result from in-plane thermal expansion (temperature-dependent lattice constants), uncoupling those effects from those due exclusively to the photodoped carriers that are the subject of our investigations. The results presented here clearly reveal profoundly momentum-dependent electron–phonon coupling in SnSe, as is expected from Fröhlich coupling in a polar lattice (16). However, the ultrafast diffuse scattering signals also show clear signatures of the “phonon dressing” (lattice distortion) that drives photocarrier localization and polaron formation (Fig. 1 D–F), even at high levels of photocarrier doping [equivalent to the doping levels previously used to optimize the power factor in SnSe (10)].     

The missing enzymatic link in syntrophic methane formation from fatty acids

The microbial production of methane from organic matter is an essential process in the global carbon cycle and an important source of renewable energy. It involves the syntrophic interaction between methanogenic archaea and bacteria that convert primary fermentation products such as fatty acids to the methanogenic substrates acetate, H₂, CO₂, or formate. While the concept of syntrophic methane formation was developed half a century ago, the highly endergonic reduction of CO₂ to methane by electrons derived from β-oxidation of saturated fatty acids has remained hypothetical. Here, we studied a previously noncharacterized membrane-bound oxidoreductase (EMO) from Syntrophus aciditrophicus containing two heme b cofactors and 8-methylmenaquinone as key redox components of the redox loop–driven reduction of CO₂ by acyl–coenzyme A (CoA). Using solubilized EMO and proteoliposomes, we reconstituted the entire electron transfer chain from acyl-CoA to CO₂ and identified the transfer from a high- to a low-potential heme b with perfectly adjusted midpoint potentials as key steps in syntrophic fatty acid oxidation. The results close our gap of knowledge in the conversion of biomass into methane and identify EMOs as key players of β-oxidation in (methyl)menaquinone-containing organisms.

The microbial conversion of natural polymers into methane plays an important role in the global carbon cycle and accounts for more than one-half of all methane produced on Earth per year (1, 2). Methane is formed in anoxic environments, including marine and freshwater sediments, but also in biogas reactors of wastewater treatment plants and other engineered systems. A complex syntrophic association between fermenting bacteria and methanogenic archaea is involved in the degradation of biomass to CH₄ and CO₂. Primary fermenting bacteria hydrolyze complex polymers into monomers and degrade them mainly into short chain fatty acids (scFA) and alcohols. Secondary fermenting bacteria then oxidize these products to the methanogenic substrates acetate, H₂, CO₂, and formate that are finally converted into methane by hydrogenotrophic or acetotrophic archaea (Fig. 1A) (3). The reduction of CO₂ to CH₄ depends on interspecies electron transfer from secondary fermenting bacteria to methanogenic archaea usually via the diffusible low-potential carriers formate and/or H₂ (3–5) or, as recently proposed, directly via nanowires (6).Open in a separate windowFig. 1.Syntrophic degradation of organic matter to methane. (A) Major metabolic processes involving primary fermenters, secondary fermenters, and methanogenic archaea (for simpler presentation, acetogenic conversion of monomers is not depicted here). (B) Model for syntrophic β-oxidation of butyrate to two acetates coupled to the reduction of protons or CO₂. The enzyme mediating electron transfer from reduced ETF to FDH has not been studied before and was assigned to noncharacterized DUF224 based on omics-based predictions.The oxidation of scFA to acetate coupled to the reduction of H⁺ or CO₂ is endergonic under standard conditions (+48 kJ/mol butyrate) but becomes clearly exergonic at an H₂ partial pressure below 10 Pa (3, 7). On the other side, the H₂ threshold partial pressure of hydrogenotrophic methanogenesis is around 8 Pa corresponding to E′(2H⁺/H₂) ∼ −290 mV or around 10 µM formate, resulting in similar values for the CO₂/formate redox couple (2). The syntrophic oxidation of the scFA model compound butyrate to acetate is accomplished by gram-positive Firmicutes (model organism Syntrophomonas wolfei) or gram-negative Deltaproteobacteria (model organism Syntrophus aciditrophicus) (3, 4, 7). It proceeds via two unequal β-oxidation steps (SI Appendix, Fig. 1) (8, 9): 1) Butyryl-CoA is oxidized to crotonyl-CoA by an acyl-CoA dehydrogenase (DH) (E°′ ∼ −10 mV) (10) with an electron-transferring flavoprotein (ETF) serving as electron acceptor, and 2) the 3-hydroxybutyryl-CoA formed by crotonase is subsequently oxidized to acetoacetyl-CoA by 3-hydroxybutyryl-CoA DH (ΔE°′ = −250 mV) (11) using NAD⁺ as acceptor. The reduction of H⁺ or CO₂ by the NADH formed is feasible under syntrophic conditions, whereas butyryl-CoA oxidation coupled to H⁺ or CO₂ reduction has to overcome a gap of ΔE ∼ −280 mV, giving ΔG°′ ∼ +54 kJ ⋅ mol^–1 (3–5). Considering that only one ATP is gained via substrate-level phosphorylation, the energy metabolism of syntrophic butyrate oxidation has remained enigmatic.Omics-based studies have led to the proposal of models for energy coupling processes during syntrophic scFA oxidation (12–16). The redox loop model is based on the identification of a putative membrane-bound gene product (DUF224) (14–16). It proposes that electrons are transferred from acyl-CoA via ETF, DUF224, and menaquinone (MK) to a membrane-bound formate dehydrogenase (FDH) or hydrogenase driven by the translocation of protons to the cytoplasm, resulting in two energetically unequal half reactions:Acyl-CoA + MK →Enoyl-CoA + MKH2 ΔG°’ = +12.5 kJ mol–1CO2+ MKH2→Formate + H++ MKΔG’ = +41.5 kJ mol–1.In agreement, a protonophore inhibited formation of H₂ from butyrate in whole-cell suspension of S. wolfei (17), and MK was reported in S. wolfei and S. aciditrophicus (12, 17). In an alternative model, an electron-confurcating ETF couples endergonic reduction of NAD⁺ by ETF_red to the exergonic reduction of NAD⁺ by reduced ferredoxin (Fd_red^–) (18). The NADH formed then may serve as an electron donor for a cytoplasmic FDH. Biochemical evidence for either of the two models is lacking.Here, we study the missing membrane components that link fatty acid oxidation to CO₂ reduction during syntrophic methane production. We provide biochemical evidence that a membrane-bound diheme oxidoreductase and a modified methylmenaquinone with perfectly adjusted redox potentials are the key players of this process. We further propose that related enzymes play a previously overlooked role in the lipid catabolism of the majority of microorganisms.     

