Sulfur radical species form gold deposits on Earth

Current models of the formation and distribution of gold deposits on Earth are based on the long-standing paradigm that hydrogen sulfide and chloride are the ligands responsible for gold mobilization and precipitation by fluids across the lithosphere. Here we challenge this view by demonstrating, using in situ X-ray absorption spectroscopy and solubility measurements, coupled with molecular dynamics and thermodynamic simulations, that sulfur radical species, such as the trisulfur ion S3−, form very stable and soluble complexes with Au⁺ in aqueous solution at elevated temperatures (>250 °C) and pressures (>100 bar). These species enable extraction, transport, and focused precipitation of gold by sulfur-rich fluids 10–100 times more efficiently than sulfide and chloride only. As a result, S3− exerts an important control on the source, concentration, and distribution of gold in its major economic deposits from magmatic, hydrothermal, and metamorphic settings. The growth and decay of S3− during the fluid generation and evolution is one of the key factors that determine the fate of gold in the lithosphere.The formation of gold deposits on Earth requires aqueous fluids that extract gold from minerals and magmas and transport and precipitate the metal as economic concentrations in ores that are three to six orders of magnitude larger than the Au mean content (∼0.001 ppm) of common crustal and mantle rocks (1–9). However, natural data on gold contents in fluids are very scarce due to difficulties of direct access to deep geothermal fluid samples, rarity of representative fluid inclusions trapped in minerals, and analytical limitations for this chemically most inert metal (1, 4, 9, 10). The paucity of direct data makes it difficult to quantify the capacity of the fluids to transport gold and the factors controlling the sources, formation, and distribution of the economic resources of gold and associated metals across the lithosphere. Thus, knowledge of gold speciation and solubility in the fluid phase is required.Terrestrial hydrothermal fluids systematically contain sulfur and chloride—compounds that have long been known to favor gold dissolution in aqueous solution (e.g., refs. 11 and 12). Following this common knowledge, the interpretation of gold transfers across the lithosphere has been based on the fundamental assumption that only hydrogen sulfide (HS⁻) and chloride (Cl⁻) can form stable complexes with aurous gold, Au⁺, which is the main gold oxidation state in hydrothermal fluids (1–6, 11–15). Among these species, aurous bis(hydrogen sulfide), Au(HS)2−, and dichloride, AuCl2−, have long been regarded as the major carriers of gold in hydrothermal fluids, depending on temperature (T), pressure (P), acidity (pH), redox potential (f_O2), and salt and sulfur concentrations (1, 5, 6, 13, 15). In addition, other minor hydroxide, chloride, and sulfide species (AuOH, AuCl, AuHS) have also been tentatively suggested in some studies to account for the low Au solubility (typically part-per-billion level, ppb) measured in dilute S- and Cl-poor experimental solutions (e.g., refs. 6 and 15). Most available data suggest that the sulfide complexes attain significant concentrations (>1 ppm Au) only in H₂S-rich neutral-to-alkaline (pH > 6–7) solutions at low-to-moderate temperatures (<250–300 °C), whereas the chloride complexes contribute to Au solubility only in highly acidic (pH < 3) chloride-rich (typically >10 wt% NaCl equivalent) and strongly oxidizing [above the oxygen fugacity of the hematite–magnetite (HM) buffer] solutions above 300 °C.In between these two contrasting hydrothermal solution compositions lies a vast domain of geological fluids, which are commonly generated by magma degassing at depth (2, 3, 9) or prograde metamorphism of sedimentary rocks at high temperatures (7, 8, 10). These fluids are characterized by variable salt content, slightly acidic to neutral pH, and the presence of both oxidized (sulfate and sulfur dioxide) and reduced (H₂S) sulfur forms in a wide temperature range (∼300–700 °C). Predicted concentrations of the gold sulfide and chloride species in such fluids are generally rather low (<0.1–1.0 ppm) to account for a number of enigmatic features of gold geochemistry such as the existence of large deposits without relation to magmatic plutons in metamorphic and sedimentary rocks (e.g., Carlin-type and orogenic) implying deep, likely mantle-derived, Au-rich sources, the observation of highly anomalous Au grades (up to thousands of parts per million) in hydrothermal veins, and huge variations (more than three orders of magnitude) of the ratio of Au to other metals (e.g., Cu, Ag, Mo) in ores (1–4, 6–10, 16). These fluids, which have created the major part of economic gold resources on Earth (1–4), may carry much higher Au concentrations, of tens to hundreds of parts per million, as reported from rare fluid inclusion analyses (4, 6, 9, 10) and a few laboratory experiments of Au solubility (17–20). How gold is transported by such fluids remains, however, controversial, and a variety of other species with H₂S, Cl, As, and alkali metal ligands (3, 14, 17–20) or Au nanoparticles (4, 6, 12) were suggested. Thus, a consistent picture of Au speciation and transport in deep and hot crustal fluids is lacking, hampering our understanding of geochemical fluxes of gold across the lithosphere and the formation of gold economic resources.In particular, all existing Au speciation models ignore sulfur radical species such as the trisulfur ion S3−, which is ubiquitous in chemical and engineering products (21) and was recently shown to be stable in the aqueous fluid phase over a wide temperature (T from 200 °C to ∼700 °C) and pressure (P from saturated vapor pressure to ∼30 kbar) range (22–24). The omission of S3− in current models of hydrothermal fluids is due to its very rapid breakdown to sulfate and sulfide in aqueous solution upon cooling, which prohibits the detection of S3− in experimental and natural fluid (and melt) samples brought to ambient conditions. It is thus only recently that the abundance and thermodynamic stability of this important sulfur species could be systematically characterized at high T−P using in situ Raman spectroscopy (22–24). These studies showed that significant amounts of trisulfur ion (>10–100 ppm) may be reached in fluids typical of magmatic and metamorphic environments, which are characterized by elevated dissolved S concentrations (>1,000 ppm), slightly acidic to neutral pH (between ∼3 and 7), and redox conditions enabling coexistence of sulfate (or sulfur dioxide) and hydrogen sulfide.To quantify the effect of S3− on Au behavior in hydrothermal fluids, here we combined in situ X-ray absorption spectroscopy (XAS) and hydrothermal reactor measurements with first-principles molecular dynamics (FPMD) and thermodynamic modeling of Au local atomic structure and solubility in aqueous solutions saturated with gold metal and containing hydrogen sulfide, sulfate and S3− (SI Appendix). These solutions are representative of fluids that formed major types of gold deposits in the crust: 200–500 °C, 300–1,000 bar, 0.1–3.0 wt% S, 3 < pH < 8, and oxygen fugacity f_O2 between the nickel−nickel oxide (NNO) and HM buffer (1–4).     

Layering transitions and metastable structures of cholesteric liquid crystals in cylindrical confinement

Our study of cholesteric lyotropic chromonic liquid crystals in cylindrical confinement reveals the topological aspects of cholesteric liquid crystals. The double-twist configurations we observe exhibit discontinuous layering transitions, domain formation, metastability, and chiral point defects as the concentration of chiral dopant is varied. We demonstrate that these distinct layer states can be distinguished by chiral topological invariants. We show that changes in the layer structure give rise to a chiral soliton similar to a toron, comprising a metastable pair of chiral point defects. Through the applicability of the invariants we describe to general systems, our work has broad relevance to the study of chiral materials.

Chiral liquid crystals (LCs) are ubiquitous, useful, and rich systems (1–4). From the first discovery of the liquid crystalline phase to the variety of chiral structures formed by biomolecules (5–9), the twisted structure, breaking both mirror and continuous spatial symmetries, is omnipresent. The unique structure also makes the chiral nematic (cholesteric) LC, an essential material for applications utilizing the tunable, responsive, and periodic modulation of anisotropic properties.The cholesteric is also a popular model system to study the geometry and topology of partially ordered matter. The twisted ground state of the cholesteric is often incompatible with confinement and external fields, exhibiting a large variety of frustrated and metastable director configurations accompanying topological defects. Besides the classic example of cholesterics in a Grandjean−Cano wedge (10, 11), examples include cholesteric droplets (12–16), colloids (17–19), shells (20–22), tori (23, 24), cylinders (25–29), microfabricated structures (30, 31), and films between parallel plates with external fields (32–40). These structures are typically understood using a combination of nematic (achiral) topology (41, 42) and energetic arguments, for example, the highly successful Landau−de Gennes approach (43). However, traditional extensions of the nematic topological approach to cholesterics are known to be conceptually incomplete and difficult to apply in regimes where the system size is comparable to the cholesteric pitch (41, 44).An alternative perspective, chiral topology, can give a deeper understanding of these structures (45–47). In this approach, the key role is played by the twist density, given in terms of the director field n by n⋅∇×n. This choice is not arbitrary; the Frank free energy prefers n⋅∇×n≈−q0=2π/p0 with a helical pitch p0, and, from a geometric perspective, n⋅∇×n≠0 defines a contact structure (48). This allows a number of new integer-valued invariants of chiral textures to be defined (45). A configuration with a single sign of twist is chiral, and two configurations which cannot be connected by a path of chiral configurations are chirally distinct, and hence separated by a chiral energy barrier. Within each chiral class of configuration, additional topological invariants may be defined using methods of contact topology (45–48), such as layer numbers. Changing these chiral topological invariants requires passing through a nonchiral configuration. Cholesterics serve as model systems for the exploration of chirality in ordered media, and the phenomena we describe here—metastability in chiral systems controlled by chiral topological invariants—has applicability to chiral order generally. This, in particular, includes chiral ferromagnets, where, for example, our results on chiral topological invariants apply to highly twisted nontopological Skyrmions (49, 50) (“Skyrmionium”).Our experimental model to explore the chiral topological invariants is the cholesteric phase of lyotropic chromonic LCs (LCLCs). The majority of experimental systems hitherto studied are based on thermotropic LCs with typical elastic and surface-anchoring properties. The aqueous LCLCs exhibiting unusual elastic properties, that is, very small twist modulus K2 and large saddle-splay modulus K24 (51–56), often leading to chiral symmetry breaking of confined achiral LCLCs (53, 54, 56–61), may enable us to access uncharted configurations and defects of topological interests. For instance, in the layer configuration by cholesteric LCLCs doped with chiral molecules, their small K2 provides energetic flexibility to the thickness of the cholesteric layer, that is, the repeating structure where the director n twists by π. The large K24 affords curvature-induced surface interactions in combination with a weak anchoring strength of the lyotropic LCs (62–64).We present a systematic investigation of the director configuration of cholesteric LCLCs confined in cylinders with degenerate planar anchoring, depending on the chiral dopant concentration. We show that the structure of cholesteric configurations is controlled by higher-order chiral topological invariants. We focus on two intriguing phenomena observed in cylindrically confined cholesterics. First, the cylindrical symmetry renders multiple local minima to the energy landscape and induces discontinuous increase of twist angles, that is, a layering transition, upon the dopant concentration increase. Additionally, the director configurations of local minima coexist as metastable domains with point-like defects between them. We demonstrate that a chiral layer number invariant distinguishes these configurations, protects the distinct layer configurations (45), and explains the existence of the topological defect where the invariant changes.     

