Gravity sensing provides a robust verticality signal for three-dimensional navigation. Head direction cells in the mammalian limbic system implement an allocentric neuronal compass. Here we show that head-direction cells in the rodent thalamus, retrosplenial cortex and cingulum fiber bundle are tuned to conjunctive combinations of azimuth and tilt, i.e. pitch or roll. Pitch and roll orientation tuning is anchored to gravity and independent of visual landmarks. When the head tilts, azimuth tuning is affixed to the head-horizontal plane, but also uses gravity to remain anchored to the allocentric bearings in the earth-horizontal plane. Collectively, these results demonstrate that a three-dimensional, gravity-based, neural compass is likely a ubiquitous property of mammalian species, including ground-dwelling animals. Head direction neurons constitute the brain’s compass, and are classically known to indicate head orientation in the horizontal plane. Here, the authors show that head direction neurons form a three-dimensional compass that can also indicate head tilt, and anchors to gravity. As such, graviception represents one of the most ubiquitous sensory modalities of living organisms5.Gravity is a ubiquitous force that profoundly affects life on earth. Gravity assists or resists movements6 orient themselves and navigate in three dimensions (3D). Preeminent neuronal classes of the mammalian’s brain, such as place cells8 and head direction (HD) cells9 operate in 3D. By providing verticality information11, gravity may mitigate the complexity of orienting in 3D12; yet gravity signals have never been identified in the brain’s navigation system. Here we tested whether mouse HD cells, which encode allocentric head orientation analogous to a neural compass, use gravity-anchored tilt signals  and azimuth signals , and tilt orientation: γ . Similarly, the example azimuth-untuned cell exhibited a tilt PD at  . The NTA of tilt was lower than that of azimuth in conjunctive ADN cells, and similar in other regions . Before analyzing the 3D properties of HD tuning, we first verified that spatial responses were similar in freely moving animals and in the rotator.To characterize tuning uniformly in 3D space, 549  neurons were tested in the rotator. Seventy-one percent (388) of these cells were significantly tuned to tilt . Similar to responses obtained on the platform, tilt-tuned cells were slightly (5%) more likely to be azimuth-tuned and reciprocally azimuth-tuned cells were slightly (7%) more likely to be tilt-tuned  plane and encode azimuth in that plane Fig. . Alternayaw Fig. , cyan anyaw Fig. , green. yaw Fig. . In contp = 0.01). In contrast, 63/285 (22%) cells were tuned when azimuth was expressed in either the EH or TA frames . As predicted, almost no cells exhibited significant tuning in a YO frame  that correlations were similar across recorded areas  and tilt-tuned or non-tilt-tuned cells . As expected , but not when rolling  or when tilted (>60° tilt) Fig. . We obseWe also found that, regardless of reference frame, azimuth tuning decreased when the animal was tilted beyond 90° from upright  and varied between groups of cells ; however there was no significant interaction effect , indicating that the azimuth tuning of all cells was equally affected by tilt. We conclude that HD cells encode azimuth in a TA reference frame, and that their azimuth response decreases when the head tilts away from upright, irrespective of tilt tuning.This was not limited to azimuth-only cells Fig. , gray: tTo further understand 3D tuning, we created a 3D HD model that incorporates the following properties Fig. : (1) tilIn general, gravity is a 3D vector, sensed in egocentric 3D Cartesian coordinates , as illustrated with two examples  had not yet attenuated. Consequently, the cell exhibited tilt and azimuth tuning simultaneously at this tilt angle, resulting in a preferred 3D orientation, visible on both the measured , asred Fig. , top andred Fig. , bottom α = 105°), where azimuth tuning had already substantially decreased. As a consequence, the cell appeared azimuth-tuned at small tilt angles, where tilt tuning was minimal  and tilt-only cells .Model fits were significantly lower when 3D curves were computed with azimuth in an EH frame . In contrast, PDs were distributed uniformly between tilt angles lower or higher than 90° . The gravity tuning curve of cells with PD located in the pitch  plane had stronger peak firing rate  tilt-tuned cells in complete darkness. Angular differences between PDs recorded in light and darkness were close to zero , although slightly lower in darkness in CIN . Similar findings were also reported in gravity-tuned cells in the monkey anterior thalamus24, suggesting that these tilt-tuned neurons may be found along a broad range of animal evolution.Azimuth tuning of HD cells persists in darkness24, a small fraction of cells also responded to tilt or azimuth velocity  tilt-tuned cells with the 3D rotation protocol after tilting the rotator and visual surround together 60° Fig. , blue frw) of gravity and vision  and between cells with PD in the pitch or roll plane . We also tested whether the peak gravity weight was significantly different from 1 on a cell-by-cell basis  and, at the population level, wpeak was still centered on 1.03 . We analyzed 19 cells  that were tuned to azimuth when moving freely and during Experiment 3-L . On a cell-by-cell basis, the partial correlation was higher when TA was referenced to gravity 8 cells  and was not significantly different between the two frames was non-significant in all other cells  plane. However, in our assessment15, this study is in fact supportive of the tilted azimuth model, which was not directly tested in that work. Furthermore, we argue that their study is inconclusive with respect to tilt tuning15  raise the possibility that the RSC may use gravity-referenced tilt signals to transform visual signals in 3D.Together with Finkelstein et al.9 observed a functional gradient of azimuth-tuned to tilt-tuned HD cells in the presubiculum. We observed no difference between the granular and dysgranular RSC, nor any obvious functional gradient in the ADN , to RSC (ADN projections) and to the cingulate cortex (RSC projections)12, which dominates vision in human verticality perception10, even though visual signals can replace gravity cues in microgravity39. Further, gravity sensing represents one of the most ubiquitous sensory modalities of terrestrial living organisms5. Gravity is likely sensed by a combination of proprioceptive and vestibular inputs41, and its computation likely involves the vestibulocerebellum44.Gravity is a fundamental vertical allocentric cue45, although some HD cells in the RSC34, and parahippocampal regions46 may not contribute to the attractor network. Fundamentally, the 1D attractor model implies that cells with similar azimuth PD are constrained to fire together. However, most azimuth-tuned HD cells are also tilt-tuned, and cells with similar azimuth PD may have different tilt PD  and rats (Rattus norvegicus) are primarily land-dwelling, they exhibit a rich 3D behavioral repertoire in the wild52, easily learn 3D spatial orientation tasks53 and are physiologically related to tree-dwelling rodents54, including other muroids  and non-muroids (e.g. squirrels). It is therefore not surprising that rodents, like bats9 and likely macaques24 and humans27, possess a three-dimensional compass, whose properties may be shared across mammals.Tilt and 3D orientation tuning had previously only been identified in aerial (bats) and tree-dwelling (macaques) species, raising the question of whether a 3D compass would be ethologically relevant to rodents. Although laboratory mice , 3–6 months old, were used in this study (Supplementary Table Neurons were recorded using 6 (mice AA1/AA2) or 4  tetrode bundles constructed with platinium-iridium wires  and platinum-plated for a target impedance of 200 kΩ using a Nano-Z  electrode plater. Tetrodes were cemented to a guide tube (26-gauge stainless steel) and connected to a linear EIB . The tetrode and guide tube were attached to the shuttle of a screw microdrive  allowing a travel length of ~5 mm into the brain.The stereotaxic coordinates for each tetrode implant was based upon Bregma as a reference point. The coordinates used to target both the ADN and the CIN were 0.2 mm posterior and 0.7 mm lateral to Bregma. The granular/dysgranular RSC were targeted by implanting 2.0 mm posterior and 0.07/0.7 mm lateral to Bregma, respectively.Raw neuronal data was manually clustered based on spike waveform and amplitude, using custom Matlab scripts. Spike clusters with similar spike waveform and firing characteristics  were attributed to a single neuron. When we observed that neurons recorded over successive days, and on a single tetrode, had similar firing characteristics and similar tuning to 3D head direction, we merged the data to avoid introducing duplicate data points in our analyses.At the end of tetrode recordings from each animal, the brain was removed for histological verification of electrode location. The animals underwent transcardial perfusion with 4% paraformaldehyde (PFA). The brains were postfixed in 4% PFA and then transferred to 30% sucrose overnight. Brain sections (40 μm) were stained , and examined using bright-field microscopy to localize tetrode tracks . We then performed the other protocols described below on a moving platform and rotator, before returning the mouse to the same arena and performing three separate 8-min sessions, first in light (Experiment 1-L1), then in darkness (Experiment 1-D), then we repeated a session in light (Experiment 1-L2).