INAUGURAL ARTICLE by a Recently Elected Academy Member:The effect of parathyroid hormone on osteogenesis is mediated partly by osteolectin

We previously described a new osteogenic growth factor, osteolectin/Clec11a, which is required for the maintenance of skeletal bone mass during adulthood. Osteolectin binds to Integrin α11 (Itga11), promoting Wnt pathway activation and osteogenic differentiation by leptin receptor⁺ (LepR⁺) stromal cells in the bone marrow. Parathyroid hormone (PTH) and sclerostin inhibitor (SOSTi) are bone anabolic agents that are administered to patients with osteoporosis. Here we tested whether osteolectin mediates the effects of PTH or SOSTi on bone formation. We discovered that PTH promoted Osteolectin expression by bone marrow stromal cells within hours of administration and that PTH treatment increased serum osteolectin levels in mice and humans. Osteolectin deficiency in mice attenuated Wnt pathway activation by PTH in bone marrow stromal cells and reduced the osteogenic response to PTH in vitro and in vivo. In contrast, SOSTi did not affect serum osteolectin levels and osteolectin was not required for SOSTi-induced bone formation. Combined administration of osteolectin and PTH, but not osteolectin and SOSTi, additively increased bone volume. PTH thus promotes osteolectin expression and osteolectin mediates part of the effect of PTH on bone formation.

The maintenance and repair of the skeleton require the generation of new bone cells throughout adult life. Osteoblasts are relatively short-lived cells that are constantly regenerated, partly by skeletal stem cells within the bone marrow (1). The main source of new osteoblasts in adult bone marrow is leptin receptor-expressing (LepR⁺) stromal cells (2–4). These cells include the multipotent skeletal stem cells that give rise to the fibroblast colony-forming cells (CFU-Fs) in the bone marrow (2), as well as restricted osteogenic progenitors (5) and adipocyte progenitors (6–8). LepR⁺ cells are a major source of osteoblasts for fracture repair (2) and growth factors for hematopoietic stem cell maintenance (9–11).One growth factor synthesized by LepR⁺ cells, as well as osteoblasts and osteocytes, is osteolectin/Clec11a, a secreted glycoprotein of the C-type lectin domain superfamily (5, 12, 13). Osteolectin is an osteogenic factor that promotes the maintenance of the adult skeleton by promoting the differentiation of LepR⁺ cells into osteoblasts. Osteolectin acts by binding to integrin α11β1, which is selectively expressed by LepR⁺ cells and osteoblasts, activating the Wnt pathway (12). Deficiency for either Osteolectin or Itga11 (the gene that encodes integrin α11) reduces osteogenesis during adulthood and causes early-onset osteoporosis in mice (12, 13). Recombinant osteolectin promotes osteogenic differentiation by bone marrow stromal cells in culture and daily injection of mice with osteolectin systemically promotes bone formation.Osteoporosis is a progressive condition characterized by reduced bone mass and increased fracture risk (14). Several factors contribute to osteoporosis development, including aging, estrogen insufficiency, mechanical unloading, and prolonged glucocorticoid use (14). Existing therapies include antiresorptive agents that slow bone loss, such as bisphosphonates (15, 16) and estrogens (17), and anabolic agents that increase bone formation, such as parathyroid hormone (PTH) (18), PTH-related protein (19), and sclerostin inhibitor (SOSTi) (20). While these therapies increase bone mass and reduce fracture risk, they are not a cure.PTH promotes both anabolic and catabolic bone remodeling (21–24). PTH is synthesized by the parathyroid gland and regulates serum calcium levels, partly by regulating bone formation and bone resorption (23–25). PTH1R is a PTH receptor (26, 27) that is strongly expressed by LepR⁺ bone marrow stromal cells (8, 28–30). Recombinant human PTH (Teriparatide; amino acids 1 to 34) and synthetic PTH-related protein (Abaloparatide) are approved by the US Food and Drug Administration (FDA) for the treatment of osteoporosis (19, 31). Daily (intermittent) administration of PTH increases bone mass by promoting the differentiation of osteoblast progenitors, inhibiting osteoblast and osteocyte apoptosis, and reducing sclerostin levels (32–35). PTH promotes osteoblast differentiation by activating Wnt and BMP signaling in bone marrow stromal cells (28, 36, 37), although the mechanisms by which it regulates Wnt pathway activation are complex and uncertain (38).Sclerostin is a secreted glycoprotein that inhibits Wnt pathway activation by binding to LRP5/6, a widely expressed Wnt receptor (7, 8), reducing bone formation (39, 40). Sclerostin is secreted by osteocytes (8, 41), negatively regulating bone formation by inhibiting the differentiation of osteoblasts (41, 42). SOSTi (Romosozumab) is a humanized monoclonal antibody that binds sclerostin, preventing binding to LRP5/6 and increasing Wnt pathway activation and bone formation (43). It is FDA-approved for the treatment of osteoporosis (20, 44) and has activity in rodents in addition to humans (45, 46).The discovery that osteolectin is a bone-forming growth factor raises the question of whether it mediates the effects of PTH or SOSTi on osteogenesis.     

Evolution and global charge conservation for polarization singularities emerging from non-Hermitian degeneracies

Core concepts in singular optics, especially the polarization singularities, have rapidly penetrated the surging fields of topological and non-Hermitian photonics. For open photonic structures with non-Hermitian degeneracies in particular, polarization singularities would inevitably encounter another sweeping concept of Berry phase. Several investigations have discussed, in an inexplicit way, connections between both concepts, hinting at that nonzero topological charges for far-field polarizations on a loop are inextricably linked to its nontrivial Berry phase when degeneracies are enclosed. In this work, we reexamine the seminal photonic crystal slab that supports the fundamental two-level non-Hermitian degeneracies. Regardless of the invariance of nontrivial Berry phase (concerning near-field Bloch modes defined on the momentum torus) for different loops enclosing both degeneracies, we demonstrate that the associated far polarization fields (defined on the momentum sphere) exhibit topologically inequivalent patterns that are characterized by variant topological charges, including even the trivial scenario of zero charge. Moreover, the charge carried by the Fermi arc actually is not well defined, which could be different on opposite bands. It is further revealed that for both bands, the seemingly complex evolutions of polarizations are bounded by the global charge conservation, with extra points of circular polarizations playing indispensable roles. This indicates that although not directly associated with any local charges, the invariant Berry phase is directly linked to the globally conserved charge, physical principles underlying which have all been further clarified by a two-level Hamiltonian with an extra chirality term. Our work can potentially trigger extra explorations beyond photonics connecting Berry phase and singularities.

