We demonstrate that contrary to previous assumptions, multiple disordered reconstructions are thermodynamically preferred and kinetically accessible within exposed B surfaces in MgB2 and other layered metal diborides at low boron chemical potentials. Such a dynamic environment and intrinsic disordering of the B surface atoms present new opportunities to realize a diverse set of 2D boron structures. We validated the predicted surface disorder by characterizing exfoliated boron-terminated MgB2 nanosheets. We further discuss application-relevant implications, with a particular view towards understanding the impact of boron surface heterogeneity on hydrogen storage performance.Layered boron compounds have attracted significant interest in applications from energy storage to electronic materials to device applications, owing in part to a diversity of surface properties tied to specific arrangements of boron atoms. Here we report the energy landscape for surface atomic configurations of MgB 2 nanosheets undergo disordering and clustering, which is experimentally confirmed in synthesized MgB2 nanosheets.Layered boron compounds attract enormous interest in applications. This work reports first-principles calculations coupled with global optimization to show that the outer boron surface in MgB As such, these layered materials and closely related borophene sheets, crystalline atomic monolayers of boron, have attracted interest in a wide variety of applications, including hydrogen storage3, superconductivity4, electrocatalysis10, optoelectronics11, and thermal13 and corrosion resistance14. In several of these applications, the specific MB2 surface properties play an outsized role in determining the overall behavior . Recognizing this fact, several recent theoretical studies documented a library of possible two-dimensional boron sheets with differing surface stoichiometries and atomic arrangements generally derived from the parent P6/mmm structure of MgB2, which has a graphitic arrangement of boron atoms18.Materials containing two-dimensional boron sheets, including metal diborides  that the stoichiometric B-terminated (0001) surface of ZrB2, when annealed, exhibited boron aggregation and formation of umbrella-like B7 clusters, suggesting the existence of competing stable surface patterns. Similarly, based on AIMD simulations, Kim et al.27 predicted that the B surface of MgB2 rapidly reconstructs upon adsorption of oxygen at 600 K, eliminating the Eg2 phonon mode coupling to the in-plane electronic states and disabling the high-Tc superconductivity. Reconstruction has also been reported for other two-dimensional boron systems. For instance, Liu et al.18 found by density functional theory (DFT) calculations that a free-standing boron sheet with an equivalent B density as MB2 abandons the hexagonal lattice and undergoes self-amorphization via small perturbations in its initial structure18. This same behavior was observed for a borophene layer coated on silver substrates. Collectively, these studies suggest that the expected extended hexagonal pattern in certain exposed 2D boron sheets may not always be favored depending on the nature of the substrate.There have been some computational studies hinting at potential boron surface reconstruction in layered metal borides. Suehara et al.2 as a model metal diboride, we explore the complex interplay between surface electronic structure and atomic rearrangement to show that, contrary to conventional assumptions, exposed boron surfaces spontaneously and dynamically disorder. Additional electronic structure analysis reveals that the disordering tendency can be attributed to partial charge transfer at the undercoordinated surface, which leads to a frustrated, elemental-like boron state. This predicted disordering is confirmed using a combination of surface-sensitive characterization techniques applied to synthesized MgB2 nanosheets. To illustrate the implications of the surface disordering, we focus on the technological application of MgB2 for hydrogen storage, showing how the introduction of heterogeneity impacts hydrogenation thermodynamics and kinetics. We then apply our insights to define design rules for deliberately prohibiting or creating boron surface disorder by surveying a diverse set of layered metal diborides, thereby enhancing the understanding of boron surface chemistry and expanding the library of possible 2D boron structures.In this work, we revisit the question of surface boron structure by combining DFT calculations with an exhaustive global optimization approach and free energy sampling. Using MgB18 in the context of chemical-vapor deposition synthesis, which corresponds to high relative chemical potential. Here, we are particularly interested in lower boron chemical potentials, in which the surface boron density is constrained to the stoichiometric composition. These conditions are broadly representative of exfoliation processes, as well as reaction conditions such as hydrogenation, for which there is no additional native boron source. We begin with a discussion on the possible ways in which the B atoms can rearrange within a monolayer of surface boron sheet in MgB2  locations on either bridge or hollow sites, ultimately obtaining 135 possible initial patterns for the 2 × 2 slab model. These structures were then relaxed to 16 unique local minima. A detailed schematic of model construction and surface structures of all local minima can be found in Supplementary Note Depending on the boron chemical potential, addition or depletion of surface boron atoms can result in a variety of different patterns. Several of these were previously explored in first-principles calculations reported by Liu et al.surface. It is immediately apparent that patterns with lower energy than the hexagonal arrangement exist, with six such patterns identified from our initial search. We further note that surface clustering.Figure surface from hollow to atop sites along their connective path, forming symmetric ten-membered B rings and exposing two subsurface Mg atoms. LM3 is structurally close to LM2, containing irregular 11-membered-B rings. Because formation of these structures results in broken B−B bonds within the hexagonal sheet, we denote it as a ring-opening process.Top-view structures of the two iso-energetic surface boron patterns with the lowest energy from our initial search  are shown alongside the pristine borophene LM1) in Fig.  in Fig. surface locations becomes impractical. Instead, we created initial structures based on optimized structures extracted from the 2 × 2 slab models, then employed a Basin-Hopping global optimization scheme to access new configurations. Details of the structure-generating procedures and all optimized structures can be found in Supplementary Note surface, achieved by abandoning extended hexagonal ring structures to form larger, asymmetrical rings and clusters. The globally optimized surface boron structure based on the 4 × 4 model, labeled as LM4 in the rightmost panel of Fig. surface lower in energy than the starting hexagonal borophene. In contrast to its conventionally crystalline nature, the borophene appears to be amorphous-like and highly disordered, containing a mixture of irregular 10-, 11-, 14-membered rings with clusters of boron, such as umbrella-like B7, and triangular B6. This behavior is similar to that reported for the annealed borophene monolayer in ZrB2 by Suehara et al.16 where boron atoms cluster and form large ring structures. Moreover, a significant fraction of subsurface Mg atoms originally masked by Bsurface are now exposed as a result of the Bsurface ring-opening process. From the side view in Fig. surface atoms in atop positions (relative to subsurface Mg) rise from the surface.To explore a broader range of configurational space, we next turned to a larger 4 × 4 slab model. Here, a full enumeration of Bmentclass2pt{minimmentclass2pt{minim18. They reported that a boron-enriched MgB2 surface can adopt an ordered boron configuration, which represents the global minimum in the zero-temperature formation energy. Because our calculations in Fig. We point out that the effect of surface composition was previously studied by Liu et al. for a range of boron chemical potentials beyond the stoichiometric composition, as represented by varying the surface boron densitysurface atoms. Multiple episodes of LM2 ↔ LM3 interconversion are detectable even within these short simulation timescales at room temperature, manifesting the highly dynamic nature of the boron surface. Collectively, the results point to a MgB2 surface structure that disorders spontaneously and dynamically under conditions of low boron chemical potential, in sharp contrast to the assumption of a static hexagonal arrangement.Figure 2 can be understood by analyzing the surface electronic properties in detail, as shown in Fig. q) of Mg and B in pristine bulk MgB2 from Bader analysis. The average q of Mg and B are +1.66 and −0.83, respectively, corresponding qualitatively to the expected formal oxidation states of +2 and −1.The surprising dynamical disordering tendency of the boron surface in MgBq in surface and subsurface layers of the lowest-energy 4 × 4 reconfigurations of the boron-terminated MgB2 surfaces. Corresponding values for the unreconstructed MgB2 surface were also included in our analysis. Figure q of the outermost Bsurface atoms within each computed 4 × 4 slab, plotted against q spans a range of >0.1 e across structures, with a minimum of about half of the q in bulk MgB2 for the hexagonal unreconstructed surface , demonstrating the heterogeneous distribution of charge among layers. Bulk-like q is attained by the second sublayer of Mg atoms and the third sublayer of B atoms (see figure caption for details). Strongly negative correlations in q were found between Bsurface atoms and their closest B and Mg sublayers, suggesting the variation in the average q of Bsurface across different surface configurations is mainly due to the surface-dependent charge distribution among these three layers.Figure surface due to substoichiometric coordination with Mg is highly correlated with B−B bond reorganization and energetically favorable surface disordering. It is reasonable to extrapolate this concept to other oxidation scenarios and different surface terminations that may lead to similar behavior. To test this hypothesis, we created another model system to examine direct oxygen attack of a Mg-terminated (0001) MgB2 surface, which mimics the oxygen susceptibility under actual operating conditions. Starting again with a 4 × 4 (0001) slab with four MgB2 layers, we relaxed the structure under the addition of an oxygen monolayer on the Mg surface. Subsurface B atoms have an average q of 0.38, confirming strong oxidation by surface oxygen. Global optimization via Basin-Hopping caused subsurface B atoms to undergo exothermic disordering into irregular rings and clusters very similar to the B-terminated clean surface, thus validating our hypothesis  charge state. This provides a clue for explaining the disordering tendency. Specifically, Ogitsu et al. reported through a global-phase space search that elemental β-rhombohedral boron contains a macroscopic amount of intrinsic defects, leading to a degenerate and disordered ground state29. The authors were able to trace this behavior to geometrical frustration of partially occupied site configurations, which mimic frustrated spin-lattice configurations and are intrinsic to elemental boron. Similarly, Liu et al. found that a free-standing charge-neutral boron sheet in vacuum strongly prefers disordering and forms amorphous-like patterns. In the case of MgB2, we propose that formation of elemental-like surface B due to substoichiometric coordination with Mg drives