Coupled CH4 production and oxidation support CO2 supersaturation in a tropical flood pulse lake (Tonle Sap Lake,Cambodia)

Carbon dioxide (CO₂) supersaturation in lakes and rivers worldwide is commonly attributed to terrestrial–aquatic transfers of organic and inorganic carbon (C) and subsequent, in situ aerobic respiration. Methane (CH₄) production and oxidation also contribute CO₂ to freshwaters, yet this remains largely unquantified. Flood pulse lakes and rivers in the tropics are hypothesized to receive large inputs of dissolved CO₂ and CH₄ from floodplains characterized by hypoxia and reducing conditions. We measured stable C isotopes of CO₂ and CH₄, aerobic respiration, and CH₄ production and oxidation during two flood stages in Tonle Sap Lake (Cambodia) to determine whether dissolved CO₂ in this tropical flood pulse ecosystem has a methanogenic origin. Mean CO₂ supersaturation of 11,000 ± 9,000 μatm could not be explained by aerobic respiration alone. ¹³C depletion of dissolved CO₂ relative to other sources of organic and inorganic C, together with corresponding ¹³C enrichment of CH₄, suggested extensive CH₄ oxidation. A stable isotope-mixing model shows that the oxidation of ¹³C depleted CH₄ to CO₂ contributes between 47 and 67% of dissolved CO₂ in Tonle Sap Lake. ¹³C depletion of dissolved CO₂ was correlated to independently measured rates of CH₄ production and oxidation within the water column and underlying lake sediments. However, mass balance indicates that most of this CH₄ production and oxidation occurs elsewhere, within inundated soils and other floodplain habitats. Seasonal inundation of floodplains is a common feature of tropical freshwaters, where high reported CO₂ supersaturation and atmospheric emissions may be explained in part by coupled CH₄ production and oxidation.

Globally, most lakes and rivers are supersaturated with dissolved carbon dioxide (CO₂) relative to the atmosphere, highlighting their outsized role in transferring and transforming terrestrial carbon (C) (1–3). Terrestrial–aquatic transfers of C can include CO₂ dissolved in terrestrial ground and surface waters (3–6), dissolved inorganic carbon (DIC) from carbonate weathering (7, 8), or organic C from various sources that is subsequently respired in lakes and rivers (9, 10). Initially, oceanic export was thought to be the only fate for terrestrial–aquatic transfers of C, but a growing body of research on sediment burial of organic C and CO₂ emissions from freshwaters prompted the “active pipe” revision to this initial set of assumptions (11). Although freshwaters are now recognized as focal points for transferring and transforming C on the landscape, most of this research has been conducted within temperate freshwaters (2, 11, 12). Few studies focus on the mechanisms of CO₂ supersaturation in tropical lakes and rivers, with most conducted in just one watershed, the Amazon (4, 13–15).CO₂ supersaturation within tropical freshwaters is likely influenced by their unique flood pulse hydrology. The canonical flood pulse concept hypothesizes that annual flooding of riparian land will lead to organic C mobilization and respiration (16). Partial pressures of CO₂ (pCO₂) have been measured in excess of 44,000 μatm in the Amazon River (13), 16,000 μatm in the Congo River (17), and 12,000 μatm in the Lukulu River (17). Richey et al. (13), Borges et al. (18), and Zuidgeest et al. (17) have each shown that that riverine pCO₂ scales with the amount of land flooded in these watersheds. Yet it was only recently that Abril and Borges (19) proposed the importance of flooded land to the “active pipe.” These authors differentiate uplands that unidirectionally drain water downhill (via ground and surface water) from floodplains that bidirectionally exchange water with lakes and rivers (19). They conceptualize how floodplains combine high hydrologic connectivity, high rates of primary production, and high rates of respiration to transfer relatively large amounts of C to tropical freshwaters (19).Methanogenesis inevitably results on floodplains after dissolved oxygen (O₂) and other electron acceptors for anaerobic respiration such as iron and sulfate are consumed (16, 19). Horizontal gradients in dissolved O₂ and reducing conditions have been observed extending from the center of lakes and rivers through their floodplains in the Mekong (20, 21), Congo (22), Pantanal (23), and Amazon watersheds (4). CH₄ production and oxidation occur along such redox gradients (4, 16, 19, 23). CH₄ is produced by acetate fermentation (Eq. 1) and carbonate reduction (Eq. 2) within freshwaters (24, 25). CH₄ production coupled with aerobic oxidation results in CO₂ (Eq. 3 and ref. 25), yet no studies have quantified the relative contribution of coupled CH₄ production and oxidation to CO₂ supersaturation within tropical freshwaters.CH3COOH→CO2+CH4,[1]CO2+8H++8e−→CH4+2H2O,[2]CH4+2O2→CO2+2H2O.[3]The relative contribution of coupled CH₄ production and oxidation to CO₂ supersaturation within tropical freshwaters can be traced with stable C isotopes of CO₂ and CH₄. Methanogenesis results in CH₄ that is depleted in ¹³C (δ¹³C = −65 to −50‰ from acetate fermentation and −110 to −60‰ from carbonate reduction) compared to other potential sources of organic and inorganic C (δ¹³C = −37 to −7.7‰; see Materials and Methods) (24–26). The oxidation of this ¹³C-depleted CH₄ results in ¹³C-depleted CO₂ (24–26). At the same time, CH₄ oxidation enriches the ¹³C/¹²C of residual CH₄ as bacteria and archaea preferentially oxidize ¹²C-CH₄ (25). This means that the ¹³C/¹²C of CO₂ and CH₄ can serve as powerful tools to determine the source of CO₂ supersaturation within freshwaters.Tonle Sap Lake (TSL) is Southeast Asia’s largest lake and an understudied flood pulse ecosystem that supports a regionally important fishery (21, 22, 27). Each May through October, monsoonal rains and Himalayan snowmelt increase discharge in the Mekong River and cause one of its tributaries, the Tonle Sap River, to reverse course from southeast to northwest (21). During this course reversal, the Tonle Sap River floods TSL. The TSL flood pulse increases lake volume from 1.6 to 60 km³ and inundates 12,000 km² of floodplain for 3 to 6 mo per year (21, 27). Holtgrieve et al. (22) have shown that aerobic respiration is consistently greater than primary production in TSL (i.e., net heterotrophy), with the expectation of consistent CO₂ supersaturation. But, the partial pressures, C isotopic compositions, and ultimately the source of dissolved CO₂ in TSL remain unquantified.To quantify CO₂ supersaturation and its origins in TSL, we measured the partial pressures of CO₂ and CH₄ and compared their C isotopic composition to other potential sources of organic and inorganic C. We carried out these measurements in distinct lake environments during the high-water and falling-water stages of the flood pulse, hypothesizing that CH₄ production and oxidation on the TSL floodplain would support CO₂ supersaturation during the high-water stage. We found that coupled CH₄ production and oxidation account for a nontrivial proportion of the total dissolved CO₂ in all TSL environments and during both flood stages, showing that anaerobic degradation of organic C at aquatic–terrestrial transitions can support CO₂ supersaturation within tropical freshwaters.     

Semiempirical method for examining asynchronicity in metal–oxido-mediated C–H bond activation

The oxidation of substrates via the cleavage of thermodynamically strong C–H bonds is an essential part of mammalian metabolism. These reactions are predominantly carried out by enzymes that produce high-valent metal–oxido species, which are directly responsible for cleaving the C–H bonds. While much is known about the identity of these transient intermediates, the mechanistic factors that enable metal–oxido species to accomplish such difficult reactions are still incomplete. For synthetic metal–oxido species, C–H bond cleavage is often mechanistically described as synchronous, proton-coupled electron transfer (PCET). However, data have emerged that suggest that the basicity of the M–oxido unit is the key determinant in achieving enzymatic function, thus requiring alternative mechanisms whereby proton transfer (PT) has a more dominant role than electron transfer (ET). To bridge this knowledge gap, the reactivity of a monomeric Mn^IV–oxido complex with a series of external substrates was studied, resulting in a spread of over 10⁴ in their second-order rate constants that tracked with the acidity of the C–H bonds. Mechanisms that included either synchronous PCET or rate-limiting PT, followed by ET, did not explain our results, which led to a proposed PCET mechanism with asynchronous transition states that are dominated by PT. To support this premise, we report a semiempirical free energy analysis that can predict the relative contributions of PT and ET for a given set of substrates. These findings underscore why the basicity of M–oxido units needs to be considered in C–H functionalization.