Pioneered by Pancharatnam, Berry, Nye, and others (1–10), Berry phase and singularities have become embedded languages all across different branches of photonics. Optical Berry phase is largely manifested through either polarization evolving Pancharatnam–Berry phase or the spin-redirection Bortolotti–Rytov–Vladimirskii–Berry phase (2, 4, 5, 11–15); while optical singularities are widely observed as singularities of intensity (caustics) (6), phase (vortices) (7), or polarization (8–10). As singularities for complex vectorial waves, polarization singularities are skeletons of electromagnetic waves and are vitally important for understanding various interference effects underlying many applications (16–20).There is a superficial similarity between the aforementioned two concepts: Both the topological charge of polarization field [Hopf index of line field (21, 22)] and Berry phase are defined on a closed circuit. Despite this, it is quite unfortunate that almost no definite connections have been established between them in optics. This is fully understandable: Berry phase is defined on the Pancharatnam connection (parallel transport) that decides the phase contrast between neighboring states on the loop (3, 4); while the polarization charge reflects accumulated orientation rotations of polarization ellipses, which has no direct relevance to the overall phase of each state. This explains why in pioneering works where both concepts were present (23–27), their interplay was rarely elaborated on.Spurred by studies into bound states in the continuum, polarization singularities have gained enormous renewed interest in open periodic photonic structures, manifested in different morphologies with both fundamental and higher-order half-integer charges (28–50). Simultaneously, the significance of Berry phase has been further reinforced in surging fields of topological and non-Hermitian photonics (1, 23, 26, 51–56). In open periodic structures involving band degeneracies, Berry phase and polarization singularity would inevitably meet, which sparks the influential work on non-Hermitian degeneracy (36) and several other following studies (40, 43, 45) discussing both concepts simultaneously. Although not claimed explicitly, those works hint that nontrivial Berry phase produces nonzero polarization charges.Aiming to bridge Berry phase and polarization singularity, we reexamine the seminal photonic crystal slab (PCS) that supports elementary two-level non-Hermitian degeneracies. It is revealed that with an invariant nontrivial π Berry phase, the corresponding polarization fields on different isofrequency contours enclosing both non-Hermitian degenerate points (or equivalently exceptional points [EPs]) (26) exhibit diverse patterns characterized by different polarization charges, even including the trivial zero charge. It is further revealed that the charge carried by the Fermi arc is actually not well defined, which could be different on opposite bands. We also discover that such complexity of field evolutions is constrained by global charge conservation for both bands, with extra points of circular polarizations (C points) playing pivotal roles. This reveals the explicit connection between globally conserved charge and the invariant Berry phase, underlying which the physical mechanisms have been further clarified by a two-level Hamiltonian with an extra chirality term (25). We show that such an unexpected connection is generically manifest in various structures, despite the fact that Berry phase and polarization charge actually characterize different entities of near-field Bloch modes and their projected far polarization fields, respectively: Bloch modes are defined on the momentum torus and can be folded into the irreducible Brillouin zone; while polarization fields are defined on the momentum sphere, due to the involvement of out-of-plane wave vectors along which there is no periodicity. Our study can spur further investigations in other subjects beyond photonics to explore conceptual interconnectedness, where both the concepts of Berry phase and singularities are present.     

Violet light suppresses lens-induced myopia via neuropsin (OPN5) in mice

Myopia has become a major public health concern, particularly across much of Asia. It has been shown in multiple studies that outdoor activity has a protective effect on myopia. Recent reports have shown that short-wavelength visible violet light is the component of sunlight that appears to play an important role in preventing myopia progression in mice, chicks, and humans. The mechanism underlying this effect has not been understood. Here, we show that violet light prevents lens defocus–induced myopia in mice. This violet light effect was dependent on both time of day and retinal expression of the violet light sensitive atypical opsin, neuropsin (OPN5). These findings identify Opn5-expressing retinal ganglion cells as crucial for emmetropization in mice and suggest a strategy for myopia prevention in humans.

Myopia (nearsightedness) in school-age children is generally axial myopia, which is the consequence of elongation of the eyeball along the visual axis. This shape change results in blurred vision but can also lead to severe complications including cataract, retinal detachment, myopic choroidal neovascularization, glaucoma, and even blindness (1–3). Despite the current worldwide pandemic of myopia, the mechanism of myopia onset is still not understood (4–8). One hypothesis that has earned a current consensus is the suggestion that a change in the lighting environment of modern society is the cause of myopia (9, 10). Consistent with this, outdoor activity has a protective effect on myopia development (9, 11, 12), though the main reason for this effect is still under debate (7, 12, 13). One explanation is that bright outdoor light can promote the synthesis and release of dopamine in the eye, a myopia-protective neuromodulator (14–16). Another suggestion is that the distinct wavelength composition of sunlight compared with fluorescent or LED (light-emitting diode) artificial lighting may influence myopia progression (9, 10). Animal studies have shown that different wavelengths of light can affect the development of myopia independent of intensity (17, 18). The effects appear to be distinct in different species: for chicks and guinea pigs, blue light showed a protective effect on experimentally induced myopia, while red light had the opposite effect (18–22). For tree shrews and rhesus monkeys, red light is protective, and blue light causes dysregulation of eye growth (23–25).It has been shown that visible violet light (VL) has a protective effect on myopia development in mice, in chick, and in human (10, 26, 27). According to Commission Internationale de l’Eclairage (International Commission on Illumination), VL has the shortest wavelength of visible light (360 to 400 nm). These wavelengths are abundant in outside sunlight but can only rarely be detected inside buildings. This is because the ultraviolet (UV)-protective coating on windows blocks all light below 400 nm and because almost no VL is emitted by artificial light sources (10). Thus, we hypothesized that the lack of VL in modern society is one reason for the myopia boom (9, 10, 26).In this study, we combine a newly developed lens-induced myopia (LIM) model with genetic manipulations to investigate myopia pathways in mice (28, 29). Our data confirm (10, 26) that visible VL is protective but further show that delivery of VL only in the evening is sufficient for the protective effect. In addition, we show that the protective effect of VL on myopia induction requires OPN5 (neuropsin) within the retina. The absence of retinal Opn5 prevents lens-induced, VL-dependent thickening of the choroid, a response thought to play a key role in adjusting the size of the eyeball in both human and animal myopia models (30–33). This report thus identifies a cell type, the Opn5 retinal ganglion cell (RGC), as playing a key role in emmetropization. The requirement for OPN5 also explains why VL has a protective effect on myopia development.     