γ) together, and these variables are therefore correlated  and tilt orientation  with the following organization: (1) one block where the platform was horizontal (duration: 8 min), (2) eight blocks where the platform was tilted 45° and the base was rotated in steps of 45° (duration: 2.5 min) and (3) eight blocks where the platform was tilted 65° and the base was rotated in steps of 45° (duration: 5 min). Note that mice tended to upright their head, therefore tilting the mesh 45° and 70° resulted in average head tilts of ~35° and 60°, respectively  across 73 tilt positions (uniformly distributed in tilt space for up to 60°). Next, we computed the entropy of dE(d) = −Σp(d).log2(p(d)), ranging from log2(73) = 6.19 (uniform distribution) to 0 (if the mouse occupies a single point). We excluded cells where E(d) < 5.6, which corresponds to mice sampling less than 2/3 of the tilt space. 45% of recorded cells , and during Experiment 2 or Experiment 3-L have been included for analyses, with the following exceptions:We first classified neurons as azimuth-tuned or non-azimuth-tuned based on their responses in the freely moving arena. Neurons could also be classified as azimuth-tuned or azimuth-untuned based on their responses in the platform and rotator. However, because azimuth responses have lower amplitude in the rotator, they often did not reach significance level. Therefore, throughout the study, azimuth-tuned refers by default to the classification based on freely moving data in the arena (Experiment 1).Similarly, neurons were classified twice as tilt-tuned or not, based on recordings on the orientable platform and in the rotator independently. As with azimuth tuning, neurons that exhibited significant tilt tuning when moving freely may not be significantly tuned in the rotator, because responses in the rotator had lower amplitude. On the contrary, some neurons that exhibited significant tilt tuning in the rotator were not significantly tuned when moving freely because this protocol sampled a limited range (~1/3) of head tilt. Nevertheless, differences were small, and the majority of neurons that were significantly tilt-tuned in one setup were also tuned to the other Fig. .Importantly, we confirmed that azimuth and tilt tuning in the rotator and freely moving were correlated in terms of amplitude and consistent in terms of spatial characteristics for neurons that were significantly tuned to azimuth or tilt in both experiments Fig. .To evaluate azimuth tuning, we computed 1D azimuth tuning curves in all conditions of Experiment 1, in Experiment 2 when the platform is horizontal, in Experiment 4-Yaw; and in data points where head tilt was less than 45° during Experiment 3-L.To evaluate tilt tuning for Experiment 2 and Experiment 3-L,D,T, data were averaged across azimuth. We also computed pitch/roll tuning curves based on Experiment 4.For each recorded neuron, we computed the following tuning curves:14, which has been explained by a framework called the dual-axis rule or tilted azimuth (TA); see Supplementary Fig. Note that tilt tuning is different from a recent finding that ADN HD cells encode azimuth in a tilt-dependent mannerGX, GY, GZ) that represent the orientation of the gravity vector  in head coordinates. Head tilt was also expressed in spherical coordinates to describe tilt tuning curves  and α = 180° in upside-down orientation (UD); and γ encodes tilt orientation: γ = 0° and γ = 180° correspond to nose-down (ND) and nose-up (NU) tilt (pitch); γ = 90° and γ = −90° correspond to left ear-down (LED) and right-ear-down (RED) tilt (roll). Spherical coordinates are transformed into Cartesian coordinates and vice-versa by GX = sin(α).cos(γ); GY = sin(α).sin(γ); GZ = −cos(α); and α = acos(−GZ); γ = atan2. Note that Cartesian coordinates and spherical coordinates can be indifferently used to compute tilt tuning curves, as long as spherical distances are computed correctly . However, the Cartesian coordinate system, which is more general, allowed modeling of seemingly bimodal tuning curves  using unimodal tuning functions , i.e. N = . Earth-horizontal azimuth is defined as the orientation of N on the earth-horizontal  plane, i.e. EHAz = atan2. EH azimuth can be transformed into tilted azimuth by the following equation:Neuronal responses were evaluated by computing tuning curves, which were smoothed using Gaussian kernels with standard deviation of 15° on both azimuth and tilt  when tilt is expressed in Cartesian coordinates). We computed 3D azimuth tuning curves in 3 different ways, by expressing azimuth in a yaw-only (YO), an earth-horizontal (EH) or a tilted (TA) frame, and found that the latter accounted for neuronal responses better  is a 3D Gaussian distribution centered on M and with covariance matrix C.To quantify tuning curves, von Mises and/or Gaussian functions were fitted and standard shuffling analysis was used to evaluate the statistical significance of azimuth and tilt tuning. 2D tilt tuning curves were fitted with Gaussian distributions Fig. , where tg(α) and expressed azimuth tuning as:κ is the parameter of the van Mises distribution. For convenience, we normalized FRAz such that its average value across all azimuths is 1 )).Azimuth tuning curves were fitted with circular normal (von Mises) distributions. Preliminary analysis revealed that the PD of azimuth tuning is maintained when the head tilts (when azimuth is expressed in a tilted frame) but that its gain changes. To account for this, we defined a tilt-dependent gain Finally, we evaluated the interaction between azimuth and tilt tuning by fitted 3D tuning curves defined as the product of the azimuth and tilt tuning cures defined above, i.e.0, A, M  and C . The normalized azimuth tuning curves had 2 free parameters (κ and PD). The tilt-dependent gain g(α) was fitted independently at 13 tilt angles α ranging from 0 to 180° by increments of 15°, resulting in 13 additional free parameters. The 3D tuning curves were computed from experimental data at 184 uniformly distributed tilt orientations and 24 azimuth orientations, i.e. 4416 points, and fitted to the 3D curve model by gradient ascent (Matlab function lsqnonlin). Note that since the average value  of FRAz was 1, the average tilt tuning curve  was FRTi.Tilt tuning curves had 11 free parameters: FRWe tested an additional model that assumes that azimuth and tilt tuning interact additively, i.e.:r to z transform, at p < 0.01), and significantly lower at the population level . Therefore, we used the multiplicative model to model 3D responses in this study.We found that this model did not fit 3D tuning curves as well as the multiplicative model: its correlation coefficient was significantly lower in 33/53 conjunctive cells, and better only in 1/53 conjunctive cell , ranging from 0 to 1, is used commonly to assess how strongly a cell is tuned  independently from its average firing rate. It allows comparing cells with a large range of peak firing rates. Thus, azimuth tuning was quantified consistently with previous studies by computing the mean vector:c = 3.6 × π/180/2/sin(1.8)56.The length of the mean vector |G =  and computing:Mean vectors can be generalized to a 2D distribution by expressing tilt in Cartesian coordinates max) and minimum (FR0) firing rate, as NTA = (FRmax − FR0)/FRmax. Thus, normalized tuning amplitude ranged from 1  to 0 (when a cell was unmodulated). Note that normalized tuning amplitude measures the cell’s modulation amplitude, but not the sharpness of the tuning curve.The resulting 2D vector has a length of 1 if all spikes occur at the same tilt and 0 if spikes are distributed uniformly or symmetrically. However, because mean vectors computed in 1D and 2D cannot be compared directly, we developed an alternative measure called normalized tuning amplitude  as the orientation at which the fitted 2D tilt tuning curve is maximal. In cells with bimodal tilt tuning  shifting the entire spike train circularly by a random value of at least ±10 s, (2) recomputing the tuning curve, (3) performing the Gaussian fit and (4) computing the azimuth and/or tilt normalized tuning amplitude. We computed the mean value m and standard deviation σ of the normalized tuning amplitude across 100 shuffled samples. The statistical p-value of the normalized tuning amplitude NTA measured in the un-shuffled data was computed as 1 − F, where F is the