Bsurface into an electronic state close to elementary frustrated B substance, which introduces a degree of electronic frustration that manifests as spontaneous dynamical disordering.It is worth pointing out that charge depletion of the B layer at the MgBsurface atoms, we synthesized MgB2 nanosheets (NSs) with predominant boron surface termination through mechanical exfoliation using high-energy ball milling, followed by dispersion in acetonitrile and subsequent centrifugation (see “Methods”)30. Using transmission electron microscopy (TEM) and atomic force microscopy (AFM), we determined that the exfoliated MgB2 NSs were flat with lateral dimensions ranging from 100 to 500 nm and thicknesses of ~4 nm  analysis  data of bulk and exfoliated MgB2 NSs  and (002) peaks corresponding to the C-stacking planes of MgB2 is highly diminished, indicating the presence of only a few layers within the crystals 31.To validate the predicted disordering of B nm Fig. . The domNSs Fig. . The exf2 sheets are predominantly B-terminated, we performed low energy ion scattering (LEIS), which can provide an elemental analysis of the outermost surface monolayer32. LEIS measurements of MgB2 NSs pressed into an indium foil suggest a primarily boron-terminated surface, based on two main observations. First, the presence of boron at the surface was confirmed with an ion energy spectrum taken with a 3 keV Ne+ beam in Fig. + into the detector. Second, to interrogate the boron surface coverage, LEIS measurements were taken with a 3 keV He+ beam. These spectra, plotted in Fig. 33, who speculated that these effects might also occur for other light elements strongly bonded to metals. The combination of these two observations demonstrates that boron is present at the surface and likely constitutes a large portion of the surface termination.In order to confirm that the MgB24. In particular, a peak near ~187 eV corresponds to B 2pxy states that are characteristic of the B−B hexagonal ring structure of bulk MgB234. XAS measurements of the exfoliated MgB2 NSs were performed in both TEY  and TFY  modes. As shown in Fig. 2 NSs. The feature at 193.7 eV corresponds to B2O3 (or other substoichiometric boron oxides), which indicates that some limited oxidation is occurring even in these pristine samples. However, the exofliated MgB2 NSs also show small peak-like features between 191.5 and 193 eV, which are not present in the B2O3, and similar features are observed in this range for a powder sample of elemental boron. This is consistent with our theoretical calculations suggesting that B-rich surfaces should feature complex structures with higher B coordination that are closer to neutral oxidation state, similar to those in elemental boron.The native disordering of the boron planes near the surface was probed using X-ray absorption spectroscopy (XAS) measurements, which was previously established as a reliable technique for assessing the intactness of the boron ring structure2 surface layers (based on the LM4 reconstruction). As the surface boron monolayers on MgB2 are predicted to be amorphous with dynamically changing configurations, we propose that XAS is actually probing a geometric ensemble and time average of surface structures. Nonetheless, contrasting the pristine borophene and LM4 surface boron patterns should qualitatively inform the effect of atomic disordering on the spectral line shapes. The results are shown in Fig. xy feature near 187 eV is retained for the pristine surface, indicating intact surface boron rings, the reconstructed surface is indeed missing this feature. The reconstructed surface also exhibits increased spectral weight between 188 and 193 eV, including a small peak near 190 eV and shoulder near 191.5 eV that are reminiscent of similar features between 191.5 and 192.5 eV in the exfoliated MgB2 B K-edge TEY XAS measurements 2, which has among the highest gravimetric hydrogen capacities of any metal hydride at around 14.9 wt.%. However, the MgB2-Mg(BH4)2 hydrogen storage system suffers from sluggish kinetics of hydrogenating MgB2 to Mg(BH4)2, necessitating high temperatures (350−400 °C) in hydrogenation half cycles. Liu et al.34 proposed that the intrinsic stability of the B−B extended hexagonal ring structure hinders the overall hydrogenation kinetics of MgB2 . As such, it is critical to understand which factors can facilitate B−B bond disruption under hydrogen-rich reaction conditions with low boron chemical potential. The current study suggests that such disruption is achievable natively at surfaces due to surface disordering, prompting a more direct investigation into the implications for hydrogenation.The native surface disorder introduces heterogeneity in local surface properties of MgB2 surface, finding an H binding energy of EH binding = −0.68 eV (referenced to H2 gas). To perform a similar analysis on the disordered MgB2 surface, we enumerated all possible bridge boron sites and accessible subsurface hollow Mg sites on the LM4 configuration. Figure H binding. A strong site-dependent heterogeneity is observed, spanning a range from −0.5 to 0.5 eV, as highlighted in the histogram in Fig. For reference, we first computed single atomic H binding to a bridge site on the unreconstructed hexagonal MgB2 dissociation kinetics exhibit a similarly wide range of local intrinsic variability on disordered MgB2. From zero-temperature CI-NEB, the reference surface H2 dissociation barrier onto two neighboring bridge sites of the unreconstructed hexagonal MgB2 surface is found to be 0.52 eV , suggesting that nanostructuring to maximize boron-surface-area-to-volume ratio is beneficial for hydrogenation kinetics of MgB2. The transition state structure, reported in Fig. 2 begins to dissociate, it stays in close contact with both Bsurface and subsurface Mg. The Lewis acid−base pair interaction created by the Mg and B  surfaces36, the resulting atomic H can then diffuse to other nearby favorable binding sites. However, one caveat is the lower density of sites with negative EH binding, which may prevent the disordered surface from attaining a high H coverage . Accordingly, the disordered surface is likely to exhibit a competition between site activity and coverage (site density).As a result, exposure of subsurface Mg upon boron surface disordering introduces a new mechanism for facile H2, we performed a general assessment of surface disordering tendency at stoichiometric surface composition for a diverse set of metal diborides with the P6/mmm space group that have been researched and reported in the literature, with metals ranging from s-metals , first-row transition d-metals , late transition d-metals  and f-elements (U). Notably, Yousaf et al.37 confirmed the feasibility of synthesizing nanosheets for most of these metal diborides through liquid phase dispersion, allowing for future experimental validation of our predictions. For each metal diboride, we simulated the modest surface distortion found for MgB2 shown in Fig. 2 and YB2, which underwent significant spontaneous structural reorganization following initial distortion, as illustrated in Supplementary Fig. E) associated with Bsurface disordering for each metal diboride. The values of ΔE vary significantly across different diborides, spanning both positive and negative regimes.Inspired by our findings for MgB2, MnB2, MgB2, YB2, and FeB2 should all exhibit native surface disordering, with FeB2 showing the strongest reconstruction tendency. In these substances, the average partial charges of Bsurface atoms, particularly in MnB2 and FeB2 , are all less negative than that in MgB2 (−0.42). Beyond the energetic benefits, surface disordering also enhances configurational entropy, which may lead to additional stabilization for diborides that are slightly positive in ΔE. This provides a rationalization for observations of reconstructed ZrB2 by Suehara et al.16. Moreover, the linkage between metal oxidation tendency and surface disordering tendency suggests that disordering could be induced in other diborides by substitutional doping with elements such as Mg, Y, or Fe, or suppressed by doping with Al, Ta, or Nb, etc. It is important to note that the predictions in Fig. 39. Nevertheless, we assert that disordering should be observable within certain ranges of boron chemical potential. In addition, surface atomic rearrangements and amorphization were also observed by Guo et al.40 for boron carbide nanosheets through Raman spectroscopy, suggesting that similar physiochemical phenomena may be relevant for a wider range of nanoscale materials.Overall, we predict that ScB2 and certain related metal diborides. This disordering, which occurs under conditions of lower boron chemical potential, can be linked to the formation of frustrated surfaces that mimic the known complex behavior of elemental boron. The behavior was confirmed in synthesized MgB2 nanosheets, which showed spectral evidence that is consistent with native disordering of the boron hexagonal ring structure. Moreover, this surface atomic reorganization is predicted to be dynamic, suggesting local surface bonding character in fact fluctuates.In conclusion, our results unravel a previously unrecognized spontaneous surface disordering phenomenon of boron surfaces of MgB41; while such an assumption may hold true for some metal diborides, mechanistic interpretations for others can be inaccurate. Moreover, when accurate surface energies are required, as in the prediction of properties of nanosized metal diborides, hexagonal surface models that do not account for stabilization upon disordering may not be sufficiently representative. Likewise, when screening surface activity based on relevant computed descriptors, for instance using H binding energy to an active site to infer its hydrogen evolution reaction activity25, an accurate determination of surface arrangement is prerequisite.One immediate consequence of our findings is that idealized surface models may give a misleading picture of the surface-relevant properties of metal diborides. Computational models generally assume hexagonal B surfaces for such compounds2 was found to expose a new H2 dissociation pathway that leverages Lewis acid−base pair interactions to significantly lower barriers. At the same time, it provides insight into how the stability of boron ring structures may be altered, which has been suggested as a first step towards rupturing the MgB2 lattice and promoting phase transformations during later-stage hydrogenation. This highlights the necessity of considering the surface atomic disordering in interrogation of mechanisms and interpretation of experimental observations, while simultaneously guiding approaches for improvement.In addition, our work points to important practical consequences. Because disordered surfaces exhibit a broader heterogeneity of local properties, this new understanding of the nature of the boron surface also has nonobvious implications for performance. One example lies in the increased richness of hydrogenation chemistry for hydrogen storage applications, for which surface disordering of MgB42, which offer a diverse palette for altering composition. The potential tunability prompts the possibility of engineering boron surfaces of nanoscale and 2D systems with specifically tailored properties—for instance, for use in coatings, composites, electronic materials, or device applications44. Likewise, the diversity of binding configurations due to the presence of surface disorder could be an important tool for realizing multifunctional catalytic applications45.Finally, we point out that the rich structural diversity of patterned borophenes has already generated intense interest due to the variety of potentially tunable properties. We suggest that natively disordered boron surfaces can