Chemokine CCL5 promotes robust optic nerve regeneration and mediates many of the effects of CNTF gene therapy

Ciliary neurotrophic factor (CNTF) is a leading therapeutic candidate for several ocular diseases and induces optic nerve regeneration in animal models. Paradoxically, however, although CNTF gene therapy promotes extensive regeneration, recombinant CNTF (rCNTF) has little effect. Because intraocular viral vectors induce inflammation, and because CNTF is an immune modulator, we investigated whether CNTF gene therapy acts indirectly through other immune mediators. The beneficial effects of CNTF gene therapy remained unchanged after deleting CNTF receptor alpha (CNTFRα) in retinal ganglion cells (RGCs), the projection neurons of the retina, but were diminished by depleting neutrophils or by genetically suppressing monocyte infiltration. CNTF gene therapy increased expression of C-C motif chemokine ligand 5 (CCL5) in immune cells and retinal glia, and recombinant CCL5 induced extensive axon regeneration. Conversely, CRISPR-mediated knockdown of the cognate receptor (CCR5) in RGCs or treating wild-type mice with a CCR5 antagonist repressed the effects of CNTF gene therapy. Thus, CCL5 is a previously unrecognized, potent activator of optic nerve regeneration and mediates many of the effects of CNTF gene therapy.

Like most pathways in the mature central nervous system (CNS), the optic nerve cannot regenerate once damaged due in part to cell-extrinsic suppressors of axon growth (1, 2) and the low intrinsic growth capacity of adult retinal ganglion cells (RGCs), the projection neurons of the eye (3–5). Consequently, traumatic or ischemic optic nerve injury or degenerative diseases such as glaucoma lead to irreversible visual losses. Experimentally, some degree of regeneration can be induced by intraocular inflammation or growth factors expressed by inflammatory cells (6–10), altering the cell-intrinsic growth potential of RGCs (3–5), enhancing physiological activity (11, 12), chelating free zinc (13, 14), and other manipulations (15–19). However, the extent of regeneration achieved to date remains modest, underlining the need for more effective therapies.Ciliary neurotrophic factor (CNTF) is a leading therapeutic candidate for glaucoma and other ocular diseases (20–23). Activation of the downstream signal transduction cascade requires CNTF to bind to CNTF receptor-α (CNTFRα) (24), which leads to recruitment of glycoprotein 130 (gp130) and leukemia inhibitory factor receptor-β (LIFRβ) to form a tripartite receptor complex (25). CNTFRα anchors to the plasma membrane through a glycosylphosphatidylinositol linkage (26) and can be released and become soluble through phospholipase C-mediated cleavage (27). CNTF has been reported to activate STAT3 phosphorylation in retinal neurons, including RGCs, and to promote survival, but it is unknown whether these effects are mediated by direct action of CNTF on RGCs via CNTFRα (28). Our previous studies showed that CNTF promotes axon outgrowth from neonate RGCs in culture (29) but fails to do so in cultured mature RGCs (8) or in vivo (6). Although some studies report that recombinant CNTF (rCNTF) can promote optic nerve regeneration (20, 30, 31), others find little or no effect unless SOCS3 (suppressor of cytokine signaling-3), an inhibitor of the Jak-STAT pathway, is deleted in RGCs (5, 6, 32). In contrast, multiple studies show that adeno-associated virus (AAV)-mediated expression of CNTF in RGCs induces strong regeneration (33–40). The basis for the discrepant effects of rCNTF and CNTF gene therapy is unknown but is of considerable interest in view of the many promising clinical and preclinical outcomes obtained with CNTF to date.Because intravitreal virus injections induce inflammation (41), we investigated the possibility that CNTF, a known immune modulator (42–44), might act by elevating expression of other immune-derived factors. We report here that the beneficial effects of CNTF gene therapy in fact require immune system activation and elevation of C-C motif chemokine ligand 5 (CCL5). Depletion of neutrophils, global knockout (KO) or RGC-selective deletion of the CCL5 receptor CCR5, or a CCR5 antagonist all suppress the effects of CNTF gene therapy, whereas recombinant CCL5 (rCCL5) promotes axon regeneration and increases RGC survival. These studies point to CCL5 as a potent monotherapy for optic nerve regeneration and to the possibility that other applications of CNTF and other forms of gene therapy might similarly act indirectly through other factors.     

Computational modeling of ovarian cancer dynamics suggests optimal strategies for therapy and screening

High-grade serous tubo-ovarian carcinoma (HGSC) is a major cause of cancer-related death. Treatment is not uniform, with some patients undergoing primary debulking surgery followed by chemotherapy (PDS) and others being treated directly with chemotherapy and only having surgery after three to four cycles (NACT). Which strategy is optimal remains controversial. We developed a mathematical framework that simulates hierarchical or stochastic models of tumor initiation and reproduces the clinical course of HGSC. After estimating parameter values, we infer that most patients harbor chemoresistant HGSC cells at diagnosis and that, if the tumor burden is not too large and complete debulking can be achieved, PDS is superior to NACT due to better depletion of resistant cells. We further predict that earlier diagnosis of primary HGSC, followed by complete debulking, could improve survival, but its benefit in relapsed patients is likely to be limited. These predictions are supported by primary clinical data from multiple cohorts. Our results have clear implications for these key issues in HGSC management.