cumulative Gaussian distribution with average m and standard deviation σ. The standard deviation of the model’s correlation across all samples is also used as an estimate of the standard error of the model’s correlation.We used a shuffling procedurep-value computed as described above was less than 0.01 and (2) the normalized tuning amplitude NTA was equal to or higher than 0.25. The second criterion was equivalent to selecting cells where the modulation was at least one third of the baseline firing rate, and was used to eliminate cells with very small but significant modulation  the p-value and amplitude across repetitions, and (2) we computed a p-value and amplitude based on data pooled across all repetitions. We tested if the values obtained with technique (1) or with technique (2) passed the criteria described above, and classified cells as azimuth-tuned if they passed any of these tests. This two-technique approach was used because pooling data yields a greater statistical power but fails if the cell’s PD shifted between sessions, whereas the second approach is not affected by shifts in the PD. In total, 37% cells passed both tests; 6.5% passed the first test only, 7.5% passed the second test only; therefore, in total, 51% cells passed one or the other and were classified as azimuth-tuned.We combined data from multiple repetitions of Experiment 1-L to assess if cells were significantly tuned to azimuth when the animal was moving freely. We used two techniques to combine multiple repetitions: (1) we analyzed each repetition independently and computed the median We used data from Experiment 3-L to assess if cells are significantly tuned to tilt, by testing if the normalized tuning amplitude of the average tilt tuning curve  passed the criteria described above. We also tested if cells are significantly tuned to azimuth in the rotator by computing the azimuth tuning curve based on data for up to 45° tilt and testing if its normalized tuning amplitude passes the criteria described above. In some cells, Experiment 2 or Experiment 3-L were repeated multiple times. We found that the preferred direction of tilt and azimuth tuning were stable across repetitions, and pooled data across all repetitions.g(α) to zero) to create a tilt-only model, and computed the sum of squared residuals ssrG. We defined the partial correlation coefficient of azimuth as ρ = sqrt((ssrG − ssr)/ssrG). Intuitively, this coefficient measures how much the tilt-only model’s error is reduced by the addition of azimuth tuning.We compared models of azimuth tuning  and then computed the time derivative of the gravity vector  as a measure of tilt velocity. Next, we fitted neuronal firing rate with FR = FR0 + A.NM,C + A’.NM’,C’. We computed the normalized tuning amplitude of tilt and tilt velocity and used the same shuffling method and criterion  as in other Gaussian fits to assess whether cells were significantly tuned to the gravity derivative. Note that the tilt tuning curves obtained with this method were identical to those obtained when fitting the 3D model that includes tilt and azimuth tuning.We performed another Gaussian curve fitting to test whether neurons carry a mixture of tilt and tilt derivative information. We expressed head tilt measured during Experiment 3-L in Cartesian coordinates (t) by computing azimuth velocity tuning curves for each cell (i.e. average firing rate as a function of dAz/dt) using all data from Experiment 1-L. The tuning curves were evaluated at all velocities ranging from −200 to 200°/s by increment of 20°/s and smoothed using a 8°/s Gaussian kernel. We computed the amplitude and normalized tuning amplitude of these curves, and used the same shuffling method and criterion  to assess whether cells were significantly tuned.We investigated whether cells encode azimuth velocity  and tilted azimuth (TAG). Motion in a visual frame was computed as if Axis IV of the system had not been tilted, and decomposed into visually referenced tilt  and tilted azimuth (TAV). Next, we assumed that HD cells encode a tilt signal computed as a weighted average of G and V (T(w), computed as w.G + (1−w).V and normalized to a length of 1) and an azimuth signal equal to TAG or TAV. We computed the cells’ 3D tuning curves for each possible value of w, ranging from −1 to 2, and based on TAG or TAV. Each tuning curve was compared to the tuning curve fitted to the data measured with the rotator upright (Experiment 3-L) by computing their pixel-by-pixel correlation. We used the shuffling procedure described above to generate 60 shuffled samples of the tuning curves in Experiment 3-T. The standard deviation of the correlation between the curve fitted to Experiment 3-L and these samples was used as an estimate of the standard error of the correlation, and 99% confidence intervals were set to 2.56 times the standard error. To compare the two models of tilted azimuth (TAG and TAV), we computed the partial correlation of azimuth tuning as described above.To analyze the results of Experiment 3T, we expressed 3D head motion (tilt and azimuth) in both gravity and visual reference frame. Motion in a gravity frame was computed based on the actual 3D position of the head, and decomposed into gravity-referenced tilt (Using the full 3D tuning curve data from Experiment 3-L, we predicted the responses to pitch and roll rotations by sampling the 3D tuning curve at the head orientations visited during pitch and roll rotations. The pitch and roll tuning curves measured during Experiment 4 and predicted based on Experiment 3 were then fitted with 1D Gaussians, and the resulting modulation amplitudes and preferred direction were compared. Data during Experiment 3 and 4 in light and darkness were averaged.26 in Supplementary Fig. We performed a similar analysis as in Peyrache et al.We confirmed that the distribution of average firing rates and CV2 were similar for all cells in the CIN, ADN, and RSC (Supplementary Fig. Further information on research design is available in the Supplementary InformationPeer Review FileReporting SummaryDescription of Additional Supplementary FilesSupplementary Movie 1Supplementary Movie 2Supplementary Movie 3Supplementary Movie 4Supplementary Movie 5Supplementary Movie 6Supplementary Movie 7Supplementary Movie 8Supplementary Movie 9


The palladium–silver interface also dynamically restructures during reduction, resulting in silver–palladium intermixing. This study clearly demonstrates the migration of reaction intermediates and catalyst material across surface interfacial boundaries in alloys with a significant effect on surface reactivity, having broad implications for the catalytic function of bimetallic materials.Heterogeneous catalysts are complex materials with multiple interfaces. A critical proposition in exploiting bifunctionality in alloy catalysts is to achieve surface migration across interfaces separating functionally dissimilar regions. Herein, we demonstrate the enhancement of more than 10 Species migration across interfacial boundaries can affect the function of bimetallic catalysts. Here the authors report that palladium oxide drives the reduction of silver oxide by facilitating molecular hydrogen dissociation and migration of hydrogen atoms across the Pd–Ag interface with concurrent surface restructuring. The increasing interest in alloy catalysts creates new challenges in understanding the effect of interfaces. Although interfaces between metal nanoparticles and the metal oxide support have been extensively investigated, less is known about interfaces that form on alloys themselves, independent of the support. Phase segregation on metallic alloy nanoparticles can form metal/metal interfaces primarily arising from differences in surface free energy of the metal components and unfavorable mixing enthalpies9. Under oxidizing conditions, complex metal/oxide and oxide/oxide interfaces can form by phase separation and surface segregation arising from differences in metal–oxygen bonding11. Therefore, a dynamic understanding of material restructuring and chemical behavior is required to most effectively use the bifunctional character of alloy catalysts.Heterogeneous catalysts are complex materials that generally contain multiple interfaces which can modify the kinetics and selectivity for key reactions, especially for the production and use of molecular hydrogen for energy generation and chemical synthesis18 and direct migration or “spillover”19 of reactive species created on one phase to a neighboring phase of differing reactivity25. The metal/oxide support interface can significantly restructure in reactive gas environments on a short timescale of minutes and long length scales of microns26. Catalyst activity can be significantly modified by interface restructuring including changes in coordination environment27, catalyst encapsulation28, and metal component transport and alloying33.Prior studies have demonstrated that the interface between metal nanoparticles and the metal oxide support can affect chemical