extend this catalog to include amorphous variants. Indeed, our study points to a possible engineering strategy for generating surface disorder in diborides via substitutional doping of metals with higher primary oxidation states, which opens up a new avenue for exploration of amorphous 2D boron structures with a wider variety of compositions. This is particularly notable in light of recent interest in high-entropy alloys of metal diborides46, using the projector augmented wave treatment of core−valence interactions48 with the Perdew−Burke−Ernzerhof (PBE)49 generalized gradient approximation for the exchange-correlation energy. Initial bulk structures of metal diborides were obtained from the Materials Project50. Enumeration of symmetry-distinct initial configurations was performed using the enumlib code51 wrapped in pymatgen52. Supercell generation was facilitated by the Atomic Simulation Environment (ASE) package53. To model the (0001) boron-terminated surface, we first cleaved bulk MgB2 into a (0001) 2 × 2 stoichiometric slab with four MgB2 layers, each with eight boron and four Mg atoms. Each slab was separated from periodic images by at least 15 Å of vacuum. Such slab separation by vacuum was confirmed to be sufficient by Effective Screening Medium54 calculations implemented in Quantum Espresso55 that showed negligible dipole−dipole interactions of slabs across successive periodic images along the z-direction. The bottom two layers containing Mg surface were fixed, and the top two layers including the boron surface are allowed to fully relax. To further sample the configurational space of boron surface atomic arrangements, we quadrupled the surface size to 4 × 4 to reduce translational symmetry imposed by periodic boundary conditions, maintained the slab thickness, and performed a selection of geometry optimizations and Basin-Hopping global optimizations. For all calculations, the energy cutoff for the plane-wave basis set was set to 500 eV, self-consistent-field electronic energies were converged to 10−4 eV and atomic forces to <0.03 eV/Å. Spin polarization was turned off unless specified, as most materials simulated are nonmagnetic. The Brillouin zone was sampled with a Γ-centered 4 × 4 × 1 k-point mesh for 2 × 2 slab structures, and a Γ-centered 3 × 3 × 1 k-point mesh for 4 × 4 slab structures. We deem such k-point sufficient as test calculations for MgB2 with higher k-point density cause only negligible differences in relative energies across structures with the same lattice. The mesh of k-points was reduced to 2 × 2 × 1 for climbing-image nudged elastic band (CI-NEB)57 calculations for 4 × 4 slabs, but was maintained as 4 × 4 × 1 for 2 × 2 slabs, allowing for direct energetic comparisons. Bader charge analyses were performed using the algorithm developed by Henkelman et al.60. For atomic H binding calculations, binding strength was quantified by referencing to gas phase H2 followingsurface + H, Esurface and EH2 are DFT-computed energies of a surface with an adsorbed atomic H, the adsorbate-free clean surface and H2 in gas phase, respectively.Plane-wave, periodic supercell DFT calculations were performed with the Vienna ab initio simulation package (VASP), version 5.4.4 k-point mesh. The timestep was set to 1 fs, and a Nose−Hoover thermostat was used to maintain the temperature. To quantify the dynamics of boron surfaces, the root mean square displacement (RMSD) of Bsurface atoms in the course of AIMD trajectories were collected after 3 ps of pre-equilibration for each system. To compute the free energy barrier of surface reconstruction at finite temperatures, metadynamics were performed starting with the 2 × 2 pristine slab. Metadynamics is a nonequilibrium molecular dynamics method capable of efficiently sampling free energy surfaces of complex reactions61. As surface reconstruction requires B−B bond breaking of the pristine surface, we selected the coordination number of an arbitrary pair of bonded Bsurface atoms as the collective variable (CV), mathematically defined asdij is the actual distance between B i and j, and do is the reference distance as the boundary of being bonded or not between the two atoms, which was set to 2 Å. A total of 3 ps of AIMD were run to pre-equilibrate the system before bias potentials were introduced. Gaussian potentials with a height of 0.002 eV and a width of 0.02 were then added to the defined CV every 10 fs. Following a previously reported protocol62, we terminated a run of metadynamics simulation after the first barrier crossing from the reactant basin into the target product basin, and computed the free energy barrier by summing up the amount of bias potentials accumulated in the reactant basin. Error bars were computed on the basis of three replicas starting with different initial configurations.NVT ab initio molecular dynamics (AIMD) were performed for 2 × 2 slabs with the energy cutoff for the plane-wave basis set reduced to 400 eV and the Brillouin zone sampled with a Γ-centered 3 × 3 × 1 64, as implemented in ASE, were performed for several 4 × 4 slab structures for which exhaustive configurational sampling was computationally demanding. In each Basin-Hopping step, only selective atoms expected to reconstruct a posteriori were randomly displaced around the initial position following a Gaussian distribution with a variance of 0.15 Å. From there a local structure optimization was performed and the final energy was used to accept or reject this move in the Metropolis Monte Carlo algorithm. The temperature was set to 600 K which allowed systems to temporarily visit high-energy local minima in order to reach other local minima potentially barred by huge “barriers”. As Basin-Hopping requires extensive local optimizations, atomic forces were only converged to 0.20 eV/Å for each step with energy cutoff for the plane-wave basis set reduced to 400 eV, and Brillouin zone sampled at Γ point only. The lowest-energy structures obtained were then re-optimized following higher-accuracy DFT parameters, energy, and force criteria described in the previous section.Global optimizations based on the Basin-Hopping algorithm46. A plane-wave cutoff of 600 eV was used and the k-point sampling was chosen such that the density of k-points was ≥64,000 per Å−3. The XAS/XES simulations were carried out in VASP using an implementation that computes the required matrix elements within the PAW formalism including a self-consistent treatment of the core-hole effects on the unoccupied states65. Spectra were broadened with a 0.25 eV Gaussian.XAS simulations of the B K-edge were performed using first-principles DFT within the the Vienna ab initio simulation package (VASP), version 5.4.4 2 powder  was subjected to solid-state mechanical exfoliation using a high-energy ball mill . The process was carried out in a zirconia (ZrO2) vial using 10-mm diameter ZrO2 balls. Briefly, 0.80 g of MgB2 powder and 20.16 g of ZrO2 balls were weighed in the argon glove box (≤0.1 ppm O2 and H2O) and added to the milling vial to obtain a ball to powder weight ratio of 25:1. The milling vial was closed tightly in the argon glove box and then subjected to HEBM for 4 h. The milled powder was collected in a glove box and stored in a vial. To separate the exfoliated nanosheets (NSs) from the milled powder, we added 90 mL of dry acetonitrile (ACN) to 0.64 g of milled MgB2 powder. We chose ACN as it has a freezing point of −45 °C and a boiling point of 82 °C, which makes it feasible to operate in the lyophilizer in the subsequent synthesis procedure. The suspension (MgB2/ACN) was mixed using a bath ultrasonicator (Cole-Parmer 8891 Ultrasonic cleaner) for 5 min. The obtained dark black uniform mixture was exposed to centrifugation (Eppendorf centrifuge-5430R) at 207.53 × g for 45 min to separate the heavier fraction. The top supernatant was collected and left undisturbed overnight to allow other heavier fractions to settle down. After settling, the top black and clear supernatant was collected, which remains a stable uniform dispersion and exhibits a strong Tyndall effect. The obtained uniform dispersion of MgB2 NSs in ACN was subjected to freeze-drying (lyophilization) to recover the nanosheets in the powder form. The dry MgB2 powder was collected in a vial and stored in a glove box until further analysis. Freeze-drying (lyophilization) was performed by taking the dispersion of MgB2 NSs in ACN (70 mL) in two 50-mL centrifuge tubes and freezing them at −80 °C overnight. The frozen samples were subsequently placed in a lyophilizer  for up to 72 h to obtain a powder of MgB2 NSs.MgBα radiation, with a CCD detector at 77 mm from the samples and an exposure time of 66 s. The recorded 2D diffraction images were integrated to produce a 1D diffraction spectrum. The powder samples were packed in 0.7- or 0.5-mm diameter glass capillaries sealed with silicone grease under argon.Powder X-ray diffraction measurements were recorded on an Oxford Diffraction Supernova in capillary mode using Cu K2 nanosheet powder and dispersing it in 10 mL of dry toluene, to prevent excessive agglomeration of the nanosheets, using a bath ultrasonicator for 5 min. Two drops (20 μL) of the dispersion were drop casted on a 300 mesh copper TEM grid coated with a lacey carbon film. The grid was air-dried for a few minutes and stored in a vial until analysis.TEM and energy-dispersive X-ray spectroscopy (EDS) were recorded on a Thermo Fisher Titan Themis Z TEM operated at 300 kV. Samples for TEM analysis were prepared by taking a small amount of MgB2 NSs dispersion (~20 μL) on a cleaned and UV Ozone treated Si/SiO2 substrate and spin-coated at a speed of 3000 rpm for 30 s at 100 ramp rate. The coated substrate was kept in a box and stored under an argon environment until analysis.AFM images were acquired with a Dimension ICON (Bruker) contained in an argon glove box. The AFM was operated in Peak-Force Tapping mode with a nominal tapping force of 1 nN. The tip used was a PFQNE-AL (Bruker) with spring constant of 0.84 nN/nm. Samples for AFM analysis were prepared by static dispensing of the MgB2 nanosheets was investigated with LEIS and DRS. These measurements were performed with an angle-resolved ion energy spectrometer (ARIES), which has been described in detail in previous works67. LEIS and DRS are complementary techniques, performed simultaneously, with sensitivity to the masses of atoms in the outermost monolayers of a surface. LEIS and DRS are performed by directing a low energy ion beam (He+ and Ne+ for this work) at a grazing angle α onto the target surface. An electrostatic analyzer (ESA) is positioned in the forward scattering direction at a chosen scattering angle θ to detect the energies of scattered incident ions and recoiled target ions to perform LEIS and DRS, respectively. From the energies of the detected ions and the scattering angle θ, the mass of surface atoms can be calculated, yielding insight into the surface composition. One key consideration is that the ESA detects only scattered and recoiled ions; incident ions neutralized by the surface, as well as recoiled neutral atoms, are not detected. As such, neutralization effects can play a substantial role in the obtained ion energy spectra.The surface termination of the MgB2O3 standard. Samples were transferred into the beamlines using vacuum suitcases (ALS) or a glove bag (CLS) to minimize exposure to atmospheric oxygen and moisture. The operating pressure of the endstations is better than 1 × 10−9 Torr.XAS measurements of boron K-edge were acquired at beamlines 7.3.1 and 8.0.1.4 at the Advanced Light Source (ALS), Lawrence Berkley National Laboratory (LBNL) and the REIXS beamline of the Canadian Light Source (CLS). Data were simultaneously collected in surface-sensitive total electron yield (TEY) measured as the drainage current from the sample and bulk-sensitive fluorescence yield (FY) measured using a channeltron electron multiplier. Spectra were normalized by dividing by incident beam intensity, which is monitored by drainage current from a gold grid located in the path of the X-ray beam immediately before the measurement chamber. A linear background was subtracted, and the absorption edge step was scaled to 1, taking the difference between pre-edge (<180 eV) and post-edge (>215 eV). The energy shift between different beamlines was calibrated using the primary peak of a BSupplementary InformationPeer Review File