Large uncertainties in global hydroxyl projections tied to fate of reactive nitrogen and carbon

The hydroxyl radical (OH) sets the oxidative capacity of the atmosphere and, thus, profoundly affects the removal rate of pollutants and reactive greenhouse gases. While observationally derived constraints exist for global annual mean present-day OH abundances and interannual variability, OH estimates for past and future periods rely primarily on global atmospheric chemistry models. These models disagree ± 30% in mean OH and in its changes from the preindustrial to late 21st century, even when forced with identical anthropogenic emissions. A simple steady-state relationship that accounts for ozone photolysis frequencies, water vapor, and the ratio of reactive nitrogen to carbon emissions explains temporal variability within most models, but not intermodel differences. Here, we show that departure from the expected relationship reflects the treatment of reactive oxidized nitrogen species (NO_y) and the fraction of emitted carbon that reacts within each chemical mechanism, which remain poorly known due to a lack of observational data. Our findings imply a need for additional observational constraints on NO_y partitioning and lifetime, especially in the remote free troposphere, as well as the fate of carbon-containing reaction intermediates to test models, thereby reducing uncertainties in projections of OH and, hence, lifetimes of pollutants and greenhouse gases.

The hydroxyl radical (OH) is a keystone chemical species in the atmosphere, determining the removal rate of many trace gases of importance to climate, composition, and human and ecosystem health (1). For example, reaction with OH in the troposphere^* is the dominant sink for methane, a powerful greenhouse gas and precursor for tropospheric ozone, a major surface pollutant and greenhouse gas itself (2). Understanding what drives variability in OH is therefore critical for forecasting future changes in the self-cleansing capability of the atmosphere. The fundamental chemistry of background OH has been well known for decades (3–5). Nevertheless, global atmospheric chemistry models show large disagreement in mean OH and its transient response to specified changes in emissions (6, 7).Fig. 1 shows global mean OH and its temporal evolution within the ensemble of simulations that participated in the Atmospheric Chemistry-Climate Model Intercomparison Project (ACCMIP) (8). The ACCMIP ensemble is a comprehensive suite of global three-dimensional atmospheric chemistry models driven by identical anthropogenic emission scenarios for the period 1850–2100 (9, 10). Despite applying identical anthropogenic emissions in all ACCMIP models, tropospheric mean abundances of OH range ± 30 % relative to the multimodel mean during the last decade of the historical simulation (gray-shaded interval of Fig. 1). The models also disagree as to whether OH increases or decreases across any prescribed emission scenario, except for a small window between 1980 and 2010 (when all increase).Open in a separate windowFig. 1Large disagreement in decadal mean tropospheric OH and its transient evolution in global atmospheric chemistry models. The models shown prescribe identical anthropogenic emissions from a historical reconstruction (9) and four possible future RCP scenarios (10). Different colors represent different models. The gray rectangle highlights the period 2000 to 2010 in each scenario. Full model names are shown in the key, with a two-letter abbreviation shown in parentheses used in subsequent figures.Our best estimates of global mean abundance and interannual variability from OH rely on proxy measurements, particularly methyl chloroform (11), as the high reactivity and short lifetime of OH make direct measurement difficult and impractical for constraining spatial and temporal variability (12). On average, global atmospheric chemistry models cannot reproduce meridional gradients in carbon monoxide (CO) and other long-lived reactants, implying possible errors in simulated OH spatial and seasonal distributions (6, 13). They also overestimate global mean OH with respect to observational constraints from the methane and methyl chloroform lifetimes (6, 7) and underestimate the magnitude of interannual variability in OH inferred from proxy observations [0.5±0.4 % of year-to-year changes in the ACCMIP ensemble versus 2.3±1.5 % derived from methyl chloroform (11)]. These findings highlight gaps in our understanding of the processes that determine the oxidative capacity of the atmosphere and its variability, thereby hindering our ability to accurately predict its future evolution.In contrast to the intermodel discrepancies in OH abundances, trends, and variability, the models tend to produce consistent simulations for key tropospheric species that are intimately coupled with OH, such as tropospheric ozone (14). This implies that some—or even all—models are capturing mean abundances and spatial and temporal trends of longer-lived species at least partly for the wrong reasons.The original analysis of OH in the ACCMIP simulations noted that the change in OH over time in a given model correlated with the ratio of change in its burden of reactive nitrogen oxides (NOx≡ NO + NO₂) to change in its CO burden, but did not provide a mechanistic explanation (6). Here, we reexamine the ACCMIP model ensemble through the lens of fundamental OH chemistry to explain the disparate behavior between the models. The key areas of uncertainty we identify provide a target for future observing strategies to advance most rapidly our understanding, as formalized in the models used to project future atmospheric abundances of pollutants and reactive greenhouse gases.     

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.