behavior by the creation of specific active sites36, structural rearrangement37, and formation of oxide/oxide interfaces in reactive gas environments11. The migration of intermediates via hydrogen atom spillover across a bimetallic interface has been demonstrated for several metal/metal interfaces41. The behavior of bimetallic oxide interfaces in promoting the migration of intermediates, though, may even be more complex than for metal/oxide support or metal/metal interfaces, as we examine in this paper.Similarly, metal/metal interfaces of alloy nanoparticles can restructure under reactive gas conditions and promote intermediate migration. The interface can significantly reorganize by segregation and dissolution of metal components44. The intermixing of palladium and silver that accompanies the acceleration of silver oxide reduction demonstrates the complexity of synergistic effects in catalysis, especially when reducible oxides are involved.Herein, we demonstrate that synergistic effects arising from interfacial energetics dramatically alter reactivity associated with hydrogen atom migration across the palladium oxide/silver oxide interface produced from oxidation of the alloy, resulting in intermixing of metal atoms at the two-dimensional bimetallic oxide interface during the reactive process at room temperature. Specifically, intermixing of palladium and silver plays a critical role in accelerating the rate of reduction of oxidized Ag(111) by molecular hydrogen because of the presence of palladium oxide islands on the silver oxide surface. The increase in reactivity is attributed to the higher activity of palladium oxide for dissociating molecular hydrogen to produce hydrogen atoms, which can either (1) spillover directly onto the silver oxide or (2) react at the palladium oxide boundary with oxygen provided by silver oxide that is supplied to the palladium as palladium oxide is reduced. In parallel, the rate of reduction of palladium oxide is retarded as silver is incorporated into its structure at the interface. The high mobility of silver and silver oxide complexes, even at room temperature, is an important factor in this mechanismx) on Ag(111) surfaces was compared using ambient-pressure X-ray photoelectron spectroscopy (AP-XPS). A palladium oxide (PdO) film was generated by oxidation of a single crystal of Pd(111) with molecular oxygen at 773 K and 2 Torr -p(4×4)O) was generated by oxidation of Ag(111) by molecular oxygen at 773 K and 2 Torr  islands surrounded by the surface oxide of Ag(111) were generated by deposition of 0.10 monolayers (ML) of palladium on Ag(111) followed by exposure to molecular oxygen at 377 K and 3 Torr for 25 min  on Pd111), silver oxide (Ag(111)-p4×4)O) on Ag(111) and palladium oxide  on Ax  before oxidation, which is attributed to the attenuation of subsurface palladium in the multilayer structures  because of a decreased palladium–silver interface area  bulk alloy47.Palladium dewets the surface when the single layer palladium islands on Ag(111) are oxidized to form domains of silver surface oxide and multilayer PdOx Figs. a, b, 3. x Figs. . During  nm Fig. . Accordix onto the surrounding silver oxide surface and the synergistic effects that drive this phenomenon are as follows:3 monolayers   on metallic palladium (Pd(111)) were readily reduced by molecular hydrogen, commencing at cumulative molecular hydrogen exposures of approximately 107 monolayers of molecular hydrogen cause no observable reduction of surface oxygen -p(4 × 4)-O is not reduced by molecular hydrogen. Cumulative exposures of up to 10x on the Ag(111) surface catalyzes the reduction of the supporting silver oxide by molecular hydrogen. The presence of PdOx on Ag(111) increases the rate of reduction of silver oxide with molecular hydrogen by more than 104 at 300 K  occurs at the same molecular hydrogen exposure as does palladium oxide reduction on the PdO surface, which indicates a similar rate for initial molecular hydrogen dissociation on both. PdOx is reduced at a much slower rate than occurs on PdO, which will be discussed later in context of structural changes during the reaction  and palladium oxide51 occurs via the activation of molecular hydrogen to form atomic hydrogen (and hydroxyls). Hydroxyl migration from PdOx to silver oxide and reaction with silver oxide would lead to no net reduction of silver oxide and therefore is implausible. The rate of migration of intermediates across the PdOx—silver oxide interface is expected to be atomic hydrogen ≈ hydroxyls > atomic oxygen based on their respective binding energies on palladium, silver, and palladium–silver alloy sites61. However, it is quite possible that atomic oxygen transfers from the Ag(111)-O (perhaps via silver oxide complexes) to the PdOx as it is reduced, significantly contributing to the rate of reduction of the silver oxide because it is known that short Ag–O chains are quite mobile on Ag(110), and the reduction of Ag(111)-p(4×4)O by carbon monoxide generates mobile silver atoms44. Direct hydroxyl migration from silver oxide to PdOx to mitigate the rate of reduction of the PdOx is unlikely, since it necessitates the formation of hydroxyls on silver oxide by the direct reaction of silver oxide with molecular hydrogen. Therefore, we propose that silver oxide reduction is initiated by atomic hydrogen migration from PdOx to silver oxide and that the reduction proceeds by hydrogen atom migration from PdOx to silver oxide. The net rate of reduction of the PdOx may be mitigated by migration of atomic oxygen from silver oxide to partially reduced PdOx. The effect of the palladium surface coverage, distribution, and oxidation state on the reduction of silver oxide is currently under investigation.The high reactivity of the silver oxide surrounding the PdOnds Fig. , red occnds Fig. , black, x on Ag(111)-O by molecular hydrogen, based on both X-ray photoelectron spectroscopy and scanning tunneling microscopy  are observed after exposure to molecular hydrogen at 300 K  by molecular hydrogen due to the presence of PdO63 however, intermixing and reconstruction during reaction was not evident. For example, single palladium atoms in copper promote molecular hydrogen dissociation on palladium and subsequent migration to the copper38. Migration of hydrogen atoms also occurs across interfaces between metal particles, e.g. cobalt, and metal surfaces, e.g. copper39. Furthermore, migration between metal and metal oxides phases has also been reported for hydrogen atoms19. For example, molecular hydrogen dissociation at a site spanning single palladium atoms on iron oxide (Fe3O4(001)) forms hydroxyls on the oxide via a heterolytic bond breaking process23. Migration of intermediates across interfaces between oxide islands of titania and ceria (TiO2 and CeO2) formed on gold and copper has also been demonstrated65. Similarly, copper oxidation was promoted by ceria (CeO2) islands, indicating that oxygen transport across interfaces is also possible66. The intermixing of metal atoms at the interface was not observed in any of these cases.Previously, migration of hydrogen atoms has been demonstrated away from single metal atoms and metal islands to either a metal or metal oxide host;The acceleration of silver oxide reduction, which is accompanied by intermixing of palladium and silver described here demonstrates the complexity of synergistic effects in alloy nanoparticle catalysis, especially when reducible oxides are involved. Such intermixing can alter reaction rates and, therefore, must be considered in modeling such behavior.x islands is accompanied by intermixing of palladium and silver. The facile intermixing of metals involved during a reaction process on a model alloy surface demonstrates the complexity of synergistic effects in alloy nanoparticle catalysis. Such intermixing, which can alter reaction rates, has not previously been established in the context of reactant migration across the interface between two different reducible oxides formed from oxidation of an alloy. This study clearly demonstrates that such intermixing must be considered in modeling the behavior of complex catalyst materials.The dramatic enhancement of the rate of silver surface oxide reduction due to the presence of PdO+) sputtering  and annealing . The Ag(111) single crystal was cleaned by several cycles of argon ion (Ar+) sputtering , molecular oxygen treatment  and annealing . Palladium was evaporated and deposited on the Ag(111) crystal when the sample was 300 K. Pd(111) and Ag(111) were oxidized in 2 Torr of molecular oxygen at 773 K for 5 min while palladium on Ag(111) was oxidized in 3 Torr of molecular oxygen at 373 K for 25 min.The Pd(111) single crystal was cleaned by several cycles of argon ion  in order to eliminate beam-induced reactivity that can occur when a significant gas pressure is present.67 background subtraction and normalization to the background at the low binding energy side of the peaks. The Ag(111) and Pd/Ag(111) spectra were fitted with a Doniach-Šunjić function68 convoluted with a Gaussian function and the Pd(111) spectra were fitted with a Mahan function69 convoluted with a Gaussian function.A photon energy of 800 eV was used to take a survey scan to check for contamination before acquiring high-resolution spectra. Photon energies of 535 eV for Pd3d and 568 eV for Ag3d were used to produce photoelectrons with kinetic energies around 200 eV for high-resolution spectra. The binding energies reported are referenced to the Fermi level as measured after each spectrum. The data was fitted after a Shirley−9 Torr) for imaging in the UHV multiprobe surface analysis system.STM experiments were perform using an Omicron VT-STM-XA 650 system (UHV Multiprobe). All samples were prepared in the preparation chamber of a lab-based ambient-pressure photoelectron spectroscopy system. The samples were then transferred in a vacuum suitcase (base pressure < 1.0 × 10Supplementary InformationPeer Review