Ploidy manipulation is effective in seedless loquat breeding, in which flesh color is a key agronomic and economic trait. Few techniques are currently available for detecting the genotypes of polyploids in plants, but this ability is essential for most genetic research and molecular breeding.2 = 0.9992) with parameter b [b = a1/(a1 + a2)], which is derived from the two normalized allele signals (a1 and a2) provided by qPCR. Cluster analysis and variance analysis from simulating triploid and tetraploid hybrids provided completely correct allelic configurations. Four genotypes  were found in triploid loquats, and four  were found in tetraploid loquats. DNA markers analysis showed that the segregation of flesh color in all F1 hybrids conformed to Mendel's law. When tetraploid B431 was the female parent, more white-fleshed triploids occurred among the progeny.We developed a system for genotyping by quantitative PCR (qPCR) that allowed flesh color genotyping in multiple tetraploid and triploid loquat varieties (lines). The analysis of 13 different ratios of DNA mixtures between two homozygous diploids (AA and aa) showed that the proportion of allele A has a high correlation (RqPCR can detect the flesh color genotypes of loquat polyploids and provides an alternative method for analyzing polyploid genotype and breeding, dose effects and allele-specific expression.The online version contains supplementary material available at 10.1186/s13007-021-00792-9. Polyploidization is an important driving force in the evolution of eukaryotes . AncientEriobotrya japonica (Thunb.) Lindl.) is a subtropical evergreen fruit tree with good flavor and rich nutritional value that is widely cultivated worldwide  and parameter b [b = a2/(a1 + a2)]. The correlation coefficient (R2) between the proportion of allele A and the θ angle was 0.9970, and that for parameter b was 0.9992, proving that the proportion of allele A showed a high correlation with the relative dose of allele A. These data indicate that the system can be used to determine the flesh color genotypes of polyploid loquats. Because the correlation coefficient of parameter b was higher, parameter b was used in subsequent experiments.The reference sequence was CH03g12, which presented stable qPCR results in loquat genomes of different ploidies  in the simulated triploid and tetraploid populations were performed Fig. . The simDiploid loquat was used for the verification of the qPCR genotyping system, and the results showed that the system could accurately determine the flesh color genotype. For the red-fleshed homozygotes (AA), parameter b was 1.31 ± 0.0585; for the red-fleshed heterozygotes (Aa), parameter b was 0.60 ± 0.0464; and for the white-fleshed homozygotes (aa), parameter b was 0.00 ± 0.0012. These results tended toward the expected values  and proved the accuracy and stability of qPCR genotyping system  included the DY lines, ‘JH1’ and H30-6, while the triploid line was B356, and the tetraploid lines were B431, B432, B433, B456, and B479. These lines (varieties) were all heterozygote except for ‘LQ1’, ‘DY2’ and ‘DY3’, which were AA homozygotes, indicating that these varieties (lines) received pollen carrying the white-fleshed recessive allele a when they were receptive to pollination. ‘SW’  and SW_3x , ‘XZ’  and XZ_3x , B356  and B456 , and K374  and K474  were generated from the same material, and the only difference between them was the difference in ploidy. The genotyping results showed that the proportion of allele A increased with increasing ploidy, which may be an important factor contributing to the difficulty of obtaining white-fleshed tetraploid materials.1 true hybrids was identified by using flow cytometry. The results showed that the hybrid ploidy was mainly the intermediate to the ploidies of the parents , but there were multiple types of ploidy variation  and B456 (AAaa) was only slightly different, but the parameter b results could be clearly divided into two types , and 27 red-/white-fleshed diploid loquat lines (varieties) were collected from the Loquat Germplasm Garden Table . The par1 hybrids were collected and brought back to the laboratory, where they were stored in the refrigerator at − 80 °C. The genomic DNA (gDNA) extraction method referred to Wen Guo's improved CTAB method  of each simulated sample were calculated. The genotypes of materials with different ploidies and different relative copy numbers were calculated as follows:The relative copy numbers of the target gene were calculated according to the 2−1(a2/a1); 0º ≤ θ ≤ 90º] of each simulated sample was also calculated for analysis.The theta angle [θ = tanThe diploid loquats were genotyped by qPCR, and the results were calibrated with the results of the color-specific molecular marker analyses to verify the effectiveness of the qPCR genotyping system. The triploid and tetraploid loquats were genotyped by qPCR, and the flesh color genotypes of the triploid and tetraploid loquats were determined. A flow diagram of the experimental operation is illustrated in Fig. 1 hybrids were identified by hybrid identification, ploidy identification, and flesh color-specific marker analysis; the segregation ratios of red-fleshed and white-fleshed loquats were calculated; and the inheritance of tetraploid flesh color was explored. SSR markers were used to identify true and false hybrids. The SSR markers were derived from loquat genome data .The ploidy of hybrids was identified by flow cytometry . Fresh yAdditional file 1:Fig. S1. Schematic diagram of qPCR genotyping primer positions.Additional file 2: Fig. S2. The qPCR amplification curves and melting curve for Cho3g12, q2A, q2A/2Ad.Additional file 3:Fig. S3. Map of EjPSY2Ad chromosome localization and different tetraploid heterozygous genotypes.Additional file 4:Table S1. Primer of flesh color specific molecular marker and qPCR genotyping. Table S2. SSR marker sequence for hybrid identification.


The strong Coulombinteraction in monolayer semiconductors representsa unique opportunity for the realization of Wigner crystals withoutexternal magnetic fields. In this work, we predict that the formationof monolayer Wigner crystals can be detected by their terahertz responsespectrum, which exhibits a characteristic sequence of internal opticaltransitions. We apply the density matrix formalism to derive the internalquantum structure and the optical conductivity of the Wigner crystaland to microscopically analyze the multipeak shape of the obtainedterahertz spectrum. Moreover, we predict a characteristic shift ofthe peak position as a function of charge density for different atomicallythin materials and show how our results can be generalized to an arbitrarytwo-dimensional system. Ever since their prediction,the experimental realization of these Wigner crystals (WCs) has remainedchallenging, considering that the prerequisite of a dominating Coulombversus kinetic energy requires very low temperatures and charge densities.Therefore, the first realizations of WCs4 have used strong magneticfields and quasi two-dimensional (2D) quantum well systems in orderto quench the kinetic energy via Landau quantization. The advancesin the research on transition-metal dichalcogenide (TMD) monolayers7 have delivered new opportunities to realize electron crystallization.Several recent studies12 have reported insulating states at fractional fillings of flat moirébands,15 which arise in the superlattices of twisted homobilayerand heterobilayer systems. However, similar to the application ofmagnetic fields, these so-called generalized Wigner crystals heavilyrely on the external moiré potential stabilizing the latticestructure and can therefore not be considered as intrinsic electronicphases.At low temperatures, electronsarrange in a crystal lattice17 Smoleński et al. haverecently demonstrated signatures of a WC formed in hBN-encapsulatedMoSe2 monolayers18 at electrondensities of up to n = 3 × 1011 cm–2 without any external fields. As an indicator forthe crystallization, the authors have used the emergence of an additionalpeak in the reflectance spectrum at visible frequencies. This peakstems from excitons with finite center-of-mass momentum that coupleto the light cone via Bragg scattering at the WC. Other rather indirectconfirmations of the WC, such as a decrease in the conductivity, alsohave been applied to verify other WC systems.12 However, a direct, more reliable and conclusive experimental proofof the WC, such as a direct spectral signature of the internal structureof the crystal, could not be provided so far.In contrast, TMDs in their monolayer form already representa uniqueplatform to achieve electron crystallization, as they exhibit largeeffective masses and a strong Coulomb interaction leading to prominentexciton physics.In this work,we propose to exploit terahertz radiation to directlyprobe the internal quantum transitions of the WC in TMD monolayers,as illustrated in 2 monolayers without any open parameters and explain the characteristicresponse shape with the help of our microscopic model. We predictthat the central energy of the internal quantum resonances shiftsfrom ∼4 meV at 109 cm–2 to 24meV at 8 × 1010 cm–2. Moreover,we demonstrate that an enhanced effective mass and reduced dielectricscreening, such as in MoSe2 on SiO2, can pushthe WC resonances up to 100 meV. Finally, we also present a unitlessstudy for ideal 2D systems, which can be rescaled to arbitrary fermionicsystems.We predict the emergence of a series of terahertz resonanceswhoseposition is a function of electron density and its characteristicpeak sequence can be explained by the nature of the involved excitedquantum states. Consequently, the predicted low frequency responsecan be used as a direct probe of the Wigner crystallization in arbitrary2D systems of interacting fermions. We apply our microscopic modelto determine the material realistic response of hBN-encapsulated WSe19 have demonstrated that the low-density crystal phase is characterizedby small correlation energies and that the WCs properties are well-reproducedwithin a Hartree–Fock description of the Coulomb interaction.20 To obtain access to the optical response ofthe WC, we start with the Hamilton operator of interacting electrons,n(p)-doped TMD monolayers,such that akσ(†) creates/annihilateselectrons (holes) in the lowest conduction band with spin up at the K point (σ = ↑) or spin down at the −K point (σ = ↓) and momentum k. For low temperatureand densities, the electron dispersion εk is determined by an effective mass m*.21 The Coulomb interaction is treatedin a mean field approximation22 via the nonlocal Hartree–Fockpotential,Vq, which includes the dielectric environment of the TMD monolayerthrough the Rytova–Keldysh potential.24 Moreover, the mean field potential also is dependent on the chargedistribution entering via the Fourier transform of the Wigner distribution wkσ(q) = ⟨ak+qσ†akσ⟩. The Hamiltonian in Akλσ† =∑Gukσλ*(G)ak+Gσ,†, where we sum over the reciprocal lattice vectors G of the WC. Here, ukσλ(G) is the complete setof Bloch functions fulfilling the periodic Hartree–Fock equation(see the Supporting Information (SI)).The latter is solved iteratively until