Ovarian cancer is the eighth most common cancer and cancer death in women worldwide (1). High-grade serous tubo-ovarian cancer (HGSC) constitutes ∼70% of all ovarian malignancies and has the worst prognosis (2). Current treatment of most patients with HGSC consists of cytoreductive surgery and combination chemotherapy with platinum-containing DNA–cross-linking drugs and taxane-based microtubule-stabilizing agents (2). Although treatment significantly improves survival, most women relapse with chemotherapy-refractory disease and eventually succumb (3). Multiple mechanisms of chemoresistance have been documented (4, 5), including reduced intracellular drug accumulation (6), detoxification by increased levels of glutathione (7), altered DNA damage repair (8, 9), dysfunctional apoptotic pathways (10, 11), and hyperactivation of various cell signaling pathways (12–14). These mechanistic studies are consistent with recent genomic analyses that reveal marked clonal evolution of HGSC during therapy (15). Other evidence, however, supports a hierarchical organization of HGSC, featuring intrinsically chemoresistant “cancer stem cells” (CSCs) that can escape initial treatment and seed recurrence (16–18).Although there is uniform agreement that HGSC patients should receive surgery and chemotherapy, the optimal order and timing of these modalities remain controversial. Two main options exist: primary debulking surgery with adjuvant chemotherapy (PDS), or neoadjuvant chemotherapy, followed by interval debulking surgery (NACT) (19–24). In either case, the surgical standard of care is to seek maximal cytoreduction, with the objective being to leave no visible residual disease. However, the precise definition of such “optimal debulking” can vary among different centers, surgeons, and reports (19, 21, 24, 25).Several studies have found similar outcomes after PDS or NACT, including two highly influential randomized trials (EORTC and CHORUS) carried out across multiple countries (22, 23, 26–28). In both trials, however, the question of potential bias in patient recruitment has been raised, favoring potentially those with more extensive disease, who are less likely benefit from “upfront” surgery (23, 28). Consistent with this interpretation, overall survival in these trials was significantly shorter than that seen in other HGSC cohorts (19, 24, 29, 30). Closer examination of these reports reveals additional factors that might have influenced their conclusions. The EORTC study had inconsistencies in optimal debulking rates between participating centers, with the PDS-associated complete debulking data highly influenced by the results from a single institution (23). The CHORUS study involved 76 clinical sites, and there were substantial differences in surgery execution and chemotherapy drug selection/dosage between them (28).At Princess Margaret Cancer Center, retrospective data showed that PDS patients with no visible disease postresection survived substantially longer (7-y survival, >60%) than those receiving NACT (7-y survival, ∼10%). Furthermore, although residual tumor postresection is a critical determinant of survival, its influence on the PDS group was far more dramatic than on NACT group (24). Of course, this report suffers from deficiencies common to all retrospective analyses, including lack of randomization to account for tumor burden at diagnosis and other factors; indeed, the NACT group in this study did have more extensive disease.Another controversy in HGSC management focuses on the potential benefit of earlier diagnosis. Earlier diagnosis of primary HGSC is generally assumed to enhance patient survival and quality of life (3). Intuitively, one might predict that the same reasoning would apply to recurrent disease; however, survival is similar in relapsed patients treated earlier, based on increasing serum CA125 levels, than in those treated only when physical symptoms of recurrence appear (31). Conceivably, the lead time between CA125 rise and clinical recurrence is too short for earlier chemotherapy to be beneficial; if so, then patient survival might be extended by more sensitive methods, such as testing for circulating tumor DNA (ctDNA) (32, 33).To address these issues, we developed a mathematical framework that models the dynamics of HGSC progression, response to surgery and chemotherapy, and recurrence. Our results, generated over a wide range of parameters and accounting for hierarchical and stochastic models of tumor initiation, argue that PDS is superior to NACT when complete debulking is feasible and suggest that, with currently available therapies, the benefits of earlier detection are intrinsically restricted to primary HGSC.     

Tropospheric carbonyl sulfide mass balance based on direct measurements of sulfur isotopes

Robust estimates for the rates and trends in terrestrial gross primary production (GPP; plant CO₂ uptake) are needed. Carbonyl sulfide (COS) is the major long-lived sulfur-bearing gas in the atmosphere and a promising proxy for GPP. Large uncertainties in estimating the relative magnitude of the COS sources and sinks limit this approach. Sulfur isotope measurements (³⁴S/³²S; δ³⁴S) have been suggested as a useful tool to constrain COS sources. Yet such measurements are currently scarce for the atmosphere and absent for the marine source and the plant sink, which are two main fluxes. Here we present sulfur isotopes measurements of marine and atmospheric COS, and of plant-uptake fractionation experiments. These measurements resulted in a complete data-based tropospheric COS isotopic mass balance, which allows improved partition of the sources. We found an isotopic (δ³⁴S ± SE) value of 13.9 ± 0.1‰ for the troposphere, with an isotopic seasonal cycle driven by plant uptake. This seasonality agrees with a fractionation of −1.9 ± 0.3‰ which we measured in plant-chamber experiments. Air samples with strong anthropogenic influence indicated an anthropogenic COS isotopic value of 8 ± 1‰. Samples of seawater-equilibrated-air indicate that the marine COS source has an isotopic value of 14.7 ± 1‰. Using our data-based mass balance, we constrained the relative contribution of the two main tropospheric COS sources resulting in 40 ± 17% for the anthropogenic source and 60 ± 20% for the oceanic source. This constraint is important for a better understanding of the global COS budget and its improved use for GPP determination.

The Earth system is going through rapid changes as the climate warms and CO₂ level rises. This rise in CO₂ is mitigated by plant uptake; hence, it is important to estimate global and regional photosynthesis rates and trends (1). Yet, robust tools for investigating these processes at a large scale are scarce (2). Recent studies suggest that carbonyl sulfide (COS) could provide an improved constraint on terrestrial photosynthesis (gross primary production, GPP) (2–12). COS is the major long-lived sulfur-bearing gas in the atmosphere and the main supplier of sulfur to the stratospheric sulfate aerosol layer (13), which exerts a cooling effect on the Earth’s surface and regulates stratospheric ozone chemistry (14).During terrestrial photosynthesis, COS diffuses into leaf stomata and is consumed by photosynthetic enzymes in a similar manner to CO₂ (3–5). Contrary to CO₂, COS undergoes rapid and irreversible hydrolysis mainly by the enzyme carbonic-anhydrase (6, 7). Thus, COS can be used as a proxy for the one-way flux of CO₂ removal from the atmosphere by terrestrial photosynthesis (2, 8–11). However, the large uncertainties in estimating the COS sources weaken this approach (10–12, 15). Tropospheric COS has two main sources: the oceans and anthropogenic emissions, and one main sink–terrestrial plant uptake (8, 10–13). Smaller sources include biomass burning, soil emissions, wetlands, volcanoes, and smaller sinks include OH destruction, stratospheric destruction, and soil uptake (12). The largest source of COS to the atmosphere is the ocean, both as direct COS emission, and as indirect carbon disulfide (CS₂) and dimethylsulfide (DMS) emissions that are rapidly oxidized to COS (10, 16–20). Recent studies suggest oceanic COS emissions are in the range of 200–4,000 GgS/y (19–22). The second major COS source is the anthropogenic source, which is dominated by indirect emissions derived from CS₂ oxidation, mainly from the use of CS₂ as an industrial solvent. Direct emissions of COS are mainly derived from coal and fuel combustion (17, 23, 24). Recent studies suggest that anthropogenic emissions are in the range of 150–585 GgS/y (23, 24). The terrestrial plant uptake is estimated to be in the range of 400–1,360 GgS/y (11). Measurements of sulfur isotope ratios (δ³⁴S) in COS may be used to track COS sources and thus reduce the uncertainties in their flux estimations (15, 25–27). However, the isotopic mass balance approach works best if the COS end members are directly measured and have a significantly different isotopic signature. Previous δ³⁴S measurements of atmospheric COS are scarce and there have been no direct measurements of two important components: the δ³⁴S of oceanic COS emissions, and the isotopic fractionation of COS during plant uptake (15, 25–27). In contrast to previous studies that used assessments for these isotopic values, our aim was to directly measure the isotopic values of these missing components, and to determine the tropospheric COS δ³⁴S variability over space and time.     