An efficient general first-principles methodology to simulate vibration-induced spin relaxation in f-block molecular nanomagnets that drastically reduces the computation time. ab initio methodologies play an important role by guiding synthetic efforts at the lab stage. Nevertheless, when evaluating vibration-induced spin relaxation, these methodologies are still far from being computationally fast enough to provide a useful predictive framework. Herein, we present an inexpensive first-principles method devoted to evaluating vibration-induced spin relaxation in molecular f-block single-ion magnets, with the important advantage of requiring only one CASSCF calculation. The method is illustrated using two case studies based on uranium as the magnetic centre. Finally, we propose chemical modifications in the ligand environment with the aim of suppressing spin relaxation.One of the main roadblocks that still hamper the practical use of molecular nanomagnets is their cryogenic working temperature. In the pursuit of rational strategies to design new molecular nanomagnets with increasing blocking temperature,  Molecular nanomagnets have been attracting enormous attention for almost three decades due to their unique properties. These magnetic molecules, also known as single-molecule magnets (SMMs),The field of molecular nanomagnetism is at a crucial point. Over the last few years, we have witnessed the discovery of new SIMs that have allowed an outstanding increase in the blocking temperature, first from 30 K to 60 K (2017)J and (ii) the barrier height that separates the two components of the bistable ground state.The target features that have commonly been addressed to block spin relaxation are (i) the ground electron spin quantum number ab initio methodologies.ab initio methods impractical when guiding efforts at the lab stage. Thus, searching for new methodologies able to circumvent this computational bottleneck is of paramount urgency. In the case of lanthanide-based SIMs, there already exist affordable semi-empirical approximations devoted to determining the electronic structure,ab initio calculations.The current pursuit of predictive power is encouraging the development of fully Ueff, relaxation pathways and relaxation times τ as a function of temperature. Crystal field parameters (CFPs) are determined by millisecond calculations, and only one CASSCF evaluation is required. The method identifies those vibrations promoting relaxation in order to re-design the given molecule and incorporates, for the first time, a temperature dependence in the spin–vibration coupling matrix elements. Contributions from spin–spin dipole coupling to Ueff and τ can be incorporated by resorting to recent first-principles models.3+ ion,ttt)2]+ of [Dy(Cpttt)2]+, which holds the latest record for the blocking temperature.3 (Tp– = trispyrazolylborate) in order to rationalize its poor performance. The method consists of the following three steps.Herein, we present an inexpensive first-principles method devoted to lanthanide and uranium SIMs, with the aim of evaluating vibration-induced spin relaxation. It allows estimating effective relaxation barriers νj}j, reduced masses {mj}j, and displacement vectors . These determine the 3D-direction in which each atom vibrates around its equilibrium position.The relevant atom set is relaxed until reaching a minimum in its potential energy surface.J + 1 energies, where J is the metal ion ground electron spin quantum number. Then, once the coordinate origin is placed at the metal ion experimental position, the crystallographic coordinates of only the metal-coordinating atoms are introduced in the code SIMPRE; see the ESI.J crystal field Hamiltonian. We apply the Radial Effective Charge (REC) model by varying the magnitude of the effective charges and their radial distance to the metal ion to fit the CASSCF energies;via effective REC parameters. Note that the contribution of the coordinating atoms to the ligand field almost recovers the whole effect of magnetic anisotropy. Nevertheless, one can include non-coordinating ligand atoms if a significant contribution is expected. To reduce computational costs, quite often it will be enough to maintain the same charge magnitude Zi and radial distance contraction Dr in each coordinating atom.We perform a CASSCF calculation on the SIM experimental structure to extract the lowest 2ab initio, but one can avoid the CASSCF evaluation and use the experimental energies if they are available. In this case, the experimental structure used in SIMPRE should be determined at the same temperature as that of the experimental energies. Now, the coordinating atom positions of the relaxed geometry are radially varied with the same fitting distance variations determined using SIMPRE. By using the same obtained charge values, SIMPRE calculates the equilibrium CFPs {(Akq〈rk〉))eq}k,q in Stevens notation. Unlike lanthanides, excited states beyond the ground J multiplet may also influence the low-lying electronic structure of actinide SIMs. Thus, in the case of U3+, to determine the charge magnitude and the radial distance variation, the energy fitting must be replaced by a fitting of the SIMPRE CFPs to either the CASSCF or experimental CFPs. Yet, the energy fitting procedure can be maintained providing SIMPRE is replaced with the package CONDON at the stage when the energy set is determined for each set of CFPs calculated using SIMPRE from the varying Zi and Dr. CONDON contains the excited states beyond the ground J multiplet, and the CFPs must be introduced in Wybourne notation.20This procedure is fully , where ηk is the Stevens coefficient and Ôkq is the Stevens equivalent operator,J + 1 equilibrium eigenstates and energies; see the ESI.3+, the diagonalization is performed in CONDON. The lowest 2J + 1 equilibrium eigenstates obtained using this code are truncated to the ordered basis set {|–J〉, …, |+, …, |+J〉} of the ground } of the ground J multiplet and then renormalized.The diagonalization in SIMPRE of the equilibrium crystal field Hamiltonian , which are also built on the above ordered basis set, account for the perturbation to the equilibrium electronic structure from each vibrational mode j; see the ESI.Akq〈rk〉))j(T) produced in (Akq〈rk〉))eq after activating each mode j. We use a model derived by us elsewhere,Qj:The perturbed Hamiltonians Ĥj allows determining the spin–vibration coupling matrix element allows determining the spin–vibration coupling matrix element 〈i|Ĥj|f〉; see the ESI.; see the ESI.nj〉 = 1/(e = 1/(ehνj/kBT – 1). The procedure to calculate the derivatives (∂2Akq〈rk〉/∂/∂Qj2)eq can be found in the ESI.Thus, each Akq〈rk〉))j would improve the molecular nanomagnet performance.i|Ĥj|f〉 and the transition rate and the transition rate γ smaller, since the perturbed Hamiltonians Ĥj are proportional to Δ(Akq〈rk〉))j. For instance, this could be undertaken by increasing the harmonic frequencies νj of the relevant vibrational modes with proper ligand modification.In any case, proper tuning of the chemical structure aimed at reducing the variations in Δ of being in an eigenstate |i〉. At a time . At a time t + dt the system may make a transition to a different eigenstate |f〉 with a probability with a probability γifdt, either by absorbing or by emitting a vibration quantum. The net difference between the incoming γfipi and outgoing γifpf spin populations equals the change in time of pi. Thus, once the transitions are assumed to be independent, these probabilities evolve as follows:This step is undertaken by solving the master equation, eqn (2),γif and γfi account for the spin population flow between |i〉 and | and |f〉, and their expressions depend on the relaxation process to model. We include two important processes: (i) Orbach and (ii) second-order Raman relaxation; see the ESI., and their expressions depend on the relaxation process to model. We include two important processes: (i) Orbach and (ii) second-order Raman relaxation; see the ESI.via a Zeeman term.The transition rates 3+, have been reported over the past few years as SIMs, although