a self-consistent solutionis found, starting with a randomized charge distribution. Hence, inthe new basis describing WC electrons the Hamiltonian readsfkλσ = ⟨Akλσ†Akλσ⟩ = δλ0.Previous numerical studieson WCs based on quantum Monte Carlo methodsEkσλ and their wave functions ukσλ(G), we can transformthe electron-light interaction into the Wigner basis and compute thedynamics of the WC using the Heisenberg’s equation of motion.26 In particular, assuming a weak perturbation through the electromagneticfield, we can derive the linear response of the system, which, e.g.,can be specified via the diagonal components of the linear opticalconductivity tensor reading:d,27 the normalizationarea A, and a phenomenological dephasing constantΓ. Theoscillator strength of transitions between different WC sub-bandswith energy ΔEkσλ = Ekσλ – Ekσ0 for ê-polarizedlight is given by the current matrix element Jkσλ=e0ℏ/m*∑Gukσλ*(G)G·êukσ0(G). All details of the derivation and the used parametersare given in the SI. The microscopic modeldescribed above is not specific to TMD monolayers and can be appliedto arbitrary 2D electron system. In principle, a similar approachcan be used to compute the optical response also in generalized WCswithin twisted bilayers.Having determined theenergy spectrum of WC electrons p-doped,hBN-encapsulated WSe2 monolayers at a density of n ≈ 3 × 1010 cm–2 (rs = 50), i.e., deep within the crystallinephase that was predicted to melt at rs = 30–40.30 The temperature is assumed low enough such that onlythe lowest band of the WC is occupied and the thermal occupation ofthe excited states can be neglected. Moreover, we focus on the spin-unpolarized(antiferromagnetic) phase, since we assume that the charge densityis controlled via an electrostatic gate. As a result, the Wigner crystalis in a chemical equilibrium with an unpolarized charge reservoir.Apart from the WC geometry, the main conclusions qualitatively alsohold for spin -polarized systems.31↑ (on a cut through the WCs Brillouin zone) as well as the wave functionsof the monolayer WC. The band structure is illustrated in Now, we apply thedeveloped model to the exemplary system of 32 with alternating spin polarization (red andblue projections). Moreover, the localized charge distributions exhibita significant triangular warping, which is usually neglected in variationalapproaches.The fully occupied ground stateis, in fact, the WC itself, i.e.,the corresponding wave functions are eigenstates of the Coulomb potentialcreated by their own collective charge distribution. Here, the chargedensity 2bexhibiSI). k = 0, whereas the contoursindicate the peaks of the ↑ (red) and ↓ charge density (blue) from 15 Consequently,the localized orbitals of higher-order bands begin to overlap at higherquantum indices and we find dispersed bands at high energies correspondingto scattering states. 34 the so-called pinning frequency.35 Incontrast, our microscopic model predicts that zero-field monolayerWigner crystals should exhibit an entire series of resonances at muchlarger frequencies.In contrast to the self-consistent ground state,the excited statesare unoccupied and therefore do not contribute to the nonlocal Hartree–Fockpotential  beginsto move toward large G vectors, corresponding to scatteringstates with a large kinetic energy. Consequently, the momentum spaceoverlap determining Jkσλ shrinks.Now, we evaluate the linearoptical conductivity from –1 cm–1, corresponds to a rather low overall absorbanceof the monolayer in the range of α = dRe(σ)/(cϵ0) ≈ 10–4, whichis due to the nanometer thickness of the sample. However, comparablyweak low-frequency responses stemming from intraexcitonic transitionshave already been used to measure time-resolved exciton dynamics inTMD monolayers.36The calculated conductivity, onthe order of 10 Ωpeak =∫ωσ(ω)dω/∫σ(ω)dω,where the integrals are only performed over positive frequencies. rs = 30, such that for higher densitiesquantum melting of the WC is expected. For all three illustrated systemswe consider p-doping, since the valence band in TMDs has a significantlylarger mass then the conduction band, which enables larger criticaldensities before quantum melting sets in. 2 are significantly larger, since the Coulombinteraction is much less screened by the substrate. In addition tothe spectral shift of the center energy, the amplitude of the opticalresponse also increases with growing densities, since the densityof optically active particles is enhanced.Now, we vary the charge densityand investigate how the spectral response shifts as the lattice parameterof the WC, Vq ∝1/q, which reproduces the results forTMD monolayers at small densities. For an ideal 2D system, the onlyrelevant system parameter is given by aB = 4πϵ0ϵℏ2/(m*e02). Using this density scale, the energies can be given in terms ofeffective Hartree EH=ℏ2/(m*aB2), such that the results given in the inset of E ≈ Epeak – Egap also grows withincreasing density, since the distance between excited states becomeslarger.We have additionally performed calculations for an ideal 2D systemwith 32 Moreover, we want to emphasize that the applied model is only validfor weak excitation conditions, i.e., assuming a negligible populationof the excited states. A lower bound for the critical power densityof the exciting laser can be obtained by estimating a lower boundfor the lifetime of excited states. Assuming that the lifetime isshorter than τ = 1 ns, the weak excitation regime can be specifiedby a power density of I ≪ n(E1 – E0)/τ, which for the systems studied in I ≪ 50 mW/cm2. For stronger excitationpowers, we expect optical nonlinearities to occur that could evenresult in a destruction of the WC.Finally, we want to note that the susceptibility derivedin ourwork results from an oscillating polarization current as a responseto the electromagnetic field. Since the oscillating electrons (holes)are forming the WC crystal itself, the optical resonances found inour work could be interpreted in a classical picture as the excitationof long-range phonon modes of the WC.In conclusion, our studydemonstrates that the terahertz responseof monolayer Wigner crystals can be used as an unambiguous fingerprint,exhibiting a characteristic sequence of internal quantum transitions.The inherent spectral shift of resonance frequencies with the chargedensity further represents a strong benchmark for the crystallization.We have predicted the peak positions for different TMD monolayers,as well as other 2D fermion systems. The presented results will guidefuture experiments toward the detection of Wigner crystallizationand the developed approach can be further exploited to theoreticallystudy the interaction dynamics in pure as well as generalized Wignercrystals in twisted bilayers.


Multivariate analysis identified “age > 65 years” , “STR” , “unmethylated MGMT status” , and “perioperative RBC transfusion”  as significantly and independently associated with 1-year mortality. Perioperative RBC transfusion compromises survival in patients with glioblastoma indicating the need to minimize the use of transfusions at the time of surgery. Obeying evidence-based transfusion guidelines provides an opportunity to reduce transfusion rates in this population with a potentially positive effect on survival.The influence of perioperative red blood cell (RBC) transfusion on prognosis of glioblastoma patients continues to be inconclusive. The aim of the present study was to evaluate the association between perioperative blood transfusion (PBT) and overall survival (OS) in patients with newly diagnosed glioblastoma. Between 2013 and 2018, 240 patients with newly diagnosed glioblastoma underwent surgical resection of intracerebral mass lesion at the authors’ institution. PBT was defined as the transfusion of RBC within 5 days from the day of surgery. The impact of PBT on overall survival was assessed using Kaplan–Meier analysis and multivariate regression analysis. Seventeen out of 240 patients (7%) with newly diagnosed glioblastoma received PBT. The overall median number of blood units transfused was 2 (95% CI 1–6). Patients who received PBT achieved a poorer median OS compared to patients without PBT (7 versus 18 months; The online version contains supplementary material available at 10.1007/s10143-021-01633-y. Perioperative anemia requires the transfusion of red blood cells (RBC) after reaching an individual threshold value, which often varies considerably for interhospital comparison. Due to the manifold effects of perioperative blood transfusion (PBT) on morbidity and mortality, opinions differ on the effect of PBT on the overall survival (OS) of cancer patients. Some studies reported an association between PBT and poorer OS, while others could not demonstrate this association , 15, 24.Especially in the context of (semi-)elective intracranial surgical procedures, current efforts in patient blood management are aimed at raising the thresholds for transfusions while maintaining patient safety, leading to a controversy between restrictive and liberal transfusion strategies . PeriopeIn the present study, we aimed at assessing a potential correlation of PBT and further pre- and intraoperatively collectable variables with impaired functional outcome and worsened overall survival in patients that had undergone neurosurgical resection of newly diagnosed glioblastoma at our institution.Newly diagnosed glioblastoma patients who underwent surgical resection at the authors’ institution between 2013 and 2018 were entered into a computerized database. Only those patients with completely available preclinical, histopathological, and perioperative data were included in further analysis. The approval for this study was obtained from the institutional ethics committee. Information, including patient characteristics, radiological features, methylation status of the MGMT promoter, age-adjusted Charlson Comorbidity Index (CCI), functional neurological status and laboratory values at admission and during treatment, and the need for peri- and/or intraoperative blood transfusion, were collected and further analyzed. MGMT promotor methylation status was determined by the local department of neuropathology by pyrosequencing as published in 2007 . The KarDuring the weekly interdisciplinary tumor advisory board meetings of the neuro-oncological center, individual treatment decisions were made in interdisciplinary consensus at the initial presentation of the patient and during follow-up.The extent of resection (EOR) was evaluated in early (< 72 h) postoperative 3-T magnetic resonance imaging (MRI). Gross total resection (GTR) was defined as the complete removal of contrast-enhancing tissue. Preoperative tumor volumes volumetrically were assessed based on gadolinium-enhanced T1-weighted MRI using commercially available software . In accordance to Flores et al. , a cutofPerioperative blood transfusions were determined as any allogeneic transfusion of red blood cells (RBC) during or within 5 days after surgery for glioblastoma. The threshold values for RBC transfusions in clinically stable patients were specified at a hemoglobin (Hb) concentration of < 7 g/dL, following the current consensus recommendations of patient blood management .Overall survival (OS) was measured from the day of glioblastoma surgery until death or last observation. All parameters were compared in terms of OS.U-test was chosen to compare continuous variables as data were not normally distributed. OS was analyzed using the Kaplan–Meier method and Gehan-Breslow-Wilcoxon test. Results with p < 0.05 were considered statistically significant. Furthermore, a backward stepwise method was used to construct a multivariate logistic regression model in order to find independent predictors of 1-year mortality in patients with glioblastoma