The functionalization of C–H bonds is one of the most challenging synthetic transformations in chemistry, in part because of the inherent large bond dissociation-free energies (BDFEs) associated with C–H bonds (BDFE_C–H) (1, 2). Monomeric metal–oxido species can overcome these barriers and cleave C–H bonds in a diverse set of substrates. The utility of metal–oxido species is exemplified within the active sites of metalloenzymes, such as heme and nonheme Fe monooxygenases (3–6) and in related, synthetic Mn– (7–15), Co– (16), and Fe–oxido complexes (17–25). Even with the advances made with these natural and synthetic metal–oxido species, key mechanistic questions about which properties of the metal complexes contribute to productive C–H cleavage persist (26–30). Much of our current understanding of metal–oxido-mediated C–H bond activation is predicated on a relationship between ground-state thermodynamics and the height of the activation barrier. Reactions of metal–oxido species with organic substrates often show a correlation between variations in substrate C–H bond strength, (BDFE_C–H, Eq. 1, where C_G is a constant that is dependent on the reference electrode and solvent) and the log of the rate constant for C–H bond cleavage. Systems for which these correlations are highly linear are said to follow a linear free energy relationship or display Bell–Evans–Polanyi (BEP)-like correlations (31, 32).BDFEC–H= 23.06(E˚) + 1.37(pKa) + CG.[1]The ground-state thermodynamics for C–H bond cleavage are determined by comparing the BDFE_C–H of the C–H bond to be cleaved to that of the O–H bond formed in the resulting M^n-1–OH species; this BDFE_O–H value is obtained from the reduction potential of the M = O species and its basicity, in a manner analogous to Eq. 1 (1, 33). The relationship between BDFE_O–H, reduction potential and basicity can be conveniently represented using a thermodynamic square scheme that contains three limiting, mechanistic paths (Fig. 1) (26): 1) proton transfer/electron transfer (PT-ET); 2) electron transfer/proton transfer (ET-PT); and 3) synchronous, proton-coupled electron transfer (PCET). An important outcome of the approach of comparing BDFE values is the recognition that the basicity of the M–oxido unit can be a key contributor to C–H bond cleavage. This concept is exemplified by the high-valent Fe–oxido intermediate in cytochrome P450s (compound I). The reduced intermediate is highly basic, promoting the abstraction of H atoms from strong C–H bonds at relatively low, one-electron reduction potentials (34, 35).Open in a separate windowFig. 1.Thermodynamic square scheme for M–oxido complexes involved in C–H bond cleavage. For 1, E_1/2'' = −1.0 V; E_1/2 = −0.18 V; pK_a = 15; pK_a'' = 28.1(2); and BDFE_O–H = 87(2) kcal/mol (SI Appendix, Eq. S1). Values measured in DMSO at room temperature. Potentials are referenced to [Fe^III/IICp₂]^+/0.We have also shown that the basicity of the oxido ligand drives the reactivity of a low-valent Mn^III–oxido complex that is competent at cleaving C–H bonds, even though its reduction potential is less than −2.0 V versus [Fe^III/IICp₂]^+/0 (7). Our initial mechanistic suggestion for this Mn^III–oxido complex was a stepwise PT-ET pathway with proton transfer (PT) being rate limiting. However, subsequent kinetic studies on a related series of Mn^III–oxido complexes showed that electron transfer (ET) must also be involved in the rate-determining step (8). To reconcile these results, we proposed a mechanism with an imbalanced transition state, in which PT precedes ET (8). This type of asynchronous PCET mechanism (36) was examined computationally (37) and experimentally to explain the cleavage of C–H bonds with Co^III–oxido (16), Ru^IV–oxido (38), and Cu^III−O₂CAr complexes (39). The involvement of asynchronous PCET processes in the cleavage of C–H bonds by high-valent M–oxido complexes, such as Fe^IV/Mn^IV–oxido species, is still uncertain. In fact, most reactions have synchronous PCET mechanisms that follow the BEP principle (31, 32) and exhibit the correlations between the BDFE_C–H values of the substrates and the log of the second-order rate constants [log (k)]. However, C–H bond cleavage via an asynchronous PCET mechanism that is driven by the basicity of the M–oxido unit would be beneficial because reactivity could occur at lower redox potentials, while still achieving the efficiency that is often associated with PCET processes. We reasoned that this type of mechanism could occur if the high-valent M–oxido complex was relatively basic and could therefore favor mechanisms that involve PT-driven, asynchronous transition states. The high-valent Mn^IV–oxido complex [Mn^IVH₃buea(O)]⁻ (1) is a suitable candidate for testing this premise because it has a relatively high basicity, as gauged by its conjugate acid, [Mn^IVH₃buea(OH)], which has an estimated pK_a of ∼15 in DMSO (7).We report here the kinetic studies of 1 with a variety of substrates, and the results of these studies support the involvement of PT-dominated, asynchronous transition states and show the applicability of this type of mechanism in the cleavage of C–H bonds by high-valent M–oxido complexes. To further evaluate our findings, we developed a semiempirical free energy analysis to estimate the relative contributions from the free energies of PT and ET within an asymmetric transition state. This analysis supports the assertion that the observed reactivity of 1 is driven by the pK_a, leading to PT-controlled, asynchronous transition states for the substrates examined. Moreover, we demonstrate that this analysis is useful in predicting whether a PCET reaction will be synchronous or asynchronous based on reactivity and thermodynamic parameters. Our method deviates from traditional, BEP-like analyses, in that it examines the behavior of log (k) versus a linear combination of PT and ET terms, rather than bond strengths. The appropriate combination of these free energy terms is determined by the linearity of plots versus log (k).     

Catalytic role of formaldehyde in particulate matter formation

Formaldehyde (HCHO), the simplest and most abundant carbonyl in the atmosphere, contributes to particulate matter (PM) formation via two in-cloud processing pathways. First, in a catalytic pathway, HCHO reacts with hydrogen peroxide (H₂O₂) to form hydroxymethyl hydroperoxide (HMHP), which rapidly oxidizes dissolved sulfur dioxide (SO_2,aq) to sulfate, regenerating HCHO. Second, HCHO reacts with dissolved SO_2,aq to form hydroxymethanesulfonate (HMS), which upon oxidation with the hydroxyl radical (OH) forms sulfate and also reforms HCHO. Chemical transport model simulations using rate coefficients from laboratory studies of the reaction rate of HMHP with SO_2,aq show that the HMHP pathways reduce the SO₂ lifetime by up to a factor of 2 and contribute up to ∼18% of global sulfate. This contribution rises to >50% in isoprene-dominated regions such as the Amazon. Combined with recent results on HMS, this work demonstrates that the one-carbon molecules HMHP and HCHO contribute significantly to global PM, with HCHO playing a crucial catalytic role.

Particulate matter (PM) formation has a significant impact on cloud properties, climate, and human health (1). Higher toxicity has been attributed to small-size particles (particles with aerodynamic diameter smaller than 2.5 μm) due to their ability to enter the respiratory and cardiovascular system, causing adverse health effects in highly polluted environments (2–7). A substantial fraction of PM corresponds to sulfate, which is primarily formed from atmospheric oxidation of SO₂ emitted anthropogenically by coal combustion and smelters (8). Important SO₂ oxidation pathways include reaction with the hydroxyl radical (OH) in the gas phase and reaction with hydrogen peroxide (H₂O₂), ozone, multifunctional organic hydroperoxides (RXOOH), and NO₂ in cloud droplets (9–13). Simple organic hydroperoxides, such as methylhydroperoxide and peroxyacetic acid, are unlikely to contribute due to their low Henry’s law constants, on the order of 10² to 10³ M ⋅ atm⁻¹ and lower rate constants for oxidation of SO₂, up to 10² M⁻¹ ⋅ s⁻¹ compared to multifunctional organic hydroperoxides (RXOOH), such as isoprene hydroxyl hydroperoxides (ISOPOOH), which have two orders of magnitude higher Henry’s law constants and at least an order of magnitude higher oxidation rate constants (9, 12). The contribution of transition metal chemistry and reactions on the surface of aerosols are more uncertain but could also play an important role (14). Formation of sulfate by SO₂ oxidation competes with removal of SO₂ by deposition (15). A complete understanding of the contribution of all pathways is important to quantify the SO₂ lifetime (τSO₂) against oxidation and the implied formation rate of sulfate, especially as recent studies showed that models underestimate sulfate in SO₂ source regions (16–23). Competition between gas-phase and condensed-phase pathways has a crucial role in new particle formation (9). Understanding sulfur oxidation pathways is especially important under changing atmospheric conditions (e.g., in areas where observed decreases in anthropogenic NO_x emissions are observed, such as in the southeast United States [SE-US]).In-cloud oxidation of SO_2,aq to sulfate is considered the main source of global PM sulfur, with H₂O₂ presumed to be the most important oxidant (9–11, 24). Atmospheric models overestimate the global sulfur dioxide concentration by ∼50%, but some also underestimate the sulfate concentration by ∼20% globally and >20% on regional scales (16–23). Kim et al. (23) reported that GEOS-Chem underestimates sulfate by 34% in the SE-US. Similarly, Pai et al. (21) showed that GEOS-Chem underestimates sulfate significantly in low-NO_x isoprene-rich regions such as the Amazon and the SE-US. Simulations using large-scale sulfate aerosol models or a global chemical tracer model have shown overestimation of SO_2(g) and underestimation of sulfate in the Northern Hemisphere during winter (16, 17). Studies with Lagrangian atmospheric models across Europe and North America also underestimate sulfate in winter but overestimate sulfate during summer (19, 20). Modeling additional SO₂ oxidation pathways in these regions could decrease τSO₂ and increase regional sulfate production and burden.Another important compound that could contribute to PM formation is formaldehyde. Formaldehyde (HCHO) is the most abundant and simplest carbonyl in the atmosphere, formed primarily via photochemical oxidation of volatile organic compounds, such as isoprene, its main biogenic precursor (25). Having a high Henry’s law constant (∼5.5⋅103 M⋅atm−1) (26), HCHO can partition into cloud and fog water. The term HCHO, as used in this work, refers to both free HCHO and its hydrated form, which is the dominant form in clouds and fog droplets. In cloud droplets, HCHO reacts with SO_2,aq to form hydroxymethanesulfonate (HMS; HOCH2SO3−) (27–30). HMS is stable at pH <6 and resistant to oxidation by hydrogen peroxide (H₂O₂) and ozone (O₃) but can be oxidized by OH to form sulfate and reform HCHO in the aqueous phase (31–34). HMS has recently received attention primarily from the perspective of the PM sulfur budget (30, 35), whereas contribution to the organic carbon budget has not been explicitly discussed. HCHO also reacts with aqueous H₂O₂ to form hydroxymethyl hydroperoxide (HMHP) (36). HMHP is also formed in the gas phase via reaction of the CH₂OO Criegee intermediate with water (36). HMHP has a higher Henry’s law constant (∼2⋅106 M⋅atm−1) (37) than H₂O₂, and as an RXOOH, it has the potential to be an efficient oxidant for SO_2,aq, as recently shown for ISOPOOH (12).In this work, we evaluate the contribution of two species with only one carbon atom, HCHO and HMHP, to PM formation. Laboratory results are integrated into the GEOS-Chem model in order to investigate the importance of HCHO and HMHP to global and regional PM. We calculate the contribution of a pathway, the oxidation of SO_2,aq by HMHP, to PM formation. We discuss the role HCHO plays, especially in the competition between 1) formation of HMS via direct reaction of HCHO with SO_2,aq and 2) formation of sulfate via reaction of HCHO with H₂O₂ to form HMHP, which subsequently oxidizes SO_2,aq to sulfate and reforms HCHO.     

Nature of dynamic gradients,glass formation,and collective effects in ultrathin freestanding films

Molecular, polymeric, colloidal, and other classes of liquids can exhibit very large, spatially heterogeneous alterations of their dynamics and glass transition temperature when confined to nanoscale domains. Considerable progress has been made in understanding the related problem of near-interface relaxation and diffusion in thick films. However, the origin of “nanoconfinement effects” on the glassy dynamics of thin films, where gradients from different interfaces interact and genuine collective finite size effects may emerge, remains a longstanding open question. Here, we combine molecular dynamics simulations, probing 5 decades of relaxation, and the Elastically Cooperative Nonlinear Langevin Equation (ECNLE) theory, addressing 14 decades in timescale, to establish a microscopic and mechanistic understanding of the key features of altered dynamics in freestanding films spanning the full range from ultrathin to thick films. Simulations and theory are in qualitative and near-quantitative agreement without use of any adjustable parameters. For films of intermediate thickness, the dynamical behavior is well predicted to leading order using a simple linear superposition of thick-film exponential barrier gradients, including a remarkable suppression and flattening of various dynamical gradients in thin films. However, in sufficiently thin films the superposition approximation breaks down due to the emergence of genuine finite size confinement effects. ECNLE theory extended to treat thin films captures the phenomenology found in simulation, without invocation of any critical-like phenomena, on the basis of interface-nucleated gradients of local caging constraints, combined with interfacial and finite size-induced alterations of the collective elastic component of the structural relaxation process.