Improved bounds on entropy production in living systems

Living systems maintain or increase local order by working against the second law of thermodynamics. Thermodynamic consistency is restored as they consume free energy, thereby increasing the net entropy of their environment. Recently introduced estimators for the entropy production rate have provided major insights into the efficiency of important cellular processes. In experiments, however, many degrees of freedom typically remain hidden to the observer, and, in these cases, existing methods are not optimal. Here, by reformulating the problem within an optimization framework, we are able to infer improved bounds on the rate of entropy production from partial measurements of biological systems. Our approach yields provably optimal estimates given certain measurable transition statistics. In contrast to prevailing methods, the improved estimator reveals nonzero entropy production rates even when nonequilibrium processes appear time symmetric and therefore may pretend to obey detailed balance. We demonstrate the broad applicability of this framework by providing improved bounds on the energy consumption rates in a diverse range of biological systems including bacterial flagella motors, growing microtubules, and calcium oscillations within human embryonic kidney cells.

Thermodynamic laws place fundamental limits on the efficiency and fitness of living systems (1, 2). To maintain cellular order and perform essential biological functions such as sensing (3–6), signaling (7), replication (8, 9) or locomotion (10), organisms consume energy and dissipate heat. In doing so, they increase the entropy of their environment (2), in agreement with the second law of thermodynamics (11). Obtaining reliable estimates for the energy consumption and entropy production in living matter holds the key to understanding the physical boundaries (12–14) that constrain the range of theoretically and practically possible biological processes (3). Recent experimental (6, 15, 16) and theoretical (17–20) advances in the imaging and modeling of cellular and subcellular dynamics have provided groundbreaking insights into the thermodynamic efficiency of molecular motors (14, 21), biochemical signaling (16, 22, 23) and reaction (24) networks, and replication (9) and adaption (25) phenomena. Despite such major progress, however, it is also known that the currently available entropy production estimators (26, 27) can fail under experimentally relevant conditions, especially when only a small set of observables is experimentally accessible or nonequilibrium transport currents (28–30) vanish.To help overcome these limitations, we introduce here a generic optimization framework that can produce significantly improved bounds on the entropy production in living systems. We will prove that these bounds are optimal given certain measurable statistics. From a practical perspective, our method requires observations of only a few coarse-grained state variables of an otherwise hidden Markovian network. We demonstrate the practical usefulness by determining improved entropy production bounds for bacterial flagella motors (10, 31), growing microtubules (32, 33), and calcium oscillations (7, 34) in human embryonic kidney cells.Generally, entropy production rates can be estimated from the time series of stochastic observables (35). Thermal equilibrium systems obey the principle of detailed balance, which means that every forward trajectory is as likely to be observed as its time reversed counterpart, neutralizing the arrow of time (36). By contrast, living organisms operate far from equilibrium, which means that the balance between forward and reversed trajectories is broken and net fluxes may arise (1, 37–39). When all microscopic details of a nonequilibrium system are known, one can measure the rate of entropy production by comparing the likelihoods of forward and reversed trajectories in sufficiently large data samples (35, 36). However, in most if not all biophysical experiments, many degrees of freedom remain hidden to the observer, demanding methods (28, 40, 41) that do not require complete knowledge of the system. A powerful alternative is provided by thermodynamic uncertainty relations (TURs), which use the mean and variance of steady-state currents to bound entropy production rates (18, 19, 26, 42–48). Although highly useful when currents can be measured (44–47), or when the system can be externally manipulated (40, 49), these methods give, by construction, trivial zero bounds for current-free nonequilibrium systems, such as driven one-dimensional (1D) nonperiodic oscillators. In the absence of currents, potential asymmetries in the forward and reverse trajectories can still be exploited to bound the entropy production rate (29, 30, 50), but to our knowledge no existing method is capable of producing nonzero bounds when forward and reverse trajectories are statistically identical. Moreover, even though previous bounds can become tight in some cases (51), optimal entropy production estimators for nonequilibrium systems are in general unknown.To obtain bounds that are provably optimal under reasonable conditions on the available data, we reformulate the problem here within an optimization framework. Formally, we consider any steady-state Markovian dynamics for which only coarse-grained variables are observable, where these observables may appear non-Markovian. We then search over all possible underlying Markovian systems to identify the one which minimizes the entropy production rate while obeying the observed statistics. More specifically, our algorithmic implementation leverages information about successive transitions, allowing us to discover nonzero bounds on entropy production even when the coarse-grained statistics appear time symmetric. We demonstrate this for both synthetic test data and experimental data (52) for flagella motors. Subsequently, we consider the entropy production of microtubules (33), which slowly grow before rapidly shrinking in steady state, to show how refined coarse graining in space and time leads to improved bounds. The final application to calcium oscillations in human embryonic kidney cells (34) illustrates how external stimulation with drugs can increase entropy production.     

Circular swimming motility and disordered hyperuniform state in an algae system

Active matter comprises individually driven units that convert locally stored energy into mechanical motion. Interactions between driven units lead to a variety of nonequilibrium collective phenomena in active matter. One of such phenomena is anomalously large density fluctuations, which have been observed in both experiments and theories. Here we show that, on the contrary, density fluctuations in active matter can also be greatly suppressed. Our experiments are carried out with marine algae (Effrenium voratum), which swim in circles at the air–liquid interfaces with two different eukaryotic flagella. Cell swimming generates fluid flow that leads to effective repulsions between cells in the far field. The long-range nature of such repulsive interactions suppresses density fluctuations and generates disordered hyperuniform states under a wide range of density conditions. Emergence of hyperuniformity and associated scaling exponent are quantitatively reproduced in a numerical model whose main ingredients are effective hydrodynamic interactions and uncorrelated random cell motion. Our results demonstrate the existence of disordered hyperuniform states in active matter and suggest the possibility of using hydrodynamic flow for self-assembly in active matter.