mostly with a poor magnetic behavior.3, Tp– = trispyrazolylborate, where the magnetic ion is directly bonded to nine pyrazole rings in a nearly exact D3h tricapped trigonal prism coordination environment.ttt)2]+, a hypothetical molecule that is analogous to the dysprosocenium SIM [Dy(Cpttt)2]+. In this system, the f-ion is sandwiched between two tert-butyl(cyclopentadienyl) (Cpttt) ligands, and this gives rise to an overall linear coordination geometry that is slightly bent. Recently, a uranium-based SIM with a metallocenium-like ligand set similar to Cpttt has been synthesized and experimentally characterized. This demonstrates the chemical viability of extending this particular family of ligands to uranium.27A handful of actinide complexes, mostly based on Uttt)2]+ and UTp3, we use the ones of [Dy(Cpttt)2]+ and NdTp3 instead.3+, we carry out geometry relaxation and vibrational spectrum calculation in both systems; see ttt)2]+ and UTp3 to obtain {(Akq〈rk〉))eq}k,q. In the case of [U(Cpttt)2]+, this is not possible and we will proceed as explained in the ESI3, we will use the spectroscopic energy scheme to obtain its equilibrium electronic structure; see also the ESISince we lack the experimental structures of [U(Cpttt)2]+, the energy level scheme of UTp3, see 3 presents a heavy mixing between the |mJ〉 components ±5/2 and ∓7/2, and this results in an almost perfect cancellation of the expectation value 〈 components ±5/2 and ∓7/2, and this results in an almost perfect cancellation of the expectation value 〉 components ±5/2 and ∓7/2, and this results in an almost perfect cancellation of the expectation value 〈Jz〉 = ±0.06. This seems to be a generalized feature that results from the combination of: (a) a non-perfect axial coordination geometry, where the ±5/2 and ∓7/2 components are favoured to the detriment of the maximum values ±9/2, and (b) the = ±0.06. This seems to be a generalized feature that results from the combination of: (a) a non-perfect axial coordination geometry, where the ±5/2 and ∓7/2 components are favoured to the detriment of the maximum values ±9/2, and (b) the D3h coordination symmetry, which results in a heavy mixing of levels differing by ΔmJ = 6 (this is precisely the case for ±5/2 and ∓7/2). On the other hand, [U(Cpttt)2]+ also displays noticeable mixing as a consequence of the C1 symmetry, although in this case the axial ligand distribution stabilizes a ground doublet mainly characterized by the component ±9/2 with a weight around 80%. This difference in the electronic structure already means that [U(Cpttt)2]+ should present a better prospect for slow relaxation of the magnetization as compared with UTp3.In contrast with that of + can be seen from their CFP thermal evolution. Indeed, the CFPs of [U(Cpttt)2]+ are almost constant, with variations of up to a few percentage points at most. In contrast, there exists a marked thermal dependence in the case of UTp3, where the relative variations are even two orders of magnitude larger.Once (ttt)2]+, the molecular symmetry is not ideal, meaning no CFPs cancel for symmetry reasons. As a consequence, there are no significant changes caused to geometrical distortions of any reasonable size. This, added to the molecular rigidity that is characteristic of metallocenium complexes, results in a relative insensibility to thermal effects. Since the molecular geometry in this case is quite axial, the B20 parameter remains dominant at all temperatures. The opposite situation happens for UTp3, where the perfect D3h symmetry means many CFPs are cancelled at the equilibrium geometry. Thus, even moderate geometrical distortions cause dramatic relative changes in many CFPs, as indeed is the result of the calculations. In the special case of B66, this CFP is governed by a spherical harmonic of D6h symmetry in such a way that all 9 donor atoms contribute with the same sign. Because the molecule presents an overall C3 symmetry, certain concerted geometrical distortions that result from molecular vibrations couple with an unusually strong strength with this CFP: B66 is at the same time the dominant parameter in the crystal field Hamiltonian and the one with the largest absolute thermal effect. All in all, the dynamical effects coincide with the static picture in discarding the potential as a SIM of UTp3 in particular, and possibly of C3-type U3+ complexes in general.Simple symmetry arguments can be used to give some intuitive meaning to these numerical results. In the case of [U(Cpttt)2]+. Unfortunately, to the best of our knowledge, the uranium-based molecular nanomagnets reported so far in the literature – including UTp3 – do not exhibit slow relaxation of the magnetization above ca. 5 K. This prevents us from applying step 3 to UTp3, since around and below this temperature a very high numerical noise leads to poorly reliable results; see the ESI.In order to illustrate step 3 of the methodology we will now focus on the most promising case, namely +.3In this thermally activated regime, the estimated effective barrier ttt)2]+ effective barrier (293 K) is one order of magnitude below those reported for [Dy(Cpttt)2]+ (1760 K)ttt)2]+ (∼40–50 K) at which the experimental relaxation time is still above the standard experimental detection limit (10–5–10–6 s) is also clearly smaller compared to that in [Dy(Cpttt)2]+ (∼112 K)ttt)2]+ Orbach prefactor τ0 = 3.0 × 10–9 s is two to three orders of magnitude above the ones corresponding to the two Dy-based SIMs .Even employing bis-metallocenium ligands, known to offer a strong axial crystal field in Dy-based SIMs,arrier 29 K is onearrier 29 K is one)2]+ ∼40–0 K at wharrier 29 K is one)2]+ ∼40–0 K at whttt)2]+ Orbach prefactor is among the smallest ones that have been experimentally determined in uranium SIMs.ttt)2]+ reaches several hundreds of kelvin (∼293 K); (ii) by assuming that the thermally activated regime dominates between 30 K and 50 K in [U(Cpttt)2]+, while it is not possible to determine relaxation times beyond ∼5 K,τ ∼ 10–5–10–6 s in the case of [U(Cpttt)2]+ would be found at 40–50 K. Thus, it seems that [U(Cpttt)2]+ is not expected to display hysteresis temperatures that compete with the ones of [Dy(Cpttt)2]+ and Dy-5* SIMs. For instance, in a typical hysteresis loop swept at 2 mT s–1 between –1 T and +1 T, which means to store classical information for 2000 s, a blocking temperature below 9 K would be observed in [U(Cpttt)2]+ according to ttt rings were optimized for dysprosium and may present somewhat different requirements in uranium. However, our methodology is efficient enough to offer a path forward in the rational design of ligands that result in uranium SIMs with optimized performance.Our [U(Cpttt)2]+ vibrations determining the transition rates that drive the relaxation pathways in ttt ring substituents. These rotations could be partially suppressed by replacing the methyl groups (–CH3) with the heavier fluorinated analogs –CF3. A quick inspection shows that there exist similar vibrations promoting relaxation in [Dy(Cpttt)2]+, Dy-5* and [U(Cpttt)2]+. On one hand, rocking deformations of the Cpttt rings where directly bonded hydrogen atoms move towards and away from the metal ion are present in [Dy(Cpttt)2]+ and [U(Cpttt)2]+. On the other hand, breathing vibrations where the two coordinating rings move towards and away from the metal ion are found in [U(Cpttt)2]+ and Dy-5*. The rocking deformations in [Dy(Cpttt)2]+, also found in [U(Cpttt)2]+, were already blocked in ttt)2]+. A possible strategy which has not yet been explored to remove the breathing vibrations could be bonding the two coordinating rings, such as in stapled bis-phthalocyanines. Moreover, the frequencies of the [U(Cpttt)2]+ detrimental vibrations, see the ESI,–1) and the first and second excited doublets (171.7 cm–1); ttt)2]+ performance would also benefit from any structural modification that takes these frequencies out of resonance with respect to these gaps.Let us now analyze the [U2]+ and find that the replacement of Dy3+ with U3+ does not result in an enhanced performance. Yet, [U(Cpttt)2]+ does seem to outperform all previously reported uranium SIMs. One of the critical factors that promote spin relaxation in [U(Cpttt)2]+ is the noticeable mixing among the |mJ〉 components in the equilibrium eigenstates. Importantly, this mixing is also found in previously reported uranium SIMs, components in the equilibrium eigenstates. Importantly, this mixing is also found in previously reported uranium SIMs,ttt)2]+ and Dy-5* even though the ligand coordination is not strictly axial.All in all, the most important conclusions of this work are the following. We have proposed a novel first-principles methodology aimed to simulate vibration-induced spin relaxation in There are no conflicts to declare.Supplementary informationClick here for additional data file.Supplementary informationClick here for additional data file.Supplementary informationClick here for additional data file.Supplementary informationClick here for additional data file.