who underwent surgical resection.Data analysis was performed using the computer software packages SPSS  and GraphPad Prism . Unpaired categorical and binary variables were analyzed in contingency tables using the Fisher exact test. The Mann–Whitney Between 2013 and 2018, a total of 240 patients with newly diagnosed glioblastoma underwent surgery at the authors’ institution. Mean age of patients with glioblastoma was 62 ± 13 years. Regarding EOR, GTR was achieved in 164 patients (68%), while subtotal resection (STR) was achieved in 76 patients (32%). Twelve patients suffered from multifocal manifestation at time of surgery (5%). Median OS for patients with glioblastoma in the current patient cohort was 16 months (95% CI 14–18)  . Patients with the necessity of PBT suffered from significantly increased intraoperative blood loss (mean 900 ± 616 mL) compared to patients without PBT . Nevertheless, admission Hb concentration did not differ between both groups (p = 0.24). Median blood loss in patients with preoperative anticoagulant medication was 200 mL (IQR 100–305) compared to 200 mL (IQR 100–390) in patients without preoperative anticoagulant medication (p = 0.75). Preoperative intake of anticoagulant medication did not significantly correlate to the extent of PBT: 5 out of 17 patients (29%) with PBT exhibited preoperative anticoagulant intake compared to 33 out of 223 patients (15%) without need for perioperative PBT (p = 0.16). Table Overall, 17 patients required PBT (7%). The overall median unit of blood transfused was 2 units (95% CI 1–6). Of 17 patients, 2 received 1 unit (12%), 9 received 2 units (53%), and 6 received more than 2 units (35%). The mean age of patients who received PBT was 71 ± 10 years at the time of surgery. Therefore, patients with PBT were significantly older compared to patients without PBT (p < 0.001). The PBT group significantly more often suffered from postoperative LAE and pneumonia: 2 out of 17 patients (12%) within the PBT group suffered from pulmonary embolism during the postoperative hospital stay compared to 3 out of 223 patients (1%) within the non-PBT group (p = 0.04). Four out of 17 patients (24%) within the PBT group suffered from pneumonia during the postoperative hospital stay compared to 7 out of 223 patients (3%) within the non-PBT group (p = 0.004). Postoperative intensified treatment did not significantly differ for the PBT and the non-PBT group: 1 out of 17 patients (6%) with PBT received postoperative treatment according to the CeTeG protocol compared to 16 out of 207 patients (8%) without PBT (p = 1.0). TTF treatment was present in 0 out of 17 patients (0%) with PBT compared to 9 out of 214 patients (4%) without PBT (p = 1.0). For detailed information regarding the PBT group, see Supplementary Table Median tumor volume was 35 mL (IQR 12–72). The receiver operating characteristics (ROC) curve resulted in an area-under-the-curve value of 67.9 mL. Based on equal weighting of sensitivity and specificity, the cutoff of 125 mL was found to be the most efficient to separate between the two PBT groups. This cutoff leads to a sensitivity of 50.0% and a specificity of 94.3%. Eight out of 17 patients (47%) with PBT exhibited a tumor volume of ≥ 125 mL compared to 10 out of 223 patients (4%) without PBT , 6 months , and 12 months  postoperatively . Figure p = 0.01).Overall survival in patients who received PBT was 7 months (95% CI 3–11). In patients who received PBT, median overall survival was significantly reduced compared to those who did not receive PBT , “STR” , “unmethylated MGMT status” , and “perioperative RBC transfusion”  as significantly and independently associated with 1-year mortality, whereas tumor volume did not in patients who had undergone glioblastoma surgery (Nagelkerke’s R2 0.37).Multivariate analysis identified “age > 65 years” elective character of these procedures. This may require transfusion of allogeneic red blood cells to maintain tissue perfusion and oxygen supply. Increasingly, it has been stated in the literature that perioperative transfusion of RBCs might lead to a reduced overall survival for different types of cancer , 12, 23.Transfusion-related immunomodulation (TRIM) is considered to be the leading factor for poor oncological outcomes related to transfusion . VariousBesides eventual immunomodulatory aspects, the necessity of PBT should also consider the patient’s pre-existing comorbidity burden as well as the complexity and expected amount of blood loss within the procedure. Furthermore, elevated tumor volumes have been reported to correlate to higher intraoperative blood loss , 20 whicNevertheless, the influence of perioperative RBC transfusion on the postoperative neurological outcome and overall survival has been evaluated as independent of potential confounding factors in the present multivariate analysis. While to the best of our knowledge this effect has now been demonstrated for the first time in glioblastoma patients, it is consistent with results from similar studies in other cancer entities , 12, 23.The present study has several limitations. Data collection was conducted retrospectively and reflects only the experience of one center. Therefore, an additional risk arises in this selected, retrospectively evaluated patient group in order to underestimate the influence of either the patient’s comorbidity, the severity of the disease, the complexity of the surgery, different postoperative treatment modalities, or the cumulative blood loss in relation to the observed results. Nevertheless, the present study provides a first-time description of a potential association of perioperative RBC transfusion with outcome and survival in patients with glioblastoma and should spark the demand for larger, multicenter studies.The present study indicates perioperative RBC transfusion to adversely affect functional neurological outcome and overall survival in patients with glioblastoma. Further studies will be needed in order to corroborate a potential need to seek options to reduce transfusion use at the time of surgery. Following evidence-based transfusion guidelines might offer an opportunity to minimize transfusion rates, which could have a positive impact on outcome and overall survival in glioblastoma patients.Supplementary file1 (DOCX 20 KB)Below is the link to the electronic supplementary material.


The nanosheets are initially forced to adopt a monodomain cofacial geometry with a large and uniform plane-to-plane distance of ~420 nm, where they are strongly correlated by competitive electrostatic repulsion and van der Waals attraction. When the electrostatic repulsion is progressively attenuated by the addition of ionic species, the nanosheets sequentially undergo coherent motions, generating a propagating wave. This elaborate wave in time and space can transport microparticles over a long distance in uniform direction and velocity. The present discovery may provide a general principle for the design of macroscopically movable devices from huge numbers of tiny components.Just like in living organisms, if precise coherent operation of tiny movable components is possible, one may generate a macroscopic mechanical motion. Here we report that ~10 Tiny movable components could generate macroscopic mechanical motion if precise coherent operation can be exerted simultaneously. Here, the authors demonstrate this by using 10^10 pieces of colloidally dispersed nanosheets to generate wave under non-equilibrium state. For such coherent operation to occur in living organisms, a large number of movable components are positioned in a spatially specific manner so that they can cooperate with each other for large-scale synchronization. Inspired by biological coherent systems, several pioneering attempts have been made to conjugate multiple synthetic movable units for the creation of a mechanical motion26. A straightforward approach is to connect them with chemical or topological bonds12, but the number of connectable units is practically limited, so that individual motions cannot be amplified into a macroscopic motion. To overcome this issue, we employed competitive repulsive and attractive forces between the movable components for strongly correlating them over a long range. We succeeded in correlating ~1010 individual pieces of colloidal nanosheets dispersed in water to form a uniformly separated (~420 nm) cofacial assembly via their competitive electrostatic repulsion and van der Waals attraction. When the electrostatic force is progressively attenuated by the addition of ionic species, we found that the nanosheets sequentially undergo coherent motions, generating an autonomously propagating wave  and extra-wide (~5 µm) dimensions  and therefore can be colloidally stable in aqueous media. As described by the Derjaguin–Landau–Verwey–Overbeek (DLVO) theory37, colloidally dispersed TiNSs are correlated with each other by electrostatic repulsion in competition with van der Waals attraction, so that they adopt a cofacial geometry with a large and uniform distance. As previously reported37, the interaction between TiNSs can be highly strengthened by thorough deionization of a TiNS dispersion. In a 10 T magnetic field, colloidally dispersed TiNSs ([TiNS] = 0.5 wt%) align perpendicular to the magnetic flux lines, thereby forming a monodomain structure with a long-range geometrical integrity  as the source for ions , because it could gradually penetrate from a slightly opened screw cap into the cuvette interior without mechanical deterioration of the TiNS orientation. As shown in Fig. −1 (Supplementary Movie −2). As expected, when the cuvette was placed in a N2-filled container, no wave was detected and the monodomain assembly was maintained for >20 h  and (v) (z = 0.8–1.0 mm) appear to be bright, because TiNSs located in these regions are oriented parallel to the xy-plane due to the surface anchoring effect of the cuvette. Meanwhile, in regions (ii)–(iv) (z = 0.2–0.8 mm), thin bright layers appear periodically along the x-axis, which correspond to the peak and trough regions of the wave  of TiNSs are governed to be synchronous by a single rule, both in time and space, to generate a macroscopic motion under the present experimental conditions .We successfully confirmed the wave structure of TiNSs by fixing their spatial orientation using two-stage in-situ polymerization of an acrylic monomer and a silica source. As shown in Fig. xis Fig. . Polarizxis Fig. . By a POave Fig. , right. ave Fig.  and timeave Fig.  show tha2 is allowed to penetrate from the slightly opened screw cap inlet into the interior of the cuvette, ions such as HCO3−, CO32−, and H3O+ are produced in the aqueous TiNS dispersion, generating an ion gradient that progressively attenuates the electrostatic repulsion between TiNSs37. Consequently, the van der Waals attraction between TiNSs prevails, thereby reducing the TiNS distance  the cofacial TiNS assembly must adopt a monodomain with a single crystal-like structural integrity and (2) constituent TiNSs must be strongly correlated with each other. In fact, no wave was detected without prior magnetic orientation of TiNSs into the monodomain geometry  to the monodomain structure of TiNSs  and conducted combined reflection/fluorescence CLSM monitoring. As shown in Fig. 2 and CO2H groups or not  from each other but strongly correlated due to competitive electrostatic repulsion and van der Waals attraction. We are sure that our finding may provide a general principle for the design of macroscopically movable devices from huge numbers of tiny componentshttp://imagej.nih.gov/ij/) was used. An aqueous dispersions of unilamellar titanate(IV) nanosheets  were purchased (Micromod Partikeltechnologie GmbH) and used after deionization.A Hitachi model CF16RXII centrifuge with a