Active matter exists over a wide range of spatial and temporal scales (1–6) from animal groups (7, 8) to robot swarms (9–11), to cell colonies and tissues (12–16), to cytoskeletal extracts (17–20), to man-made microswimmers (21–25). Constituent particles in active matter systems are driven out of thermal equilibrium at the individual level; they interact to develop a wealth of intriguing collective phenomena, including clustering (13, 22, 24), flocking (11, 26), swarming (12, 13), spontaneous flow (14, 20), and giant density fluctuations (10, 11). Many of these observed phenomena have been successfully described by particle-based or continuum models (1–6), which highlight the important roles of both individual motility and interparticle interactions in determining system dynamics.Current active matter research focuses primarily on linearly swimming particles which have a symmetric body and self-propel along one of the symmetry axes. However, a perfect alignment between the propulsion direction and body axis is rarely found in reality. Deviation from such a perfect alignment leads to a persistent curvature in the microswimmer trajectories; examples of such circle microswimmers include anisotropic artificial micromotors (27, 28), self-propelled nematic droplets (29, 30), magnetotactic bacteria and Janus particles in rotating external fields (31, 32), Janus particle in viscoelastic medium (33), and sperm and bacteria near interfaces (34, 35). Chiral motility of circle microswimmers, as predicted by theoretical and numerical investigations, can lead to a range of interesting collective phenomena in circular microswimmers, including vortex structures (36, 37), localization in traps (38), enhanced flocking (39), and hyperuniform states (40). However, experimental verifications of these predictions are limited (32, 35), a situation mainly due to the scarcity of suitable experimental systems.Here we address this challenge by investigating marine algae Effrenium voratum (41, 42). At air–liquid interfaces, E. voratum cells swim in circles via two eukaryotic flagella: a transverse flagellum encircling the cellular anteroposterior axis and a longitudinal one running posteriorly. Over a wide range of densities, circling E. voratum cells self-organize into disordered hyperuniform states with suppressed density fluctuations at large length scales. Hyperuniformity (43, 44) has been considered as a new form of material order which leads to novel functionalities (45–49); it has been observed in many systems, including avian photoreceptor patterns (50), amorphous ices (51), amorphous silica (52), ultracold atoms (53), soft matter systems (54–61), and stochastic models (62–64). Our work demonstrates the existence of hyperuniformity in active matter and shows that hydrodynamic interactions can be used to construct hyperuniform states.     

Hidden symmetries generate rigid folding mechanisms in periodic origami

We consider the zero-energy deformations of periodic origami sheets with generic crease patterns. Using a mapping from the linear folding motions of such sheets to force-bearing modes in conjunction with the Maxwell–Calladine index theorem we derive a relation between the number of linear folding motions and the number of rigid body modes that depends only on the average coordination number of the origami’s vertices. This supports the recent result by Tachi [T. Tachi, Origami 6, 97–108 (2015)] which shows periodic origami sheets with triangular faces exhibit two-dimensional spaces of rigidly foldable cylindrical configurations. We also find, through analytical calculation and numerical simulation, branching of this configuration space from the flat state due to geometric compatibility constraints that prohibit finite Gaussian curvature. The same counting argument leads to pairing of spatially varying modes at opposite wavenumber in triangulated origami, preventing topological polarization but permitting a family of zero-energy deformations in the bulk that may be used to reconfigure the origami sheet.

Origami-inspired materials are thin sheets whose two-dimensional crease patterns control their three-dimensional mechanical response, now manufacturable at the macroscopic scale using shape-memory alloys (1, 2) and at the microscopic scale using graphene bilayers (3) or polymer films (4–6). Origami principles are used to engineer deployable solar cells (7), stent grafts (8), flexible electronics (9, 10), impact mitigation devices (11), and tunable antennas (12) as well as to characterize patterns in biological systems (13). Yet determining whether a crease pattern can be rigidly folded into a particular shape is a nondeterministic in polynomial-time–hard problem (14) due to nonlinear geometric constraints (15) that can lead to disjoint (16) or branched (17–20) configuration spaces with multiple energetic minima (21, 22).Periodic origami sheets yield uniform mechanical properties such as negative Poisson ratios (23–27) and high stiffness-to-weight ratios (28), making them apt for the design of mechanical metamaterials. However, the study of origami tessellations has typically focused on crease patterns with inherent symmetries, such as the parallelogram faces of the Miura-ori (23, 24), which both simplify their analysis and generate rigid folding motions (29–31) that would cost energy in the absence of these symmetries (32). One might naively expect such symmetries are required as triangulations of all convex polyhedra are rigid (33). However, Tachi (34) recently found origami sheets composed of repeating unit cells with triangular but otherwise generic faces rigidly fold between cylindrical configurations, indicating that crease topology (the number of edges and vertices) may play as important a role as crease geometry (the angles between these edges) in determining origami kinematics.In the present work, we similarly consider generic triangulations, which inform the general case in three vital ways. First, the rigidly foldable configurations of any origami sheet can be derived as a subset of its triangulation’s configurations. Second, the low-energy deformations of origami sheets are often well approximated by the rigid configurations of their triangulations (35, 36). Finally, the triangulations are at the “Maxwell point”: They have an equal number of constraints and degrees of freedom (37, 38), which we emphasize by calling them Maxwell origami. Mechanical systems at the Maxwell point generically possess large numbers of both zero-energy modes and force-bearing modes (39, 40) which can be localized to the boundary via topological polarization (37, 38, 41), provide directional response in the bulk (42, 43), and be tuned by reconfigurations of the network (44). However, origami sheets possess a geometrical duality between these two classes of modes (33, 45, 46) that, as we show, both permits the rigid foldability (34) and modifies its topological class, prohibiting the topological polarization (47) of Maxwell origami which limits the ability to engineer directional response.The remainder of this paper is organized as follows. First, we review the work of Tachi (34) to show Maxwell origami generically approximates a cylindrical sheet with two degrees of freedom. Next, we construct an index theorem that pairs folding motions with continuous symmetries in Maxwell origami. We then show the restriction to cylindrical configurations leads to distinct branches of nonlinearly foldable origami configurations that we confirm through numerical simulation. Finally, we extend our index theorem to accommodate spatially varying modes to explain the observed lack of topological polarization in Maxwell origami (47) and report lines of bulk modes with real wavenumber.     

Naphthylphthalamic acid associates with and inhibits PIN auxin transporters

N-1-naphthylphthalamic acid (NPA) is a key inhibitor of directional (polar) transport of the hormone auxin in plants. For decades, it has been a pivotal tool in elucidating the unique polar auxin transport-based processes underlying plant growth and development. Its exact mode of action has long been sought after and is still being debated, with prevailing mechanistic schemes describing only indirect connections between NPA and the main transporters responsible for directional transport, namely PIN auxin exporters. Here we present data supporting a model in which NPA associates with PINs in a more direct manner than hitherto postulated. We show that NPA inhibits PIN activity in a heterologous oocyte system and that expression of NPA-sensitive PINs in plant, yeast, and oocyte membranes leads to specific saturable NPA binding. We thus propose that PINs are a bona fide NPA target. This offers a straightforward molecular basis for NPA inhibition of PIN-dependent auxin transport and a logical parsimonious explanation for the known physiological effects of NPA on plant growth, as well as an alternative hypothesis to interpret past and future results. We also introduce PIN dimerization and describe an effect of NPA on this, suggesting that NPA binding could be exploited to gain insights into structural aspects of PINs related to their transport mechanism.