With two application examples, a digital droplet polymerase chain reaction (ddPCR) and digital droplet loop mediated isothermal amplification (ddLAMP), we demonstrate the compatibility of the droplet production for two main amplification techniques. Both applications show a high degree of linearity , which demonstrates that the cartridge and the droplet generation method do not compromise assay performance.We present a versatile tool for the generation of monodisperse water-in-fluorinated-oil droplets in standard reaction tubes by centrifugal step emulsification. The microfluidic cartridge is designed as an insert into a standard 2 mL reaction tube and can be processed in standard laboratory centrifuges. It allows for droplet generation and subsequent transfer for any downstream analysis or further use, does not need any specialized device, and manufacturing is simple because it consists of two parts only: A structured substrate and a sealing foil. The design of the structured substrate is compatible to injection molding to allow manufacturing at large scale. Droplets are generated in fluorinated oil and collected in the reaction tube for subsequent analysis. For sample sizes up to 100 µL with a viscosity range of 1 mPa·s–4 mPa·s, we demonstrate stable droplet generation and transfer of more than 6 × 10 Water-in-oil (W/O) droplets are widely used for the generation of micro-compartments that find application in various biochemical reactions. The fields of application range from DNA and RNA analysis ,2,3,4 to−3 [−3 [−3 [For off-chip solutions, many different droplet generation systems exist ,18,19,20−3 ) cause t−3 [−3 ) to desc [−3 [−3 ) resultsIn this work, we present an off-chip system that uses centrifugal step emulsification ,16 to geStable droplet generation and transfer is demonstrated for common sample viscosities between 1 mPa·s to 4 mPa·s. Biochemical compatibility of the cartridge is demonstrated with two exemplary amplification reactions, a digital droplet polymerase chain reaction (ddPCR) and a digital droplet loop-mediated isothermal amplification (ddLAMP) reaction.3 (h·w·d), is designed to fit into a standard 2 mL centrifuge tube and consists of two parts: a monolithic fluidic layer and an adhesive cover foil (for detailed description see The cartridge has a size of 33.6 × 7.8 × 3.4 mm1) and sample (Q2). One crucial requirement for droplet transfer out of the cartridge into the tube, is an oil co-flow Q1 to transport the droplets through the outlet channel. In the present cartridge, the maintenance of this oil co-flow is ensured by fluidic design. Both inlets (i and ii) are designed with the same hydrostatic height and are supplied with the same volume. Since the oil has a higher density, the propelling centrifugal pressure is higher for the oil phase. To realize a slower transfer of the oil anyhow, the supply channel for oil supply (iv) is equipped with a higher fluidic resistance than the sample supply channel (ii), as long as the viscosity of the sample remains ≥ 4 mPa·s. Details of the fluidic design calculations and channel and chamber dimensions are listed in The fluidic layer of the cartridge houses six microfluidic elements see b: Inlets2  in order to allow the generation of droplets with a diameter of about 66 µm  gene and a ddLAMP targeting the enniatin synthetase gene of In both application examples, reaction mixes containing the amplification reagents and template DNA were emulsified in the cartridge as described in 2 ≥ 0.994; ddLAMP: R2 ≥ 0.998) and in case of the ddPCR a good concordance to the expected DNA concentrations. This demonstrates that the cartridge does not compromise the performance of the two assays.As visible on the fluorescent microscopy images of the droplet mono layers of the ddPCR see a and the(1)Manufacturing of a master mold by micromachining  in PMMA . Followed by a quality check of the manufactured structures using a confocal microscope .(2)Manufacturing of a positive molding tool in Polydimethylsiloxan (PDMS) by pouring a mixture of Elastosil 607 and Elastosil 675  into the milled substrate and applying centrifugal force .(3)Replication by hot embossing using the manufactured molding tool in cyclo olefin-copolymere (COC) .(4)Manual sealing of the cartridge using a pressure sensitive adhesive film .The cartridge was designed using network simulation-based CAD modeling   which prevents water adhesion at the channel walls.(a)For observation of droplet generation and transfer, a programmable centrifuge  with a modification for stroboscopic imaging  were used.(b)For in-tube droplet generation and collection, a standard laboratory centrifuge  was used.Throughout this work, two configurations for centrifugal actuation were used:Throughout all experiments, fluorinated oil  and gel loading pipette tips . The used pipette tips allow to reach down to the inlet chamber bottom during pipetting, to prevent an air bubble entrapment during inlet filling.The viscosities of the glycerol water mixtures were calculated by following the density model developed by Volk et al. ,34. Mixt−1 hering sperm DNA . For sequence information see The ddPCR reaction mix was prepared using following final concentrations: 1× ddPCR Supermix for probes (No dUTP) , 900 nM primers, 250 nM probe and 4000 nM Alexa 647-fluorophor  for improved recognition of negative droplets. gBlock DNA  was diluted in 0.2× TE buffer containing 10 ng µLFusarium Poae DNA, Leibniz Institute DSMZ GmbH, Braunschweig, Germany) was prepared using low DNA bind tubes  with Ndase/Rnase free water . Each LAMP reaction contained final primer concentrations as follows: 1.6 μM of primers FIP and BIP, 0.4 μM of primer LB and 0.2 μM of primers F3 and B3  was added. Of the complete reaction mix 22.5 µL was transferred to the sample inlet and emulsified using the presented cartridge. After droplet generation, the emulsion was transferred to a 200 µL low DNA bind tubes  and inserted into a thermal cycler . The emulsion was incubated at 63 °C for 40 min.The ddLAMP reaction mix was prepared using 2× LyoLAMP Mastermix containing Isotherm2G DNA polymerase . A background flourophor with a concentration of 4000 nM was added for better droplet recognition of negative droplets . A dilution series of target DNA .Bright field images were recorded with the microscope Observer Z1 , followed by an automated droplet diameter measurement using a custom-made ImageJ-Script  followed by automated droplet readout and counting using the software .Graphs were generated by using the graphing software Origin Pro 9 .5 monodisperse droplets of 66 µm diameter (CV ≤ 4%). Droplet generation rates were up to 1161 droplets·s−1 (depending on sample viscosity), produced into standard reaction tubes by centrifugal step emulsification. With this cartridge, we were able to generate monodisperse water-in-fluorinated-oil droplets over a common range of sample viscosities directly into a standard 2 mL reaction tube. The use of fluorinated oil ensures high biocompatibility and ideal conditions for biochemical assays. The entire encapsulation process runs automatically without the need for further control. Further, no tubing, pressure pumps or any other equipment are required, which ensures ease of use even for inexperienced operators. With respect to biochemical analysis, we demonstrated that the cartridge does not compromise the assay performance of two main amplification methods for digital analysis, namely ddPCR and ddLAMP.In this work, we present a centrifugal microfluidic cartridge for the generation of up to 6.65 × 10As the current design can easily be transferred to injection molding, the next step will allow the mass production of the cartridge making it a low-cost tool for droplet generation. Since the cartridge can be processed in a standard 2 mL reaction tube on standard laboratory equipment, no further investments are necessary.For the current design, samples with viscosities between 1 to 4 mPa·s can be emulsified, which covers a broad range of sample types. For higher viscosities minor adjustments to the fluidic resistances of the supply channels are necessary. The same minor changes can be employed to adjust the droplet size, simply by modifying the nozzle dimensions as discussed previously by Schuler et al. . By impl


Effect Direction MEta-analysis (EDME) to quantify pleiotropy using GWAS of 34 Cholesky-decorrelated traits in 44,000+ cattle with sequence variants. The effect-direction agreement between independent bull and cow datasets was used to quantify the false discovery rate by effect direction (FDRed) and the number of affected traits for prioritised variants. Variants with multi-trait p < 1e–6 affected 1∼22 traits with an average of 10 traits. EDME assigns pleiotropic variants to each trait which informs the biology behind complex traits. New pleiotropic loci are identified, including signals from the cattle FTO locus mirroring its bystander effects on human obesity. When validated in the 1000-Bull Genome database, the prioritized pleiotropic variants consistently predicted expected phenotypic differences between dairy and beef cattle. EDME provides robust approaches to control GWAS FDR and quantify pleiotropy.In genome-wide association studies (GWAS), variants showing consistent effect directions across populations are considered as true discoveries. We model this information in an  Xiang et al. developed an Effect Direction Meta-analysis (EDME) approach to identify true pleiotropy. They used Cholesky-transformation to decorrelate the traits and identified many pleiotropic variants that consistently predicted phenotypic differences in cattle. From this, a p value can be calculated for the null hypothesis that the variant has no association with the trait. Using the p values and the number of significant variants, it is common to calculate a false-discovery rate (FDR)1. However, this conventional FDR depends on the calibration of the p value which in turn depends on the data conforming to the statistical model assumed in calculating the p value.Genome-wide association studies (GWAS) find mutations associated with complex traits. A GWAS produces estimates of the effect of each variant on a trait measured by a regression coefficient