Spatially heterogeneous dynamics in glass-forming liquids confined to nanoscale domains (1–7) play a major role in determining the properties of molecular, polymeric, colloidal, and other glass-forming materials (8), including thin films of polymers (9, 10) and small molecules (11–15), small-molecule liquids in porous media (2, 4, 16, 17), semicrystalline polymers (18, 19), polymer nanocomposites (20–22), ionomers (23–25), self-assembled block and layered (26–33) copolymers, and vapor-deposited ultrastable molecular glasses (34–36). Intense interest in this problem over the last 30 y has also been motivated by the expectation that its understanding could reveal key insights concerning the mechanism of the bulk glass transition.Considerable progress has been made for near-interface altered dynamics in thick films, as recently critically reviewed (1). Large amplitude gradients of the structural relaxation time, τ(z,T), converge to the bulk value, τ_bulk(T), in an intriguing double-exponential manner with distance, z, from a solid or vapor interface (13, 37–42). This implies that the corresponding effective activation barrier, F_total(z,T,H) (where H is film thickness), varies exponentially with z, as does the glass transition temperature, T_g (37). Thus the fractional reduction in activation barrier, ε(z,H), obeys the equation ε(z,H)≡1−Ftotal(z,T,H)/Ftotal,bulk(T)=ε0⁡exp(−z/ξF), where F_total,bulk(T) is the bulk temperature-dependent barrier and ξ_F a length scale of modest magnitude. Although the gradient of reduction in absolute activation barriers becomes stronger with cooling, the amplitude of the fractional reduction of the barrier gradient, quantified by ε₀, and the range ξ_F of this gradient, exhibit a weak or absent temperature dependence at the lowest temperatures accessed by simulations (typically with the strength of temperature dependence of ξ_F decreasing rather than increasing on cooling), which extend to relaxation timescales of order 10⁵ ps. This finding raises questions regarding the relevance of critical-phenomena–like ideas for nanoconfinement effects (1). Partially due to this temperature invariance, coarse-grained and all-atom simulations (1, 37, 42, 43) have found a striking empirical fractional power law decoupling relation between τ(z,T) and τ_bulk(T):τ(T,z)τbulk(T)∝(τbulk(T))−ε(z).[1]Recent theoretical analysis suggests (44) that this behavior is consistent with a number of experimental data sets as well (45, 46). Eq. 1 also corresponds to a remarkable factorization of the temperature and spatial location dependences of the barrier:Ftotal(z,T)=[1−ε(z)]Ftotal,bulk(T).[2]This finding indicates that the activation barrier for near-interface relaxation can be factored into two contributions: a z-dependent, but T-independent, “decoupling exponent,” ε(z), and a temperature-dependent, but position-insensitive, bulk activation barrier, F_total,bulk(T). Eq. 2 further emphasizes that ε(z) is equivalent to an effective fractional barrier reduction factor (for a vapor interface), 1−Ftotal(z,T,H)/Ftotal,bulk(T), that can be extracted from relaxation data.In contrast, the origin of “nanoconfinement effects” in thin films, and how much of the rich thick-film physics survives when dynamic gradients from two interfaces overlap, is not well understood. The distinct theoretical efforts for aspects of the thick-film phenomenology (44, 47–50) mostly assume an additive summation of one-interface effects in thin films, thereby ignoring possibly crucial cooperative and whole film finite size confinement effects. If the latter involve phase-transition–like physics as per recent speculations (14, 51), one can ask the following: do new length scales emerge that might be truncated by finite film size? Alternatively, does ultrathin film phenomenology arise from a combination of two-interface superposition of the thick-film gradient physics and noncritical cooperative effects, perhaps in a property-, temperature-, and/or thickness-dependent manner?Here, we answer these questions and establish a mechanistic understanding of thin-film dynamics for the simplest and most universal case: a symmetric freestanding film with two vapor interfaces. We focus on small molecules (modeled theoretically as spheres) and low to medium molecular weight unentangled polymers, which empirically exhibit quite similar alterations in dynamics under “nanoconfinement.” We do not address anomalous phenomena [e.g., much longer gradient ranges (29), sporadic observation of two distinct glass transition temperatures (52, 53)] that are sometimes reported in experiments with very high molecular weight polymers and which may be associated with poorly understood chain connectivity effects that are distinct from general glass formation physics (54–56).We employ a combination of molecular dynamics simulations with a zero-parameter extension to thin films of the Elastically Cooperative Nonlinear Langevin Equation (ECNLE) theory (57, 58). This theory has previously been shown to predict well both bulk activated relaxation over up to 14 decades (44–46) and the full single-gradient phenomenology in thick films (1). Here, we extend this theory to treat films of finite thickness, accounting for coupled interface and geometric confinement effects. We compare predictions of ECNLE theory to our previously reported (37, 43) and new simulations, which focus on translational dynamics of films comprised of a standard Kremer–Grest-like bead-spring polymer model (see SI Appendix). These simulations cover a wide range of film thicknesses (H, from 4 to over 90 segment diameters σ) and extend to low temperatures where the bulk alpha time is ∼0.1 μs (10⁵ Lennard Jones time units τ_LJ).The generalized ECNLE theory is found to be in agreement with simulation for all levels of nanoconfinement. We emphasize that this theory does not a priori assume any of the empirically established behaviors discovered using simulation (e.g., fractional power law decoupling, double-exponential barrier gradient, gradient flattening) but rather predicts these phenomena based upon interfacial modifications of the two coupled contributions to the underlying activation barrier– local caging constraints and a long-ranged collective elastic field. It is notable that this strong agreement is found despite the fact the dynamical ideas are approximate, and a simple hard sphere fluid model is employed in contrast to the bead-spring polymers employed in simulation. The basic unit of length in simulation (bead size σ) and theory (hard sphere diameter d) are expected to be proportional to within a prefactor of order unity, which we neglect in making comparisons.As an empirical matter, we find from simulation that many features of thin-film behavior can be described to leading order by a linear superposition of the thick-film gradients in activation barrier, that is:ε(z,H)=1−Ftotal(z,T,H)/Ftotal,bulk(T)≈ε0[exp(−z/ξF)+exp(−(H−z)/ξF)],[3]where the intrinsic decay length ξ_F is unaltered from its thick-film value and where ε₀ is a constant that, in the hypothesis of literal gradient additivity, is invariant to temperature and film thickness. We employ this functional form [originally suggested by Binder and coworkers (59)], which is based on a simple superposition of the two single-interface gradients, as a null hypothesis throughout this study: this form is what one expects if no new finite-size physics enters the thin-film problem relative to the thick film.However, we find that the superposition approximation progressively breaks down, and eventually entirely fails, in ultrathin films as a consequence of the emergence of a finite size confinement effect. The ECNLE theory predicts that this failure is not tied to a phase-transition–like mechanism but rather is a consequence of two key coupled physical effects: 1) transfer of surface-induced reduction of local caging constraints into the film, and 2) interfacial truncation and nonadditive modifications of the collective elastic contribution to the activation barrier.     

Mechanism of H+ dissociation–induced O–O bond formation via intramolecular coupling of vicinal hydroxo ligands on low-valent Ru(III) centers

The understanding of O–O bond formation is of great importance for revealing the mechanism of water oxidation in photosynthesis and for developing efficient catalysts for water oxidation in artificial photosynthesis. The chemical oxidation of the Ru^II₂(OH)(OH₂) core with the vicinal OH and OH₂ ligands was spectroscopically and theoretically investigated to provide a mechanistic insight into the O–O bond formation in the core. We demonstrate O–O bond formation at the low-valent Ru^III₂(OH) core with the vicinal OH ligands to form the Ru^II₂(μ-OOH) core with a μ-OOH bridge. The O–O bond formation is induced by deprotonation of one of the OH ligands of Ru^III₂(OH)₂ via intramolecular coupling of the OH and deprotonated O⁻ ligands, conjugated with two-electron transfer from two Ru^III centers to their ligands. The intersystem crossing between singlet and triple states of Ru^II₂(μ-OOH) is easily switched by exchange of H⁺ between the μ-OOH bridge and the auxiliary backbone ligand.

Water oxidation to produce O₂ (Eq. 1) is an important biological reaction in photosynthesis. The geometric structure of the active site with a manganese-oxo core (Mn₄CaO₅) for water oxidation, so called oxygen-evolving complex (OEC), has been characterized by recently advanced X-ray crystallographic analysis (1–5). The elucidation of the water oxidation mechanism at OEC on the basis of their geometric structure is a high-interest topic in photosynthesis studies. On the other hand, water oxidation is also a crucial process to use water as an electron source for the solar fuel production in artificial photosynthesis technology that is participated as a future solar energy conversion system (6–8). There has been a great deal of interest in developing active catalysts to promote water oxidation to establish efficient artificial photosynthesis systems (9–13). The elucidation of the water oxidation mechanism provides a key clue of the guideline for developing active catalysts for water oxidation.2H2O→O2+ 4H++ 4e−.[1]In a water oxidation process to produce O₂ (Eq. 1), formation of an O–O bond from two molecules of water is necessary with removal of either consecutive or concerted four electrons and four protons from the water (14–16). Commonly, the O–O bond formation is assisted by catalysts (OEC in photosynthesis) with one or two molecules of water bound on them to decrease thermodynamic energy for formation of the intermediate species. Two main classes of the mechanism for the O–O bond formation on metal centers of the catalysts have been reported: water nucleophilic attack (WNA) on metal-oxo centers (Mⁿ = O) (17–22) and interaction of two Mⁿ = O centers (I2M) (23–29). In the WNA mechanism (17–20), a water molecule nucleophilically attacks onto the Mⁿ = O center to generate a Mⁿ⁻²-OOH hydroperoxide intermediate. Therefore, the high-valent Mⁿ = O center (e.g., Ru^{IV or V}) with electrophilic properties is required. In the I2M mechanism (23–27), the coupling of either two Mⁿ⁻¹-O· oxyl radicals (formally Mⁿ = O) or coupling of one Mⁿ⁻¹-O· oxyl radical with another unit (e.g., Mⁿ = O) of nonradical character affords a Mⁿ⁻¹-OO-Mⁿ⁻¹ peroxide intermediate. For this mechanism, the high-valent Mnⁿ = O centers are not necessarily attained, in contrast to the required high-valent Mⁿ = O center in the WNA mechanism. However, O–O bond formation via coupling of relatively low-valent Mⁿ = O units (e.g., Ru^III) has not been demonstrated so far.proximal,proximal-[Ru₂(tpy)₂(pyan)(OH)(OH₂)]³⁺ (Ru^II₂(OH) (OH₂)) (tpy = 2,2′;6′,2″-terpyridine and pyan = 5-phenyl-2,8-di(2-pyridyl)-1,9,10-anthyridine) with the vicinal OH and OH₂ ligands in the Ru^II₂ core was reported to work efficiently for electrocatalytic water oxidation in a homogenous solution (26). The O–O bond formation via intramolecular coupling between the Ru^V = O units, derived from the Ru^II₂ core with the vicinal OH and OH₂ ligands, was suggested for O₂ production. Recently, we reported that O₂ is produced via the intramolecular coupling between the Ru^IV = O and Ru^IV-OH units for the proximal,proximal-[Ru₂(cptpy)₂(pyan)(OH)(OH₂)]⁺ (Hcptpy = 4′-(4-carboxyphenyl)-2,2′;6′,2″-terpyridine) derivative with 4-carboxyphenyl linkers adsorbed on the TiO₂ surface (27). However, the direct spectroscopic evidence has not yet been provided for the O–O bond formation via intramolecular coupling between the Ru^{IV or V} = O units. Herein, we spectroscopically and theoretically investigate chemical oxidation of Ru^II₂(OH)(OH₂) by a Na₂S₂O₈ oxidant in an aqueous solution to provide a mechanistic insight into the O–O bond formation in the unique Ru₂ core. We demonstrate that the O–O bond formation via intramolecular coupling of vicinal OH ligands on Ru^III-OH units is induced by dissociation of one proton of two OH ligands in the core. This is an observation of the O–O bond formation at the low-valent Ru^III centers. The mechanism of the O–O bond formation is revealed to propose the important role of the central N atom (N_c) of the anthyridine moiety on the pyan backbone ligand as a neighboring proton acceptor site for concerted intramolecular electron/proton transfers.     