Many aspects of plant growth are controlled by the hormone auxin. A distinct feature of auxin is that its hormonal action requires it to be actively transported between cells and ultimately throughout the whole plant in a controlled directional or polarized manner, a process known as polar auxin transport (PAT). The ability of plants to perform PAT is ascribed to the auxin export activity of PIN transporters (1). Plasma membrane PINs can be restricted to a specific side of cells (2), and when this polarity is maintained in continuous plant cell files, the combined activity of identically localized PINs results in auxin flowing in that direction (3). This lays the vectorial foundations for PAT to create local auxin gradients and plant-wide PAT streams that are critical for auxin action and normal plant growth (4, 5).Synthetic PAT inhibitors such as N-1-naphthylphthalamic acid (NPA) were initially developed as herbicides and then subsequently exploited by researchers to identify and characterize the unique PAT-based mechanisms that drive plant development (6). Having been used for over six decades, the question as to how NPA actually inhibits PAT has been keenly pursued. Several putative modes of action have been proposed, but the topic remains to date not fully or satisfactorily resolved (6).Early studies established NPA binding with high affinity to membrane-integral components of plant membranes (7–10). With the later discovery of pin1 mutants bearing their distinct bare inflorescences reminiscent of NPA-treated plants (11), followed by identification of the PIN gene family and gradual confirmation that PINs were NPA-sensitive auxin transporters that mediated PAT (1–5), it was apparent that the physiological and genetic evidence overwhelmingly linked NPA to inhibition of PIN activity (6). However, direct molecular association of NPA with PINs has never been reported (6). Instead, a substantial body of data has accumulated suggesting that the NPA target is not PIN itself, but rather other proteins or complexes that either actively coparticipate in PAT or are indirectly involved in control of PAT components (6, 12). Members of the B-family of ABC transporters, such as ABCB1 and ABCB19, showed high-affinity NPA binding and NPA-sensitive auxin export (1, 12–15), thus leading to proposals that they may either physically interact with PINs, or functionally interact such that their nonpolar auxin export activity contributes to PAT and/or to regulation of PINs (12, 16). In these scenarios, PIN/PAT would be rendered vulnerable to the NPA sensitivity of ABCB. However, these schemes are not yet fully resolved, are not fully consistent with key genetic and physiological data (6), and are particularly obfuscated by ABCB1/19 functioning both interactively and independently from PINs (1, 12, 15–20), with ABCB-PIN interaction occurring in an as-yet-unclarified manner (15, 18).A further twist in assigning ABCBs as the main NPA target is their regulation by their chaperone TWD1/FKBP42 (14, 16), with TWD1 itself also being an NPA-binding protein (14, 17). NPA interferes with this regulation and affects TWD1-ABCB interaction, but curiously NPA cannot bind stably to the ABCB-TWD1 complex (14, 17). As TWD1 has also been implicated in NPA-sensitive actin-based PIN trafficking (17), this has led to a model proposing that TWD1 could mediate the NPA sensitivities of both ABCB and PINs, thus presenting TWD1 as a modulator of PAT (17, 21). In an analogous scheme in some plant species, CYPA immunophilins such as tomato DGT, which are functionally similar to TWD1/FKBP42, are suggested to replace TWD1 in modulating auxin transporters and transducing NPA effects to PINs (12, 21).Similar to TWD1, BIG/TIR3 has also been associated with NPA and PIN trafficking (22). Given the undisputed role of trafficking in controlling PIN polarity (5), these reported effects warrant attention, although they are inconsistent with other reports that NPA perturbs neither vesicular trafficking nor actin dynamics in conditions where auxin transport is inhibited (23, 24). Together with trafficking, phosphorylation is another key modulator of PIN polarity as well as activity (5), so it is not surprising to find hypotheses suggesting that NPA could interfere with critical phosphorylation events (6), particularly as PID, a kinase crucial for PIN trafficking and activation, has also been connected to ABCB function and TWD1/ABCB/NPA interactions (25). Others propose that NPA may mimic natural compounds in their capacity as endogenous regulators of PAT, with plant flavonoids being suspected candidates (6, 26). Since flavonoids can compete with or inhibit ATP-binding in mammalian kinases and ABC transporters (27, 28), and as flavonoids can bind to and inhibit PID (25), a phosphorylation-based NPA mode of action would overlap with this hypothesis and poses the question whether NPA acts similarly as an ATP mimic.With these many potential NPA-affected pathways, there is a need to distinguish between low- and high-affinity NPA targets and possible secondary effects due to prolonged PAT inhibition. Current consensus is that low concentrations of NPA (<10 µM) cause direct inhibition of auxin transporters in PAT (21) and the consequent physiological effects seen in planta (IC₅₀ 0.1 to 10 µM) (7, 9, 19, 23, 29). This is associated with high-affinity binding to membranes (K_d 0.01 to 0.1 µM) (7, 8) and the inhibition of PIN/ABCB activity in short-term auxin transport assays (1, 14, 18, 20, 23). In contrast, NPA is thought to affect trafficking (21, 30) and other non-PAT processes (31) when used at higher doses (50 to 200 µM NPA), presumably via binding to its lower-affinity targets, although excessive NPA exposure may also have fast-acting toxic side effects (23). As the in vitro affinity of TWD1 for NPA is surprisingly low (K_d ∼100 µM) (17), the TWD1-mediated NPA effects on PIN/PAT are thought to be of the low-affinity type and linked to trafficking perturbations (17, 21). However, as NPA is always externally applied to plants or cells, it is not clear how or where the drug distributes or accumulates, and thus there may be discrepancies between actual and reported/apparent effective concentrations, as might be the case for TWD1 (17). Finally, NPA also binds with low affinity to inhibit APM1, an aminopeptidase implicated in auxin-related plant growth, but as with trafficking effects, this low-affinity NPA interaction is not connected to direct regulation of PAT (31).Thus, the available data proffer various indirect mechanisms that could lead to NPA inhibition of PIN-mediated PAT, but the proposed schemes have complicating aspects and struggle at times to satisfactorily explain the prime effects of NPA. Here we propose an alternative simpler scenario involving a more direct link between NPA and PINs that would resolve some of these currently outstanding issues. We present evidence from heterologous transport assays, classical in situ membrane binding, and oligomerization studies which collectively suggest that NPA can interact directly in a high-affinity manner with PINs, leading to conformational or structural effects and inhibition of auxin export activity.     