Hitachi model T15A41 rotor was used for the deionization of TiNS dispersions. A JASTEC model JMTD-10T100 superconducting magnet with a vertical bore of 100 mm was used for magnetic orientation of TiNSs. Optical microscopy was performed on a KEYENCE model VHX-5000 digital microscope. SEM was performed on a Hitachi model SU8010 field-emission SEM. POM was performed on a Nikon model Eclipse LV100POL optical polarizing microscope. CLSM was performed on a Leica TCS SP8 confocal microscope system. Reflection spectra were recorded on a microscopic visible/near infrared (Vis/NIR) spectrometer composed of a Nikon model Eclipse LV100POL optical polarizing microscope equipped with an Ocean Optics model USB4000 spectrometer. For retardation measurement, an Olympus model U-CBE Berek compensator and an Olympus 43IF550W45 interference green filter (550 nm) was used. For DLS measurement, a Hamamatsu model H7421-40 photon counting head was used for detecting the scattered light at various scattering angles and an LS Instruments model LSI correlator for processing the signal pulses to obtain autocorrelation functions. For analysis of POM and CLSM images, the software ImageJ (g at 25 °C for 1 h. The supernatant (~35 mL) was removed from the centrifugation tube, and the residue was redispersed in the same volume of water. This procedure was repeated ~10 times to afford an aqueous dispersion of deionized TiNSs. After this deionizing procedure, the electrostatic repulsive force between TiNSs was drastically enhanced, resulting in an increase in the TiNS distance enough to exhibit a vivid structural color37.Typically, an aqueous dispersion (40 mL) of TiNSs ([TiNS] = 0.4 wt%) was centrifuged at 20,000 × 37.Typically, a quartz cuvette (40 × 10 × 1 mm) filled with an aqueous dispersion of TiNSs  was placed in the bore of a superconducting magnet (10 T) at 70 °C for 30 min such that the 1-mm side of the cuvette was directed parallel to the magnetic flux lines. The cuvette was then allowed to be cooled down to 25 °C for ~1 h, affording a single crystal-like monodomain cofacial assembly of colloidally dispersed TiNSs that are oriented parallel to the cuvette surface37:According to the DLVO theory, the total potential (–9 m)thickness of the nanosheet (=0.75 × 10–19 J)Hamaker constant (=1.0 × 1023 mol–1)Avogadro constant (=6.02 × 10–23 J K–1)Boltzmann constant (=1.38 × 10temperature (=298 K)–19 C)charge of an electron free-ion concentrationwhere the Debye screening length relative permittivity of water (=80)–12 C V–1 m–1)permittivity of vacuum  filled in a quartz cuvette (40 × 10 × 1 mm) treated with a 10-T magnetic field was measured at a selected area of the dispersion, using a microscopic Vis/NIR spectrometer  in the reflection spectra, together with the following equation and parameters, the TiNS distances were calculated reflection wavelengthangle between the incident light and the TiNS planes (=90°)TiNS distanceaveraged reflective index of the TiNS dispersion (=1.3)A TiNS dispersion, deionized and magnetically treated as descried above, contains TiNSs that adopt a monodomain structure with a uniform distance between the nanosheets and therefore reflects light with a specific wavelength33. For the initial state of our theoretical model, we consider an elastic lamellar structure confined between two parallel flat surfaces separated by a distance xy-plane. When an external stimulus is applied to the lamellar structure, a local displacement of the layers, denoted by volume of the lamellar layerstilting angle of the lamellar layers compressive elastic modulus of the lamellar layersbending elastic modulus of the lamellar layersThe reason why the contraction of the TiNS distance results in forming the wave can be theoretically explained by considering the deformation of an elastic lamellar structureMinimization of the free energy density In order to correlate this solution with the wave structure with TiNSs, we introduce characteristic parameters In the present case ([TiNS] = 0.5 wt%; ess Fig. , where tSupplementary Information filePeer Review FileDescription of Additional Supplementary FilesSupplementary Movie 1Supplementary Movie 2Supplementary Movie 3Supplementary Movie 4Supplementary Movie 5Supplementary Movie 6


Model experiments show that ~75% of the low latitude twilight zone develops anomalously low δ15N by 2060, predominantly due to the effects of climate change that alter ocean circulation, with implications for the nitrogen source-sink balance. Our results highlight that δ15N changes in the low latitude twilight zone may provide a useful constraint on emerging changes to nitrogen limitation and NPP over the 21st century.The open ocean nitrogen cycle is being altered by increases in anthropogenic atmospheric nitrogen deposition and climate change. How the nitrogen cycle responds will determine long-term trends in net primary production (NPP) in the nitrogen-limited low latitude ocean, but is poorly constrained by uncertainty in how the source-sink balance will evolve. Here we show that intensifying nitrogen limitation of phytoplankton, associated with near-term reductions in NPP, causes detectable declines in nitrogen isotopes (δ Projected declines in marine primary production are underpinned by a slowdown in nitrogen supplied to surface waters. Here the authors detail a new means to detect this slowdown and describe major shifts in the 21st century oceanic nitrogen cycle. Two major anthropogenic drivers, atmospheric nitrogen deposition and climate change, are altering the open-ocean nitrogen cycle3. Atmospheric nitrogen deposition to the ocean has doubled since the preindustrial era5 and is currently the main input of anthropogenic nitrogen to the open ocean6, causing documented increases in nitrate in certain locations7. It is greatest in the Northern Hemisphere and is expected to peak by year 2030 as clean air initiatives are implemented8. Meanwhile, climate change is accelerating9 and, by altering the properties and circulation of seawater12, modifies biogeochemical processes and the distribution of bioavailable nitrogen3. These anthropogenic drivers threaten to alter the twenty-first century nitrogen cycle and the nature of this alteration could either mitigate or amplify projected marine ecosystem productivity decline in the coming centuries13.Nitrogen limits phytoplankton growth in the low latitudes (45°S to 45°N), making the oceanic nitrogen cycle an important regulator of net primary production (NPP), which is essential for ecosystem health and carbon sequestration10, identify their drivers14 and assess their detectability using concepts like the Time of Emergence (ToE), which quantify when anthropogenic signals emerge from natural variability15. Although multi-century projections herald massive NPP declines associated with increasing nutrient limitation of phytoplankton13, near-term ToE assessments suggest that variables related to nitrogen cycling, such as surface nitrate concentrations and NPP, only show detectable trends near the end of the twenty-first century, if at all16. This highlights the challenge of detecting and predicting change in the nitrogen cycle, which is underpinned by a suite of overlapping biological processes that are highly sensitive to environmental change and may show strong variability. For instance, key nitrogen cycle processes will be altered directly as warming changes biogeochemical rates 18 and indirectly as circulation alters substrate supply19. Identifying the primary drivers and responses of the nitrogen cycle would facilitate improved understanding of the evolution of its source-sink balance and provide greater confidence in long-term projections of key ecosystem flows, such as NPP.Earth System Models (ESMs) are used to project anthropogenic trends15N, where δ15N = (15N:14Nsample/15N:14Nstandard − 1) × 1000) is altered uniquely by different processes, such that nitrogen isotopes can record changes in the sources , sinks (denitrification in the sediments and water column) and internal transformations  of nitrogen. In general, nitrogen assimilation by phytoplankton and nitrogen sinks increase δ15N of nitrate (δ15NNO3), whereas sources of nitrogen decrease δ15NNO322. However, increases associated with phytoplankton assimilation are also modulated by the extent to which nitrogen is limiting, with phytoplankton in nitrogen-limited systems showing much weaker preference for the light isotope24. This utilization effect results in peak δ15NNO3 values at the boundary between nitrogen-replete and nitrogen-limited regimes, and the lateral transport of 15N-enriched nitrogen into the gyres25. Palaeoceanographers have long used nitrogen isotopes to probe past changes in nitrogen cycling and utilization28, and yet how nitrogen isotopes fingerprint anthropogenic impacts over the twenty-first century is unknown.Nitrogen isotopes offer a sensitive means to detect such shifts. The isotopic composition of nitrogen  and indirect  effects of climate change to reveal the primary drivers of change. We find that nitrogen isotopes fingerprint the dominant role of climate change, specifically how circulation changes can intensify nitrogen limitation of lower latitude ecosystems, leading to decreased NPP and nitrogen sinks, and subsequently alter the bioavailable nitrogen budget.Here we use a global ocean-biogeochemical model29 forced by output from the Institut Pierre-Simon Laplace Climate Model 5A (IPSL-CM5A). These simulations included a preindustrial control scenario (1801–2100), an anthropogenic scenario that combined historical (1851–2005) and future projections (2006–2100) of atmospheric nitrogen deposition and climate change (using the high emissions RCP8.5 scenario), as well as two additional simulations with each anthropogenic driver considered in isolation (see ‘Methods’). The anthropogenic effects on nitrogen cycling were quantified by comparing mean conditions at the end of the twenty-first century (2081–2100) with mean conditions at the end of the preindustrial control simulation.To assess the impact of atmospheric nitrogen deposition and climate change on the marine nitrogen cycle and its isotopes, we performed four simulations using the Pelagic Interactions Scheme for Carbon and Ecosystem Studies version 2 (PISCES-v2) biogeochemical model8 increased from 16.1 Tg N yr−1 between 1801 and 1850 to peak at 41.9 Tg N yr−1 by 2030, and declined thereafter to 40.0 Tg N yr−1 by 2081–2100  by 2081–2100, consistent with other ESM simulations that considered increasing nitrogen deposition36, and displayed a clear tropical to subtropical shift , consistent with other ESM projections38  and a decrease in sinks (denitrification (−13.6 Tg N yr−1) and burial (−3.1 Tg N yr−1); Supplementary Fig. −1  or was rapidly removed by a local acceleration of denitrification (+6.4 Tg N yr−1) and burial  and nitrogen deposition (+4.9 Tg N yr−1), while not perfectly additive, combined to cause the net accumulation of nitrogen in the ocean (+27.5 Tg N yr−1).An important point is that climate change dominated the alteration of the marine nitrogen budget. By 2081–2100, climate change had increased the bioavailable nitrogen budget by 23.7 Tg N yr −1 Fig.  due to s15N of nitrate  in both the euphotic and twilight zones, as well as vertically integrated NPP and nitrogen fixation , the pattern was reversed, with 31.9% of the ocean showing emergent trends due to climate change compared to only 14.2% due to nitrogen deposition. The dominance of climate change continued to 2081–2100 with an additional emergence of 10–20% . Here we demonstrate that changes ultimately linked to increasing nitrogen limitation were responsible for the broad, simulated δ15NNO3 declines that emerged in the twilight zones of the low-latitude oceans. Namely, a decrease in phytoplankton