Enhanced microscopic dynamics in mucus gels under a mechanical load in the linear viscoelastic regime

Mucus is a biological gel covering the surface of several tissues and ensuring key biological functions, including as a protective barrier against dehydration, pathogen penetration, or gastric acids. Mucus biological functioning requires a finely tuned balance between solid-like and fluid-like mechanical response, ensured by reversible bonds between mucins, the glycoproteins that form the gel. In living organisms, mucus is subject to various kinds of mechanical stresses, e.g., due to osmosis, bacterial penetration, coughing, and gastric peristalsis. However, our knowledge of the effects of stress on mucus is still rudimentary and mostly limited to macroscopic rheological measurements, with no insight into the relevant microscopic mechanisms. Here, we run mechanical tests simultaneously to measurements of the microscopic dynamics of pig gastric mucus. Strikingly, we find that a modest shear stress, within the macroscopic rheological linear regime, dramatically enhances mucus reorganization at the microscopic level, as signaled by a transient acceleration of the microscopic dynamics, by up to 2 orders of magnitude. We rationalize these findings by proposing a simple, yet general, model for the dynamics of physical gels under strain and validate its assumptions through numerical simulations of spring networks. These results shed light on the rearrangement dynamics of mucus at the microscopic scale, with potential implications in phenomena ranging from mucus clearance to bacterial and drug penetration.

Mucus is a biogel ubiquitous across both vertebrates and invertebrates (1–3). The main mucus macromolecular components are a family of glycosylated proteins called mucins (4–6). Hydrophobic, hydrogen-bonding, and Ca2+-mediated (7) interactions between mucins are responsible for macromolecular associations determining the viscoelastic properties of mucus, which, in turn, control its biological functions (2, 5). Alteration of the viscoelastic properties compromises mucus functionality, resulting in severe diseases (8, 9).Mucus viscoelasticity stems from the reversible nature of the bonds between its constituents, which ensure solid-like behavior on short time scales while allowing flow on longer time scales. Rheological studies on mucus reporting the frequency dependence of the storage, G′, and loss, G″, components of the dynamic modulus reveal G′>G″, with G′ only weakly dependent on angular frequency ω on time scales of 0.1 to 100 s (8–10), a behavior typical of soft solids (11). Stress-relaxation tests probe viscoelasticity on longer time scales, up to thousands of seconds. They reveal a power law or logarithmic decay of the shear stress with time (12–14), indicative of a wide distribution of relaxation times, ascribed to the variety of macromolecular association mechanisms and the mucus complex, multiscale structure (7, 14, 15).Alongside conventional rheology, microrheology has gained momentum since it investigates the mechanical response of mucus on the length scales relevant to its biological functions, from a fraction of a micrometer up to ∼10 μm (7, 8, 16–19). Microrheology infers the viscoelastic moduli from the microscopic dynamics of tracer particles embedded in the sample (20), either due to spontaneous thermal fluctuations or externally driven, e.g., by a magnetic field. Mucus viscoelasticity as measured by microrheology is found to depend on the size of the tracer particles, the local environment they probe, and the length scale over which their motion is tracked (7, 8, 16, 17, 19, 21). Below ≈1 μm, microrheology data are dominated by the diffusion of the probe particles within the mucus pores, as inferred from the analysis of the localization of the tracers’ trajectories (7, 17), their dependence on probe size (8, 16, 21), and on the amplitude of the external drive in active microrheology (16). On larger length scales, microrheology reports the local viscoelasticity, which converges toward the macroscopic one above ≈10 μm, as revealed by the probe-size and drive-amplitude dependence of active microrheology (16).In vivo, mucus is submitted to stresses of various origin, involving strain on the microscopic scale, as in cilia beating in muco-ciliary clearance (22) and bacterial penetration (23, 24), up to macroscopic scales, e.g., during coughing and peristalsis (3, 25). Stresses due to the osmotic pressure exerted by the environment (26) or resulting from changes in hydration (27, 28) can modify the structure of mucus and, e.g., impair mucus clearance. By contrast, little is known on the impact of stress on the dynamics of mucus, in particular, at the microscopic level. Conventional rheology indicates that mucus is fluidized upon applying a large stress (29, 30), beyond the linear regime. This behavior is typical of soft solids (31–33); in concentrated nanoemulsions and colloidal suspensions and in colloidal gels, fluidization in the nonlinear regime has been shown to stem from enhanced microscopic dynamics (34–40). However, for mucus, we still lack knowledge of the effect of an applied stress on the microscopic dynamics.Here, we couple rheology and light and X-ray photon correlation methods to investigate the microscopic dynamics of pig gastric mucus under an applied shear stress. Surprisingly, we find that small stresses, well within the macroscopic linear viscoelastic regime, transiently enhance the mucus dynamics by up to 2 orders of magnitude. We propose a simple, yet general, model for the dynamics of physical gels under strain that rationalizes these findings.     

Transient conformational fluctuation of TePixD during a reaction

Knowledge of the dynamical behavior of proteins, and in particular their conformational fluctuations, is essential to understanding the mechanisms underlying their reactions. Here, transient enhancement of the isothermal partial molar compressibility, which is directly related to the conformational fluctuation, during a chemical reaction of a blue light sensor protein from the thermophilic cyanobacterium Thermosynechococcus elongatus BP-1 (TePixD, Tll0078) was investigated in a time-resolved manner. The UV-Vis absorption spectrum of TePixD did not change with the application of high pressure. Conversely, the transient grating signal intensities representing the volume change depended significantly on the pressure. This result implies that the compressibility changes during the reaction. From the pressure dependence of the amplitude, the compressibility change of two short-lived intermediate (I₁ and I₂) states were determined to be +(5.6 ± 0.6) × 10⁻² cm³⋅mol⁻¹⋅MPa⁻¹ for I₁ and +(6.6 ± 0.7)×10⁻² cm³⋅mol⁻¹⋅MPa⁻¹ for I₂. This result showed that the structural fluctuation of intermediates was enhanced during the reaction. To clarify the relationship between the fluctuation and the reaction, the compressibility of multiply excited TePixD was investigated. The isothermal compressibility of I₁ and I₂ intermediates of TePixD showed a monotonic decrease with increasing excitation laser power, and this tendency correlated with the reactivity of the protein. This result indicates that the TePixD decamer cannot react when its structural fluctuation is small. We concluded that the enhanced compressibility is an important factor for triggering the reaction of TePixD. To our knowledge, this is the first report showing enhanced fluctuations of intermediate species during a protein reaction, supporting the importance of fluctuations.Proteins often transfer information through changes in domain–domain (or intermolecular) interactions. Photosensor proteins are an important example. They have light-sensing domains and function by using the light-driven changes in domain–domain interactions (1). The sensor of blue light using FAD (BLUF) domain is a light-sensing module found widely among the bacterial kingdom (2). The BLUF domain initiates its photoreaction by the light excitation of the flavin moiety inside the protein, which changes the domain–domain interaction, causing a quaternary structural change and finally transmitting biological signals (3, 4). It has been an important research topic to elucidate how the initial photochemistry occurring in the vicinity of the chromophore leads to the subsequent large conformation change in other domains, which are generally apart from the chromophore.It may be reasonable to consider that the conformation change in the BLUF domain is the driving force in its subsequent reaction; that is, the change in domain–domain interaction. However, sometimes, clear conformational changes have not been observed for the BLUF domain; its conformation is very similar before and after photo-excitation (5–13). The circular dichroism (CD) spectra of BLUF proteins AppA and PixD from thermophilic cyanobacterium Thermosynechococcus elongatus BP-1 (TePixD) did not change on illumination (5, 13). Similarly, solution NMR studies of AppA and BlrB showed only small chemical shifts on excitation (9, 10). The solution NMR structure of BlrP1 showed a clear change, but this was limited in its C-terminal extension region and not core BLUF (11). Furthermore, the diffusion coefficient (D) of the BLUF domain of YcgF was not changed by photo-excitation (12), although D is sensitive to global conformational changes. These results imply that a minor structural change occurs in the BLUF domain. In such cases, how does the BLUF domain control its interdomain interaction? Recently, a molecular dynamics (MD) simulation on another light-sensing domain, the light-oxygen-voltage (LOV) sensing domain, suggested that fluctuation of the LOV core structure could be a key to understanding the mechanism of information transfer (14–16).Because proteins work at room temperature, they are exposed to thermal fluctuations. The importance of such structural fluctuations for biomolecular reactions has been also pointed out: for example, enzymatic activity (17–20). Experimental detections of such conformation fluctuations using single molecular detection (21) or NMR techniques such as the hydrogen-deuterium (H-D) exchange, relaxation dispersion method, and high-pressure NMR (22–24) have succeeded. However, these techniques could not detect the fluctuation of short-lived transient species. Indeed, single molecule spectroscopy can trace the fluctuation in real time, but it is still rather difficult to detect rapid fluctuations for a short-lived intermediate during a reaction. Therefore, information about the fluctuation of intermediates is thus far limited.A thermodynamic measurement is another way to characterize the fluctuation of proteins. In particular, the partial molar isothermal compressibility [K¯T=−(∂V¯/∂P)T] is essential, because this property is directly linked to the mean-square fluctuations of the protein partial molar volume by 〈(V¯−〈V¯〉)2〉≡〈δV¯2〉=kBTK¯T (25). (Here, <X> means the averaged value of a quantity of X.) Therefore, isothermal compressibility is thought to reflect the structural fluctuation of molecules (26). However, experimental measurement of this parameter of proteins in a dilute solution is quite difficult. Indeed, this quantity has been determined indirectly from the theoretical equation using the adiabatic compressibility of a protein solution, which was determined by the sound velocity in the solution (26–31). Although the relation between volume fluctuations and isothermal compressibility is rigorously correct only with respect to the intrinsic part of the volume compressibility, and not the partial molar volume compressibility (32), we considered that this partial molar volume compressibility is still useful for characterizing the fluctuation of the protein structure including its interacting water molecules. In fact, the relationship between β¯T and the volume fluctuation has been often used to discuss the fluctuation of proteins (17, 26–28), and the strong correlation of β¯T of reactants with the functioning for some enzymes (17, 33, 34) has been reported. These studies show the functional importance of the structural fluctuation represented by β¯T. However, thermodynamic techniques lack time resolution, and it has been impossible to measure the fluctuations of short-lived intermediate species.Recently, we developed a time-resolving method for assessing thermodynamic properties using the pulsed laser induced transient grating (TG) method. Using this method, we thus far succeeded in measuring the enthalpy change (ΔH) (35–38), partial molar volume change (ΔV¯) (12, 35, 37), thermal expansion change (Δα¯th) (12, 37), and heat capacity change (ΔC_p) (36–38) for short-lived species. Therefore, in principle, the partial molar isothermal compressibility change (ΔK¯T) of a short-lived intermediate become observable if we conduct the TG experiment under the high-pressure condition and detect ΔV¯ with varying external pressure.There are several difficulties in applying the traditional high-pressure cell to the TG method to measure thermodynamic parameters quantitatively. The most serious problem is ensuring the quantitative performance of the intensity of TG signals measured under the high-pressure condition. On this point, our group has developed a new high-pressure cell specially designed for TG spectroscopy (39) and overcome this problem. In this paper, by applying this high-pressure TG system to the BLUF protein TePixD, we report the first measurement, to our knowledge, of ΔK¯T of short-lived intermediates to investigate the mechanism underlying signal transmission by BLUF proteins, from the view point of the transient fluctuation.TePixD is a homolog of the BLUF protein PixD, which regulates the phototaxis of cyanobacterium (40) and exists in a thermophilic cyanobacterium Thermocynechococcus elongates BP-1 (Tll0078). TePixD is a relatively small (17 kDa) protein that consists only of the BLUF domain with two extended helices in the C-terminal region. In crystals and solutions, it forms a decamer that consists of two pentameric rings (41). The photochemistry of TePixD is typical among BLUF proteins (42–45); on blue light illumination, the absorption spectrum shifts toward red by about 10 nm within a nanosecond. The absorption spectrum does not change further, and the dark state is recovered with a time constant of ∼5 s at room temperature (40, 43). The spectral red shift was explained by the rearrangement of the hydrogen bond network around the chromophore (6, 46–48). The TG method has revealed the dynamic photoreaction mechanism, which cannot be detected by conventional spectroscopic methods. The TG signal of TePixD (Fig. S1) showed that there are two spectrally silent reaction phases: a partial molar volume expansion with the time constant of ∼40 μs and the diffusion coefficient (D) change with a time constant of ∼4 ms. Furthermore, it was reported that the pentamer and decamer states of TePixD are in equilibrium and that the final photoproduct of the decamer is pentamers generated by its dissociation (13, 49). On the basis of these studies, the reaction scheme has been identified as shown in Fig. 1. Here, I₁ is the intermediate of the spectrally red-shifted species (generated within a nanosecond) and I₂ is the one created on the subsequent volume expansion process of +4 cm³⋅mol⁻¹ (∼40 μs). Furthermore, an experiment of the excitation laser power dependence of its TG signal revealed that the TePixD decamer undergoes the original dissociation reaction when only one monomer in the decamer is excited (50). In this study, we investigated the transient compressibility of the intermediates I₁ and I₂ of the photoreaction of TePixD and found a direct link between their fluctuation and reactivity.Open in a separate windowFig. 1.Schematic illustration of the photoreaction of TePixD. Yellow circles represent the TePixD monomer in the ground state, which constructs the decamer and pentamer states. In the dark state, these two forms are in equilibrium. The excited, spectral red-shifted state of the TePixD monomer is indicated by a red circle. The square represents the I₂ state of the monomer, which is created by the volume expansion process.     