Environmental noise degrades hippocampus-related learning and memory

The neural mechanisms underlying the impacts of noise on nonauditory function, particularly learning and memory, remain largely unknown. Here, we demonstrate that rats exposed postnatally (between postnatal days 9 and 56) to structured noise delivered at a sound pressure level of ∼65 dB displayed significantly degraded hippocampus-related learning and memory abilities. Noise exposure also suppressed the induction of hippocampal long-term potentiation (LTP). In parallel, the total or phosphorylated levels of certain LTP-related key signaling molecules in the synapses of the hippocampus were down-regulated. However, no significant changes in stress-related processes were found for the noise-exposed rats. These results in a rodent model indicate that even moderate-level noise with little effect on stress status can substantially impair hippocampus-related learning and memory by altering the plasticity of synaptic transmission. They support the importance of more thoroughly defining the unappreciated hazards of moderately loud noise in modern human environments.

The noise pollution accompanying industrialization is a risk factor to human health. Earlier studies have extensively examined the deleterious impacts of noise in the auditory systems of both humans and animal models (1–6), showing that noise exposure either early or late in life can induce progressive hearing loss, change neural coding along the auditory pathway, and alter auditory-related perception and behavior.The auditory system, however, contains direct and indirect pathways to other systems and structures of the brain that are necessary for functional integration. For example, earlier studies found that the hippocampus, the core area of the brain associated with learning and memory processes, receives neuronal inputs from the auditory system through the lemniscal and nonlemniscal pathways (7–11). It is thus conceivable that noise-evoked activities might be transmitted via these connections to the hippocampus, thereby affecting learning and memory. Indeed, animal studies have shown that exposure to loud noise (e.g., above a sound pressure level [SPL] of 95 dB) that induces temporary or permanent shifts in the auditory threshold disrupts hippocampal histology, decreases neurogenesis in the hippocampus, and impairs hippocampus-related learning and memory abilities (12–16). In addition, epidemiological studies have demonstrated that environment noise has substantially negative effects on children’s learning outcomes and cognitive abilities (17–19). While the usual explanations for the origins of these noise-induced effects on nonauditory functions have relied on stress-related processes (15, 16, 20–23), the underlying neural mechanisms remain largely unknown.In this study, we exposed rat pups to structured noise delivered at ∼65 dB SPL for a 7-wk period. Exposure to a moderate level of modulated broad-spectrum noise more realistically models the noise environments people encountered in industrial workplaces and other modern acoustic settings (2, 4, 24–26). We then evaluated the behavioral consequences of noise exposure on hippocampus-related learning and memory for these noise-exposed rats. In addition, we explored the mechanisms underlying possible postexposure changes in learning and memory via physiological and molecular assessments of the hippocampus.     

Cadherin cis and trans interactions are mutually cooperative

Cadherin transmembrane proteins are responsible for intercellular adhesion in all biological tissues and modulate tissue morphogenesis, cell motility, force transduction, and macromolecular transport. The protein-mediated adhesions consist of adhesive trans interactions and lateral cis interactions. Although theory suggests cooperativity between cis and trans bonds, direct experimental evidence of such cooperativity has not been demonstrated. Here, the use of superresolution microscopy, in conjunction with intermolecular single-molecule Förster resonance energy transfer, demonstrated the mutual cooperativity of cis and trans interactions. Results further demonstrate the consequent assembly of large intermembrane junctions, using a biomimetic lipid bilayer cell adhesion model. Notably, the presence of cis interactions resulted in a nearly 30-fold increase in trans-binding lifetimes between epithelial-cadherin extracellular domains. In turn, the presence of trans interactions increased the lifetime of cis bonds. Importantly, comparison of trans-binding lifetimes of small and large cadherin clusters suggests that this cooperativity is primarily due to allostery. The direct quantitative demonstration of strong mutual cooperativity between cis and trans interactions at intermembrane adhesions provides insights into the long-standing controversy of how weak cis and trans interactions act in concert to create strong macroscopic cell adhesions.

Cadherin adhesion proteins are essential for the hierarchical organization of all multicellular organisms, and their dysfunction is associated with several pathologies (1–8). For example, deficiencies in cadherin-mediated adhesion are correlated with the onset and metastasis of multiple cancers and tissue diseases (6–8). Cadherin-mediated adhesion involves the formation of adherens junctions (9, 10), which entail interactions between cadherin extracellular domains in cis and trans configurations, where cis interactions occur between proteins on the same cell membrane, and trans interactions occur between proteins on opposing membranes (11–26). Theory suggests that these cis and trans bonds form cooperatively (11–26). For example, cis interactions are believed to enhance molecular ordering (15) and may increase intercellular adhesion through cluster avidity (16, 27, 28), with potential applications related to angiogenesis and therefore cancer therapies (29–31). Early studies suggested that cis interactions enhanced the cadherin adhesive function (16). However, observations of lateral cis interactions between cadherin extracellular domains have been elusive because of their low affinity and the challenges of studying membrane-bound proteins (32–34). Observations of cis interactions in crystal structures and the disruption of cadherin organization within junctions by putative cis mutants suggested that they operate in tandem with trans interactions (15, 35). One hypothesis was that initial trans binding enhances the cis-binding affinity, leading to lateral clustering, junction nucleation, and growth (36). Such trans → cis cooperativity was predicted theoretically but not verified experimentally (37).Recent single-molecule (SM) studies successfully demonstrated that cis interactions induced clustering between cadherin extracellular domains on a supported lipid bilayer (SLB) (38, 39). The latter result suggested that conformational constraints associated with membrane immobilization increased the cis-binding affinity sufficiently to induce clustering, even in the absence of trans interactions. This observation raised the possibility of the reciprocal cooperativity (i.e., cis → trans), in which initial cis binding may enhance adhesion. Although the probability (but not the strength) of trans binding was found to increase for cadherin dimer constructs, relative to the monomer (34), the connection to cis interactions, if any, remains unclear. Demonstrating cis/trans cooperativity would require demonstrating that the presence of cis interactions alters the strength of trans bonds quantitatively and vice versa.In this study, we systematically identified and quantified cis/trans cooperativity, using dynamic SM Förster resonance energy transfer (FRET). These measurements determine whether cis interactions increase trans-binding lifetimes and, conversely, whether trans interactions increase cis-binding lifetimes. They further elucidated the putative role of cis/trans cooperativity in the formation and growth of cadherin junctions between opposing membranes. We find that cis and trans interactions are strongly and mutually cooperative. Most importantly, results show that cis interactions dramatically increase trans-binding lifetimes by more than an order of magnitude, and these cooperative interactions are shown to facilitate the assembly of large junctions. A detailed analysis of trans-binding kinetics as a function of cluster size provide insight into the molecular mechanism of the elevated trans lifetimes. The results presented suggest that specific cis interactions allosterically activate trans-binding interactions.