production and fractionation potentially supplemented by a tropical–subtropical shift of nitrogen fixation.Although low δ15N-depleted organic matter sinking from the overlying euphotic zone is a first-order driver of the δ15NNO3 declines in the twilight zone. Widespread declines in euphotic zone δ15NPOM . Biogeochemical fluxes tended to deplete δ15NNO3 across the tropics and subtropics, and the ensuing changes to δ15NNO3 were greater than observed in the full model  in the tropical Pacific and Atlantic euphotic zones  meant that more 15N was used to create organic matter in increasingly nitrogen-limited upwelling regions and was subsequently lost via sinking  model that follows nitrogen uptake and fractionation by phytoplankton in a water parcel , twilight zone δ15NNO3 (rs = 0.94), twilight zone δ15NPOM (rs = 0.95), NPP (rs = 0.69), zooplankton grazing (rs = 0.69) and water column denitrification (rs = 0.88) and sedimentary denitrification (rs = 0.90) seen in the full model  and indirect effect simulations (rs = 0.61) suggested that both warming and circulation changes were equally important in determining its full response, but that nitrogen fixation by itself was not sufficient to force the isotopic trends associated with climate change. The effect of climate change on biogeochemical processes via altering substrate availability was therefore a major cause of twenty-first century increases in nitrogen limitation, resultant NPP declines, shifts in the sources and sinks of nitrogen, and the accompanying trends in nitrogen isotopes that fingerprint the response of the nitrogen cycle.We examined the direct  and indirect effects  of climate change in two additional experiments. First, warming was imposed on biogeochemical processes under otherwise preindustrial conditions to mimic its effect on rates. Second, preindustrial temperatures were imposed, while climate change altered the circulation to mimic its effect on substrate availability (see ‘Methods’). Direct effects of warming on biogeochemical processes showed a limited ability to reproduce the full suite of climate-driven trends, with the exception of the poleward shift in nitrogen fixers Fig. . In cont rs = 0.9, twiligh46 and expected to intensify this century37. Importantly, these changes are clearly fingerprinted by detectable declines in the isotopic composition of nitrate and particulate organic matter within twilight zones across much of the lower latitude ocean  and Atlantic (N = 890) have been made near peak rates of nitrogen deposition (median age of data = 2008)20. As future deposition is expected to plateau7, any future trends should be dominated by climate-driven signals.Our experiments demonstrate the dominant role of climate change in the twenty-first century alteration of the marine nitrogen cycle, despite a 2.5-fold increase in atmospheric nitrogen deposition since the preindustrial period. Central to the climate-driven perturbation was increasing nitrogen limitation of phytoplankton in the low latitudes due to changes in ocean circulation, likely due to increasing stratification, which is ongoingean Fig. . Althoug40 and data-constrained modelling41 to highlight how the expected declines in low-latitude NPP10 associated with increasing nitrogen limitation may reduce nitrogen sinks as less organic matter sinks out of euphotic zones. Although this may contradict expectations associated with an expansion of oxygen minimum zones49, mesopelagic nitrogen loss processes are highly sensitive to organic matter flux41. A primary dependency on organic matter flux is reflected in our experiments, where nitrogen sinks declined despite a slight increase in hypoxic (O2 < 80 mmol m−3) water volume of 0.6% by 2081–2100, relative to preindustrial conditions. If nitrogen sinks do decline as less organic matter sinks out of the euphotic zone, then our results suggest that the bioavailable nitrogen reservoir may accumulate , dissolved oxygen, the full carbon system and accounts for two phytoplankton (nanophytoplankton and diatoms) and two zooplankton types (microzooplankton and mesozooplankton). Bioavailable nitrogen in our simulations is considered to be the combination of nitrate and ammonium. Its nitrogen cycle includes nitrogen fixation, nitrification, burial, denitrification in both the water column and sediments, and coupled nitrification–denitrification. Nitrogen isotopes were integrated within PISCES-v2 for the purposes of this study, using nine new tracers  general ocean circulation model30. The biogeochemical model (PISCES-v2) was run offline from the physical model (NEMO-v4) using monthly transports and other physical conditions generated by the low resolution version of the IPSL-CM5A ESM57.We conducted simulations under both preindustrial control and climate change scenarios. The preindustrial control scenario from 1801 to 2100 maintained preindustrial greenhouse gas concentrations and only included internal modes of variability. The climate change simulation from 1851 to 2100 included natural variability, prescribed changes in land use, as well as historical changes in concentrations of greenhouse gases and aerosols until 2005, after which future concentrations associated with RCP8.5 were imposed15NNO320 supplemented with recent data to assess the isotopic routines in the model and conducted a thorough model-data skill assessment at replicating observed patterns in space  and modern/future fields . These fields were provided by Hauglustaine et al.The historical rise in anthropogenic nitrogen deposition was assessed by including it in additional simulations under both preindustrial control and climate change scenarios. Four initial experiments were therefore conducted: preindustrial control; preindustrial control plus anthropogenic nitrogen deposition; climate change; and climate change plus anthropogenic nitrogen deposition.We undertook four initial simulations to quantify the impacts of anthropogenic climate change and nitrogen deposition: a preindustrial control simulation from 1801 to 2100; a full anthropogenic scenario from 1851 to 2100; a climate change-only scenario without the increase in anthropogenic nitrogen deposition from 1851 to 2100; and a nitrogen deposition scenario without anthropogenic climate change from 1851 to 2100. Anthropogenic effects to nitrogen cycling were quantified by comparing mean conditions over the final 20 years of the twenty-first century (2081–2100) with mean conditions over the final 20 years of the preindustrial control simulation, whereas effects on nitrogen isotopes were quantified by comparing mean conditions over the final 20 years of the twenty-first century (2081–2100) with mean conditions over the historical period (1986–2005) from the same simulation.To understand the direct and indirect effects of climate change, we undertook two additional idealized simulations. First, we imposed temperature changes on biogeochemical rates, while maintaining ocean circulation associated with the preindustrial control scenario, to assess the direct effects of warming on biogeochemical processes. Second, we imposed the preindustrial control temperature field on biogeochemical processes, while altering the circulation in line with the climate change scenario, to assess the indirect effects of climate change . Each experiment was run from 1851 to 2100 and without the anthropogenic increase in atmospheric nitrogen deposition, parallel with the full climate change simulation.15NNO3, euphotic zone δ15NPOM, and vertically integrated NPP, zooplankton grazing, nitrogen fixation, water column denitrification and sedimentary denitrification.Agreement between the climate change simulation without anthropogenic nitrogen deposition was quantified using a pixel-by-pixel correlation analysis using Spearman’s rank correlation based on the non-parametric nature of the two-dimensional fields used for comparison. Fields were euphotic zone nitrate, twilight zone δ42. The twilight zone was also defined using light, as advocated by Kaartvedt et al.58. Depths between 0.1% and 0.0001% of incident irradiance defined the twilight zone. These definitions typically returned euphotic zone thicknesses of 137 ± 23 m (mean ± SD), and twilight zone thicknesses of 233 ± 37 m. The boundary between these depth zones were deepest in oligotrophic tropical and subtropical waters, and were shallowest in equatorial and temperate waters  and using annually averaged fields of ocean tracers. We therefore ignored temporal trends and variability at seasonal and sub-seasonal scales. Raw time series were first detrended and normalized using the linear slope and mean of the preindustrial control experiment, such that the preindustrial control time series varied about zero, while anomalous trends in experiments with climate change and/or nitrogen deposition deviated from zero. These detrended and normalized time series were smoothed using a boxcar (flat) moving average with a window of 11 years to filter decadal variability . A signal emerged from the noise if it exceeded 2 SDs, a threshold that represents with 95% confidence that a value was anomalous and is therefore a conservative envelope to distinguish normality from anomalyFurthermore, we required that anomalous values must consistently exceed the noise of the preindustrial control experiment until the end of the simulation (2100) to be registered as having emerged. Temporary emergences were therefore rejected, making our ToE estimates more conservative. A graphical representation of this process is shown in Supplementary Fig. 15NO3 and NO3 into and out of each model grid cell within the twilight zone, to determine whether the trends in δ15NNO3 were related to biogeochemical or physical changes. Fluxes of 15NO3 and NO3 included a net source from nitrification (NO3nitr) and net sinks due to new production (NO3new) and denitrification (NO3den). Although nitrification did not directly alter the 15N : 14N ratio in our simulations, the release of 15NO3 and NO3 by nitrification conveyed an isotopic signature determined by prior fractionation processes that produce ammonium (NH4). These processes include remineralization of particulate and dissolved organic matter, excretion by zooplankton and nitrogen fixation. The isotopic signatures of these processes were thus included implicitly in NO3nitr. For each grid cell, we calculated the biogeochemical tendency to alter δ15NNO3 based on the ratio of inputs minus outputs:We analysed the biogeochemical fluxes of 15NNO3.This calculation excluded any upstream biological changes and circulation changes that might have altered δ15N, PO15N and Exp15N) in units of mmol N m−3 over 100 days given initial conditions and constants listed in Supplementary Table We simulated the nitrogen isotope dynamics in a recently upwelled water parcel during transit to the subtropics by building a 0D model. The model simulates state variables of dissolved inorganic nitrogen (DIN), particulate organic nitrogen (PON) and exported particulate nitrogen (ExpN), as well as their heavy isotopes (DIμmax) in units of day−1  is constant at 5‰ but is decreased towards 0‰ by the nitrogen limitation term , Kresp (units of mmol N m−3) and Pmort (units of (mmol N m−3)−1 day−1) are constants , but the degree of increase associated with warming is scaled down by a constant factor equal to Trec  as output (Eqs. 14N), whereas the DI15N, PO15N and Exp15N pools represent the relative enrichment in 15N compared to a standard ratio. For simplicity, we make the standard ratio equal to 1. Therefore, taking the ratio of the DI15N to DIN pools and subtracting one returns the isotopic signature. Multiplying this by 1000 converts this signature to per mil units (‰).Finally, we calculate the δput Eqs. –24. We aSupplementary InformationPeer Review File