Methane emissions from Alaska in 2012 from CARVE airborne observations

We determined methane (CH₄) emissions from Alaska using airborne measurements from the Carbon Arctic Reservoirs Vulnerability Experiment (CARVE). Atmospheric sampling was conducted between May and September 2012 and analyzed using a customized version of the polar weather research and forecast model linked to a Lagrangian particle dispersion model (stochastic time-inverted Lagrangian transport model). We estimated growing season CH₄ fluxes of 8 ± 2 mg CH₄⋅m⁻²⋅d⁻¹ averaged over all of Alaska, corresponding to fluxes from wetlands of 56−13+22 mg CH₄⋅m⁻²⋅d⁻¹ if we assumed that wetlands are the only source from the land surface (all uncertainties are 95% confidence intervals from a bootstrapping analysis). Fluxes roughly doubled from May to July, then decreased gradually in August and September. Integrated emissions totaled 2.1 ± 0.5 Tg CH₄ for Alaska from May to September 2012, close to the average (2.3; a range of 0.7 to 6 Tg CH₄) predicted by various land surface models and inversion analyses for the growing season. Methane emissions from boreal Alaska were larger than from the North Slope; the monthly regional flux estimates showed no evidence of enhanced emissions during early spring or late fall, although these bursts may be more localized in time and space than can be detected by our analysis. These results provide an important baseline to which future studies can be compared.Recent studies have raised concerns about an increase in methane (CH₄) emissions from Arctic regions as temperatures warm (1–3). Carbon stocks in polar regions are estimated to be as large as 1,700 Pg of soil organic carbon (4), preserved by cold, wet conditions that inhibit decomposition. Over the last 20 y, temperatures have increased more rapidly at these latitudes than the rest of the world (5); continuation of this trend will lead to permafrost warming and thawing (6), potentially releasing vast quantities of carbon dioxide (CO₂) and CH₄ into the atmosphere (7–10). A recent synthesis of carbon emissions predicted by permafrost models reported releases in the range of 120 ± 85 Pg C by 2100 (11). Large uncertainties are likewise associated with estimates of CH₄ emissions (12–90 Tg CH₄⋅y⁻¹) (12). The potential for large increases in CH₄ emissions are a particular concern because CH₄ strongly impacts both atmospheric chemistry and climate (13). Estimates of the impact of permafrost carbon emissions on future global temperatures range from ∼0.1–0.2 °C (14) to 0.3 ± 0.2 °C (11) by 2100, with increased carbon emissions expected to continue after 2100 (11).Recent global inversion studies find no evidence for increasing CH₄ emissions from these regions in the last 10 y (15, 16), despite warming, similar to earlier studies (17–19) and some biogeochemical models (14). Surface CH₄ flux observations across the pan-Arctic from 1990–2006 have ranged widely and measurement locations have changed, making it difficult to detect any trend over those years (ref. 20; cf. ref. 21).The present paper derives estimates of CH₄ surface fluxes in Alaska from May to September 2012, based on an extensive program of regional-scale airborne measurements of atmospheric CH₄, the Carbon in Arctic Reservoirs Vulnerability Experiment (CARVE). We quantify the monthly mean CH₄ emissions from Alaska during the growing season, providing a snapshot of the interactions between climate and the vast reservoir of preserved soil organic matter in the Arctic.     

High-value decisions are fast and accurate,inconsistent with diminishing value sensitivity

It is a widely held belief that people’s choices are less sensitive to changes in value as value increases. For example, the subjective difference between $11 and $12 is believed to be smaller than between $1 and $2. This idea is consistent with applications of the Weber-Fechner Law and divisive normalization to value-based choice and with psychological interpretations of diminishing marginal utility. According to random utility theory in economics, smaller subjective differences predict less accurate choices. Meanwhile, in the context of sequential sampling models in psychology, smaller subjective differences also predict longer response times. Based on these models, we would predict decisions between high-value options to be slower and less accurate. In contrast, some have argued on normative grounds that choices between high-value options should be made with less caution, leading to faster and less accurate choices. Here, we model the dynamics of the choice process across three different choice domains, accounting for both discriminability and response caution. Contrary to predictions, we mostly observe faster and more accurate decisions (i.e., higher drift rates) between high-value options. We also observe that when participants are alerted about incoming high-value decisions, they exert more caution and not less. We rule out several explanations for these results, using tasks with both subjective and objective values. These results cast doubt on the notion that increasing value reduces discriminability.

Are decision-makers sensitive to the average value of their options? For example, when shopping for a car, does the choice process differ at a bargain lot compared to a luxury dealership? Is it easier to choose between two cars valued at $5,000 or $50,000?To answer this question, we must first define what we mean by “easier.” There are two basic features of easy decisions: they are consistent and fast. For instance, it is well established that choices are inconsistent and slow when the choice options are similar in value to each other, while they are consistent and fast when there is a large difference in the options’ values (1–5). The effect of value difference on the stochasticity of choice is predicted by many popular models, dating back at least to Luce (6), and the effect of value difference on response time (RT) is predicted by sequential sampling models (7–12). In fact, the effect of value difference on both choice frequencies and RT has been documented in many laboratory experiments (10, 13).In comparison, there has been much less research into the effects of overall value (OV), holding value difference constant. Among conventional stochastic choice models, a common assumption is that OV should be irrelevant. One popular economic model is the additive random utility model (2), which implies the probability of choosing an option i over another alternative j should be an increasing function of μ_i − μ_j, where for any option i the utility assigned to it is μ_i (before the addition of the random error term). Therefore, a constant utility difference should imply the same choice frequencies regardless of whether μ_i and μ_j are two small quantities or two large quantities. The logit (softmax) choice function, commonly used to fit preference models to experimental data, similarly posits choice frequencies of the formP[i≻j]=eλμieλμi+ eλμj=(1+e−λ(μi−μj))−1for some “inverse temperature” parameter λ > 0. This model again implies that only utility differences matter. Finally, choice frequencies and RT are often jointly modeled using sequential sampling models. The most popular of these models, the drift diffusion model (DDM), commonly assumes that the drift rate of the decision variable is proportional to the difference in value between the two options (9, 10). Under this assumption, the DDM predicts that both choice frequencies and mean RT should depend only on the value difference and not on OV.The aforementioned models imply that OV is irrelevant only under the assumption that value representations (i.e., utilities) are linear, monotonic functions of the values measured by the experimenter. However, there are many theories of value representation that instead posit that utilities are nonlinear functions of the measured values, i.e., μ_i = μ(V_i). In this case, choice frequencies and RT would depend on more than just the value difference ΔV = V_i − V_j measured by the experimenter.What form should the function μ(V) take? A natural proposal would be to assume that μ(V) is increasing but strictly concave, so that the marginal utility μ′(V) decreases as V increases. The assumption of diminishing marginal utility is commonplace in economic modeling, dating back to Bernoulli (14). It is typically invoked to explain the imperfect substitutability between different goods in a bundle (15), imperfect substitutability of consumption over time (16), or risk aversion (17)—contexts that might seem orthogonal to stochastic choice or issues of discriminability. Nonetheless, one might conjecture that the same mechanisms that generate diminishing marginal utility in these other contexts should also determine the relationship between measured values and utilities in a random utility model of stochastic choice.Similarly, Prospect Theory is predicated on the assumption that choices are made based on subjective values generated by nonlinear transformations of objective values (17). Notably, this value function is assumed to reflect diminishing marginal sensitivity to increasing values. Kahneman and Tversky use this value function to explain modal choices but do not propose any model of the stochasticity of observed choices or of RT. They motivate their incorporation of diminishing marginal sensitivity based on an analogy to the psychophysics of perceptual judgements, in which objective sensory magnitudes are often mapped onto an internal scale (18) with a nonlinear function that is typically expected to be concave (as with the logarithmic mapping postulated by the Weber-Fechner Law). The key evidence for such nonlinearity is the way in which the discriminability between two stimuli declines with increases in the absolute magnitudes of the two stimuli (holding the difference constant). Kahneman and Tversky also expected this to be true of comparisons involving economic values, and others have formalized this assumption within stochastic versions of Prospect Theory fit to experimental data (19).Another way to motivate this type of nonlinear function is with the theory of divisive normalization in neural coding. An influential literature in neuroscience has determined that neural firing rates that represent sensory magnitudes are normalized in such a way that a given difference in objective magnitudes results in a smaller difference in the respective firing rates when the two objective magnitudes increase (20–23). Recent work in neuroeconomics has applied divisive normalization to stochastic, value-based choice under the assumption that there is a one-to-one relationship between the neural representation of value in firing rates and the choice behavior it generates (24–30). A theory of stochastic choice predicated on divisive normalization thus predicts that option discriminability will decrease as OV increases (see SI Appendix for details).Despite the intuitive appeal of diminishing marginal sensitivity and the evidence for it in other sensory domains, there is little direct evidence that OV decreases discriminability once you control for value difference. The behavioral evidence on accuracy rates is controversial (31). Furthermore, the notion that utility differences decrease with OV is typically inferred from the presence of risk-averse behavior, which could arise for other reasons (32–35).One possible reason for the mixed behavioral evidence is that increasing OV may also increase perceived importance, motivating decision-makers to approach high-value decisions more cautiously (36–40). The well-known speed–accuracy tradeoff (5, 9) implies that more caution could counteract losses in discriminability. On the other hand, there is abundant evidence that high-value decisions tend to be fast (10, 41–45). Even nonhuman primates will choose between juices (including identical ones) faster as the amount of juice increases (46). Based on these results, it appears unlikely that high-value decisions are made more cautiously, but we cannot be sure because both discriminability and response caution affect RT (47).To properly determine how OV influences discriminability while accounting for response caution, we require analyses that consider both accuracy and RT. Using the DDM, we can account for response caution while simultaneously estimating the effect of OV on discriminability (48).In this paper, we applied the DDM to behavior in three studies, each with the same structure but different types of decisions. Each experiment involved a series of binary choices, separated into blocks with three categories of OV (low, middle, and high). To study OV effects in naturalistic settings, studies 1 and 2 used snack foods and abstract art, respectively. Subjects first rated how much they liked various items, then later chose between them. These tasks are commonly used in the literature, but also come with a drawback: they rely on subjective ratings. Subjective ratings noisily represent subjects’ true values (49), and ratings on different parts of the scale may be more or less noisy (50). To rule out these concerns, study 3 used a paradigm with learned values that were objective and identically distributed in each OV condition.In each study, we first tested core predictions about discriminability varying with OV in a baseline condition. Specifically, we used the DDM to estimate discriminability (via drift rate) as a function of OV while accounting for response-caution differences (via boundary separation) between OV categories. We tested the hypothesis that discriminability would be reduced in higher OV contexts against the null hypothesis that OV would have no effect on discriminability.To investigate the impacts of OV on response caution, we included a condition with cues that indicated the value category for the upcoming block. These cues did not provide any additional information. We included the value cues because in the DDM framework, decision-makers adjust their decision boundaries at the block level. Thus, we reasoned that the value cues would allow subjects to set (and reveal to us) their desired level of response caution for each value category. If decision-makers view higher-value decisions as more (less) important, value cues should increase (decrease) boundaries in high-value blocks.To preview the results, across all three studies (for which studies 2 and 3 were preregistered), we find heightened, not reduced, discriminability as OV increases; we observe both faster and more accurate choices at high OV and a tendency toward slower and less accurate choices at low OV. However, we find that value cues increase response caution for high-value compared to middle-value trials, indicating that decision-makers are motivated to be slower and more accurate for high-value decisions. We find these same effects in all three studies, indicating that they are not due to familiarity/accessibility (51), different uses of the rating scale, or variability within value categories.     

Structures and topological defects in pressure-driven lyotropic chromonic liquid crystals

Lyotropic chromonic liquid crystals are water-based materials composed of self-assembled cylindrical aggregates. Their behavior under flow is poorly understood, and quantitatively resolving the optical retardance of the flowing liquid crystal has so far been limited by the imaging speed of current polarization-resolved imaging techniques. Here, we employ a single-shot quantitative polarization imaging method, termed polarized shearing interference microscopy, to quantify the spatial distribution and the dynamics of the structures emerging in nematic disodium cromoglycate solutions in a microfluidic channel. We show that pure-twist disclination loops nucleate in the bulk flow over a range of shear rates. These loops are elongated in the flow direction and exhibit a constant aspect ratio that is governed by the nonnegligible splay-bend anisotropy at the loop boundary. The size of the loops is set by the balance between nucleation forces and annihilation forces acting on the disclination. The fluctuations of the pure-twist disclination loops reflect the tumbling character of nematic disodium cromoglycate. Our study, including experiment, simulation, and scaling analysis, provides a comprehensive understanding of the structure and dynamics of pressure-driven lyotropic chromonic liquid crystals and might open new routes for using these materials to control assembly and flow of biological systems or particles in microfluidic devices.

Lyotropic chromonic liquid crystals (LCLCs) are aqueous dispersions of organic disk-like molecules that self-assemble into cylindrical aggregates, which form nematic or columnar liquid crystal phases under appropriate conditions of concentration and temperature (1–6). These materials have gained increasing attention in both fundamental and applied research over the past decade, due to their distinct structural properties and biocompatibility (4, 7–14). Used as a replacement for isotropic fluids in microfluidic devices, nematic LCLCs have been employed to control the behavior of bacteria and colloids (13, 15–20).Nematic liquid crystals form topological defects under flow, which gives rise to complex dynamical structures that have been extensively studied in thermotropic liquid crystals (TLCs) and liquid crystal polymers (LCPs) (21–29). In contrast to lyotropic liquid crystals that are dispersed in a solvent and whose phase can be tuned by either concentration or temperature, TLCs do not need a solvent to possess a liquid-crystalline state and their phase depends only on temperature (30). Most TLCs are shear-aligned nematics, in which the director evolves toward an equilibrium out-of-plane polar angle. Defects nucleate beyond a critical Ericksen number due to the irreconcilable alignment of the directors from surface anchoring and shear alignment in the bulk flow (24, 31–33). With an increase in shear rate, the defect type can transition from π-walls (domain walls that separate regions whose director orientation differs by an angle of π) to ordered disclinations and to a disordered chaotic regime (34). Recent efforts have aimed to tune and control the defect structures by understanding the relation between the selection of topological defect types and the flow field in flowing TLCs. Strategies to do so include tuning the geometry of microfluidic channels, inducing defect nucleation through the introduction of isotropic phases or designing inhomogeneities in the surface anchoring (35–39). LCPs are typically tumbling nematics for which α2α3 < 0, where α2 and α3 are the Leslie viscosities. This leads to a nonzero viscous torque for any orientation of the director, which allows the director to rotate in the shear plane (22, 29, 30, 40). The tumbling character of LCPs facilitates the nucleation of singular topological defects (22, 40). Moreover, the molecular rotational relaxation times of LCPs are longer than those of TLCs, and they can exceed the timescales imposed by the shear rate. As a result, the rheological behavior of LCPs is governed not only by spatial gradients of the director field from the Frank elasticity, but also by changes in the molecular order parameter (25, 41–43). With increasing shear rate, topological defects in LCPs have been shown to transition from disclinations to rolling cells and to worm-like patterns (25, 26, 43).Topological defects occurring in the flow of nematic LCLCs have so far received much more limited attention (44, 45). At rest, LCLCs exhibit unique properties distinct from those of TLCs and LCPs (1, 2, 4–6, 44). In particular, LCLCs have significant elastic anisotropy compared to TLCs; the twist Frank elastic constant, K2, is much smaller than the splay and bend Frank elastic constants, K1 and K3. The resulting relative ease with which twist deformations can occur can lead to a spontaneous symmetry breaking and the emergence of chiral structures in static LCLCs under spatial confinement, despite the achiral nature of the molecules (4, 46–51). When driven out of equilibrium by an imposed flow, the average director field of LCLCs has been reported to align predominantly along the shear direction under strong shear but to reorient to an alignment perpendicular to the shear direction below a critical shear rate (52–54). A recent study has revealed a variety of complex textures that emerge in simple shear flow in the nematic LCLC disodium cromoglycate (DSCG) (44). The tumbling nature of this liquid crystal leads to enhanced sensitivity to shear rate. At shear rates γ˙<1 s−1, the director realigns perpendicular to the flow direction adapting a so-called log-rolling state characteristic of tumbling nematics. For 1 s−1<γ˙<10 s−1, polydomain textures form due to the nucleation of pure-twist disclination loops, for which the rotation vector is parallel to the loop normal, and mixed wedge-twist disclination loops, for which the rotation vector is perpendicular to the loop normal (44, 55). Above γ˙>10 s−1, the disclination loops gradually transform into periodic stripes in which the director aligns predominantly along the flow direction (44).Here, we report on the structure and dynamics of topological defects occurring in the pressure-driven flow of nematic DSCG. A quantitative evaluation of such dynamics has so far remained challenging, in particular for fast flow velocities, due to the slow image acquisition rate of current quantitative polarization-resolved imaging techniques. Quantitative polarization imaging traditionally relies on three commonly used techniques: fluorescence confocal polarization microscopy, polarizing optical microscopy, and LC-Polscope imaging. Fluorescence confocal polarization microscopy can provide accurate maps of birefringence and orientation angle, but the fluorescent labeling may perturb the flow properties (56). Polarizing optical microscopy requires a mechanical rotation of the polarizers and multiple measurements, which severely limits the imaging speed. LC-Polscope, an extension of conventional polarization optical microscopy, utilizes liquid crystal universal compensators to replace the compensator used in conventional polarization microscopes (57). This leads to an enhanced imaging speed and better compensation for polarization artifacts of the optical system. The need for multiple measurements to quantify retardance, however, still limits the acquisition rate of LC-Polscopes.We overcome these challenges by using a single-shot quantitative polarization microscopy technique, termed polarized shearing interference microscopy (PSIM). PSIM combines circular polarization light excitation with off-axis shearing interferometry detection. Using a custom polarization retrieval algorithm, we achieve single-shot mapping of the retardance, which allows us to reach imaging speeds that are limited only by the camera frame rate while preserving a large field-of-view and micrometer spatial resolution. We provide a brief discussion of the optical design of PSIM in Materials and Methods; further details of the measurement accuracy and imaging performance of PSIM are reported in ref. 58.Using a combination of experiments, numerical simulations and scaling analysis, we show that in the pressure-driven flow of nematic DSCG solutions in a microfluidic channel, pure-twist disclination loops emerge for a certain range of shear rates. These loops are elongated in the flow with a fixed aspect ratio. We demonstrate that the disclination loops nucleate at the boundary between regions where the director aligns predominantly along the flow direction close to the channel walls and regions where the director aligns predominantly perpendicular to the flow direction in the center of the channel. The large elastic stresses of the director gradient at the boundary are then released by the formation of disclination loops. We show that both the characteristic size and the fluctuations of the pure-twist disclination loops can be tuned by controlling the flow rate.     

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.     

Submesoscale dispersion in the vicinity of the Deepwater Horizon spill

Reliable forecasts for the dispersion of oceanic contamination are important for coastal ecosystems, society, and the economy as evidenced by the Deepwater Horizon oil spill in the Gulf of Mexico in 2010 and the Fukushima nuclear plant incident in the Pacific Ocean in 2011. Accurate prediction of pollutant pathways and concentrations at the ocean surface requires understanding ocean dynamics over a broad range of spatial scales. Fundamental questions concerning the structure of the velocity field at the submesoscales (100 m to tens of kilometers, hours to days) remain unresolved due to a lack of synoptic measurements at these scales. Using high-frequency position data provided by the near-simultaneous release of hundreds of accurately tracked surface drifters, we study the structure of submesoscale surface velocity fluctuations in the Northern Gulf of Mexico. Observed two-point statistics confirm the accuracy of classic turbulence scaling laws at 200-m to 50-km scales and clearly indicate that dispersion at the submesoscales is local, driven predominantly by energetic submesoscale fluctuations. The results demonstrate the feasibility and utility of deploying large clusters of drifting instruments to provide synoptic observations of spatial variability of the ocean surface velocity field. Our findings allow quantification of the submesoscale-driven dispersion missing in current operational circulation models and satellite altimeter-derived velocity fields.The Deepwater Horizon (DwH) incident was the largest accidental oil spill into marine waters in history with some 4.4 million barrels released into the DeSoto Canyon of the northern Gulf of Mexico (GoM) from a subsurface pipe over ∼84 d in the spring and summer of 2010 (1). Primary scientific questions, with immediate practical implications, arising from such catastrophic pollutant injection events are the path, speed, and spreading rate of the pollutant patch. Accurate prediction requires knowledge of the ocean flow field at all relevant temporal and spatial scales. Whereas ocean general circulation models were widely used during and after the DwH incident (2–6), such models only capture the main mesoscale processes (spatial scale larger than 10 km) in the GoM. The main factors controlling surface dispersion in the DeSoto Canyon region remain unclear. The region lies between the mesoscale eddy-driven deep water GoM (7) and the wind-driven shelf (8) while also being subject to the buoyancy input of the Mississippi River plume during the spring and summer months (9). Images provided by the large amounts of surface oil produced in the DwH incident revealed a rich array of flow patterns (10) showing organization of surface oil not only by mesoscale straining into the loop current “Eddy Franklin,” but also by submesoscale processes. Such processes operate at spatial scales and involve physics not currently captured in operational circulation models. Submesoscale motions, where they exist, can directly influence the local transport of biogeochemical tracers (11, 12) and provide pathways for energy transfer from the wind-forced mesoscales to the dissipative microscales (13–15). Dynamics at the submesoscales have been the subject of recent research (16–20). However, the investigation of their effect on ocean transport has been predominantly modeling based (13, 21–23) and synoptic observations, at adequate spatial and temporal resolutions, are rare (24, 25). The mechanisms responsible for the establishment, maintenance, and energetics of such features in the Gulf of Mexico remain unclear.Instantaneous measurement of all representative spatiotemporal scales of the ocean state is notoriously difficult (26). As previously reviewed (27), traditional observing systems are not ideal for synoptic sampling of near-surface flows at the submesoscale. Owing to the large spacing between ground tracks (28) and along-track signal contamination from high-frequency motions (29), gridded altimeter-derived sea level anomalies only resolve the largest submesoscale motions. Long time-series ship-track current measurements attain similar, larger than 2 km, spatial resolutions, and require averaging the observations over evolving ocean states (30). Simultaneous, two-point accoustic Doppler current profiler measurements from pairs of ships (25) provide sufficient resolution to show the existence of energetic submesoscale fluctuations in the mixed layer, but do not explicitly quantify the scale-dependent transport induced by such motions at the surface. Lagrangian experiments, centered on tracking large numbers of water-following instruments, provide the most feasible means of obtaining spatially distributed, simultaneous measurements of the structure of the ocean’s surface velocity field on 100-m to 10-km length scales.Denoting a trajectory by x(a, t), where x(a, t₀) = a, the relative separation of a particle pair is given by D(t,D0)=x(a1,t)−x(a2,t)=D0+∫t0tΔv(t′,D0)dt′, where the Lagrangian velocity difference is defined by Δv(t, D₀) = v(a₁, t) − v(a₂, t). The statistical quantities of interest, both practically and theoretically, are the scale-dependent relative dispersion D²(t) = 〈D ⋅ D〉 (averaged over particle pairs) and the average longitudinal or separation velocity, Δv(r), at a given separation, r. The velocity scale is defined by the second order structure function Δv(r)=〈δv2〉, where δv(r) = (v(x + r) − v(x)) ⋅ r/∥r∥ (31, 32) where the averaging is now conditioned on the pair separation r.The applicability of classical dispersion theories (32–34) developed in the context of homogeneous, isotropic turbulence with localized spectral forcing, to ocean flows subject to the effects of rotation, stratification, and complex forcing at disparate length and time scales remains unresolved. Turbulence theories broadly predict two distinct dispersion regimes depending upon the shape of the spatial kinetic energy spectrum, E(k) ∼ k^−β, of the velocity field (35). For sufficiently steep spectra (β ≥ 3) the dispersion is expected to grow exponentially, D ∼ e^λt with a scale-independent rate. At the submesoscales (∼ 100 m–10 km), this nonlocal growth rate will then be determined by the mesoscale motions currently resolved by predictive models. For shallower spectra (1 < β < 3), however, the dispersion is local, D ∼ t^2/(3−β), and the growth rate of a pollutant patch is dominated by advective processes at the scale of the patch. Accurate prediction of dispersion in this regime requires resolution of the advecting field at smaller scales than the mesoscale.Whereas compilations of data from dye measurements broadly support local dispersion in natural flows (36), the range of scales in any particular dye experiment is limited. A number of Lagrangian observational studies have attempted to fill this gap. LaCasce and Ohlmann (37) considered 140 pairs of surface drifters on the GoM shelf over a 5-y period and found evidence of a nonlocal regime for temporally smoothed data at 1-km scales. Koszalka et al. (38) using ??(100) drifter pairs with D₀ < 2 km launched over 18 mo in the Norwegian Sea, found an exponential fit for D²(t) for a limited time (t = 0.5 − 2 d), although the observed longitudinal velocity structure function is less clearly fit by a corresponding quadratic. They concluded that a nonlocal dispersion regime could not be identified. In contrast, Lumpkin and Elipot (39) found evidence of local dispersion at 1-km scales using 15-m drogued drifters launched in the winter-time North Atlantic. It is not clear how the accuracy of the Argos positioning system (150–1,000 m) used in these studies affects the submesoscale dispersion estimates. Schroeder et al. (40), specifically targeting a coastal front using a multiscale sampling pattern, obtained results consistent with local dispersion, but the statistical significance (maximum 64 pairs) remained too low to be definitive.     

Unusual magnetotransport in twisted bilayer graphene

We present transport measurements of bilayer graphene with a 1.38^∘ interlayer twist. As with other devices with twist angles substantially larger than the magic angle of 1.1^∘, we do not observe correlated insulating states or band reorganization. However, we do observe several highly unusual behaviors in magnetotransport. For a large range of densities around half filling of the moiré bands, magnetoresistance is large and quadratic. Over these same densities, the magnetoresistance minima corresponding to gaps between Landau levels split and bend as a function of density and field. We reproduce the same splitting and bending behavior in a simple tight-binding model of Hofstadter’s butterfly on a triangular lattice with anisotropic hopping terms. These features appear to be a generic class of experimental manifestations of Hofstadter’s butterfly and may provide insight into the emergent states of twisted bilayer graphene.

The mesmerizing Hofstadter butterfly spectrum arises when electrons in a two-dimensional periodic potential are immersed in an out-of-plane magnetic field. When the magnetic flux Φ through a unit cell is a rational multiple p / q of the magnetic flux quantum Φ0=h/e, each Bloch band splits into q subbands (1). The carrier densities corresponding to gaps between these subbands follow straight lines when plotted as a function of normalized density n/ns and magnetic field (2). Here, n_s is the density of carriers required to fill the (possibly degenerate) Bloch band. These lines can be described by the Diophantine equation (n/ns)=t(Φ/Φ0)+s for integers s and t. In experiments, they appear as minima or zeros in longitudinal resistivity coinciding with Hall conductivity quantized at σxy=te2/h (3, 4). Hofstadter originally studied magnetosubbands emerging from a single Bloch band on a square lattice. In the following decades, other authors considered different lattices (5–7), the effect of anisotropy (6, 8–10), next-nearest-neighbor hopping (11–15), interactions (16, 17), density wave states (9), and graphene moirés (18, 19).It took considerable ingenuity to realize clean systems with unit cells large enough to allow conventional superconducting magnets to reach Φ/Φ0∼1. The first successful observation of the butterfly in electrical transport measurements was in GaAs/AlGaAs heterostructures with lithographically defined periodic potentials (20–22). These experiments demonstrated the expected quantized Hall conductance in a few of the largest magnetosubband gaps. In 2013, three groups mapped out the full butterfly spectrum in both density and field in heterostructures based on monolayer (23, 24) and bilayer (25) graphene. In all three cases, the authors made use of the 2% lattice mismatch between their graphene and its encapsulating hexagonal boron nitride (hBN) dielectric. With these layers rotationally aligned, the resulting moiré pattern was large enough in area that gated structures studied in available high-field magnets could simultaneously approach normalized carrier densities and magnetic flux ratios of 1. Later work on hBN-aligned bilayer graphene showed that, likely because of electron–electron interactions, the gaps could also follow lines described by fractional s and t (26).In twisted bilayer graphene (TBG), a slight interlayer rotation creates a similar-scale moiré pattern. Unlike with graphene–hBN moirés, in TBG there is a gap between lowest and neighboring moiré subbands (27). As the twist angle approaches the magic angle of 1.1^∘ the isolated moiré bands become flat (28, 29), and strong correlations lead to fascinating insulating (30–37), superconducting (31–33, 35–37), and magnetic (34, 35, 38) states. The strong correlations tend to cause moiré subbands within a fourfold degenerate manifold to move relative to each other as one tunes the density, leading to Landau levels that project only toward higher magnitude of density from charge neutrality and integer filling factors (37, 39). This correlated behavior obscures the single-particle Hofstadter physics that would otherwise be present.In this work, we present measurements from a TBG device twisted to 1.38^∘. When we apply a perpendicular magnetic field, a complicated and beautiful fan diagram emerges. In a broad range of densities on either side of charge neutrality, the device displays large, quadratic magnetoresistance. Within the magnetoresistance regions, each Landau level associated with ν=±8,±12,±16,… appears to split into a pair, and these pairs follow complicated paths in field and density, very different from those predicted by the usual Diophantine equation. Phenomenology similar in all qualitative respects appears in measurements on several regions of this same device with similar twist angles and in two separate devices, one at 1.59^∘ and the other at 1.70^∘ (see SI Appendix for details).We reproduce the unusual features of the Landau levels (LLs) in a simple tight-binding model on a triangular lattice with anisotropy and a small energetic splitting between two species of fermions. At first glance, this is surprising, because that model does not represent the symmetries of the experimental moiré structure. We speculate that the unusual LL features we experimentally observe can generically emerge from spectra of Hofstadter models that include the same ingredients we added to the triangular lattice model. With further theoretical work it may be possible to use our measurements to gain insight into the underlying Hamiltonian of TBG near the magic angle.