Effect Direction MEta-analysis (EDME) for effect direction meta-analysis. EDME is easily extended to calculate the FDR by effect directions (FDRed) for a multi-trait GWAS. This will allow us to know the number of traits that a significant variant is associated with and precisely which traits these are.The important implication of FDR is that true discoveries would be confirmed in a powerful, independent experiment. In this paper we directly use the ability to confirm a finding in an independent study to estimate the FDR by using the proportion of sequence variants which have an effect in the same direction in two independent datasets. We call this FDRed for ‘effect direction’ based on a statistical model we call 3, meta-analysis of public GWAS summary statistics significantly improved our understanding of pleiotropy8. Naturally, traits that are genetically correlated must share part of their causal variants, however, if traits are uncorrelated, can we still detect widespread pleiotropy?Due to the recent availability of many GWAS results with large sample sizes in humans9. After GWAS, we focus on using the information of the consistency of variant effect directions to identify pleiotropic variants associated with uncorrelated traits, instead of distinguishing different types of pleiotropy10. We aim to use: (1) the consistency of variant effects in different populations to evaluate the FDRed independent of their p values; (2) the information on the consistency of variant effects for multiple traits across different populations to quantify pleiotropy at both the variant and trait levels. We propose an EDME of GWAS of 34 complex traits of over 44,000 dairy bulls and cows with over 17.6 million sequence variants. A validation analysis with the 1000-bull genome database confirms the informativeness of pleiotropic variants prioritised by the EDME model.Our study starts with multi-trait GWAS of individual data where the traits are decorrelated by a Cholesky transformation9 to be applied to the 34 traits. The Cholesky transformation decorrelates the 34 traits by ordering the traits from 1 to 34 and correcting each trait for all the traits before it in the list. We use this method because the traits vary in their completeness, i.e., some traits have more records than others. By ordering the traits from the trait with most complete data to the trait with least complete data, we can make use of all the data because the Cholesky transformation of the Kth trait in the list only needs data on the K − 1 traits and individuals with trait K to have data on all K − 1 traits. Thus the Cholesky transformation produces uncorrelated traits and makes maximal use of incomplete data 11. On average at p < 1e−6, 1900 (±813) variants were significant per trait in bulls and 2018 (±795) in cows. The FDR calculated by conventional methods  at p = 1e−6 was 0.22 (±0.045) for bulls and 0.1(±0.021) for cows across 34 CT traits.On average across 34 CT traits, the heritability was 0.42  in bulls and 0.164 (±0.029) in cows  variants that truly decrease the trait value, the ‘true positive’ (T+) variants that truly increase the trait value and the ‘true zero’ (T0) variants with no reliable effects on the trait  was the observed number of variants with inconsistent effect directions (‘+−’ and ‘−+’) and n(B) was the observed number of variants with consistent effect directions (‘++’ and ‘−−’) in GWAS of two different populations. Tr denoted the combined number of T− and T+. Then, the FDR and TDR by effect directions  were calculated as Eqs. We assume that true positives were always observed in the ++ class and true negatives in the −− class and that true zero effect variants have one-fourth probability of being in any of the four classes. This then allowed the calculationsn(A)), the FDRed and conventional FDR averaged across 34 CT traits were compared within a range of p value thresholds imposed in both sexes  at p = 1e−6, to 14(±12) at p = 1e−100  significant variants for both sexes, the single-trait FDRed was 0.032(±0.015) while the conventional FDR was 0.98(±0.015). At the p = 1e−9 level, amongst 408(±213) significant variants for both sexes, the single-trait FDRed dropped to 0 and the conventional FDR was 1.6e−05(±3.4e−06)  Fig. . When imt values of both sexes . For a group of variants, Π values allowed the use of the same logic calculating the single-trait FDRed  was the total number of variants selected.The single-trait EDME was extended to multiple traits (see Methods) to calculate FDRed and quantify pleiotropy. For each variant, the dot product of the vector of signed mentclass2pt{minimTrue Effect (TE) for each variant , As well as this multi-trait estimate of FDR, it is also possible, for each sequence variant, to count the number of traits with the same direction of effect in population 1 (bulls) and population 2 (cows). Allowing for the fact that half the traits were expected to be in the same direction by chance, the EDME logic can estimate the number of traits showing a iant Eq. . While tn(variant), Eq. trait, suggesting pleiotropic variants that affect each trait (illustrated in the following results).The estimated number of TE averaged across a group of variants p value threshold in both sexes  and it dropped to 0 at the p = 1e−6 level where the estimated number of TE per variant was 9.63. That is, the average number of traits affected by a single-nucleotide polymorphisms (SNP) in this group is 9.63. Additional analysis with functional data13 indicated that both single-trait and multi-trait FDRed can help find informative variants at lenient p value thresholds where conventional FDR was large  < 1e−6 from the weighted meta-analysis combining GWAS results of bulls and cows , and their Π values, which indicate the effect direction agreement for multi-trait analysis, were correlated with their conventional FDR based on pwm  (Supplementary Data ZNF613 (Chr18:58.1M) which was close to the CTU1 region (Chr18:57.5M). Variants from the CTU1 region had observed TE on 20 CT traits. Both GC and CTU1 loci were reported as lead dairy cattle pleiotropic loci in the 2017 pleiotropy study9. Other commonly known major loci for dairy cattle (see refs. 16) were also captured, including DGAT1 (Chr14:1.8M) that had TE on up to 17 CT traits, MGST1 (Chr5:93.9M) that had TE on ∼13 CT traits, CSN1S1 (Chr6:87.1M) that had TE on ∼12 CT traits, GHR (Chr20:32M) that had TE on ∼15 CT traits and ENSBTAG00000048091 (beta-lactoglobulin-2-like), a potentially duplicated gene of the adjacent PAEP  that had TE on ∼11 CT traits.The most pleiotropic variants accounting for 0.00003% of the genome with observed TE on 22 CT traits were close to the egion Chr:88.8M (SPC (Chr29:45.6M), coding for the enzyme pyruvate carboxylase which is needed for gluconeogenesis and lipogenesis, had TE on ∼18 CT traits. A pleiotropic locus with TE on ∼12 CT traits was SLC22A6 (Chr29:41.9M) which had reported roles in regulating water metabolism in mammals17. In addition, variants from the X chromosome (chromosome 30) with pleiotropic effects were also identified. Tagged genes included CD40LG (Chr30:20.2M) and ARHGEF6 (Chr30:20.3M), although these variants only affected 2–3 CT traits . Each set of variantstrait was tested for whether the variantstrait had specific associations with the trait that they were assigned to. For each trait, the single-trait FDRed was calculated using the trait-related variantstrait. Such single-trait FDRed (average < 0.1) was much smaller than the single-trait FDRed calculated using those general pleiotropic variants associated with any one of the 34 traits   in the variantstrait related to dairy cattle CT stature (trait 19)  and they had significant sharing of pleiotropic variantstrait amongst themselves, CT milk production traits did not have significant sharing of pleiotropic variantstrait with every other CT trait. Although traits like CT body condition score (BCS) had the least amount of pleiotropic variantstrait, CT BCS had significant sharing of pleiotropic variantstrait with a wide range of other CT traits.Among the 900,820 combinations of trait by variant, we counted the number of variants that affected each pair of CT traits Fig. . Many patrait sharing index, i.e., the number of pleiotropic variantstrait overlapping divided by the number in the union for each trait pair, averaged across the other 33 traits was calculated. As shown in Fig. trait sharing index was used to rank CT traits from ‘influential’ (sharing pleiotropic variantstrait with many traits) to ‘independent’ (sharing pleiotropic variantstrait with few traits). The first trait protein yield was ranked as the most influential trait, followed by other CT milk production traits. The CT type trait Bone (trait 21), the original trait of which indicated the flatness of legbone of the cattle but is negatively correlated with fatness, ranked the fifth for its influence. The last CT trait BCS ranked relatively high for its influence, given its small number of pleiotropic variantstrait. The CT temperament (trait 8) and the overall type  were ranked as relatively independent amongst traits analysed  using variants as instrumental variables implemented in GSMR20 were conducted for 50 raw trait pairs that had the least amount of variant sharing after Cholesky transformation . Raw somatic cell count (SCC) also had some putative causal effects on raw mammary related traits  of these variants were detailed in Supplementary Data IGFBP7 (Chr6:74.5 M)23, DNMT3B (Chr13:62.6M)24, SLC24A4 (Chr21:57.6M)25, SLC37A126 and FTO (Chr18:22.1M)27 which were reported as single-trait or production trait QTL previously. However, there were also many loci not previously reported in cattle, such as intergenic variants tagging MCF2 (ChrX:23M), CTNNA2 (Chr11:54.9M), NSF (Chr19:46M) and KRT14 (Chr19: 42.4M).To the best of our knowledge, we defined the novel pleiotropic variants as those which were outside the ±2 Mb region of the 1181 pleiotropic SNPs with FTO gene had pleiotropic effects on raw fat percentage, milk yield and many raw linear assessment traits, including likeability (Like), rear teat placement (TeatPR) and teat length (TeatL)  already indicated the existence of multiple QTL in this region .Two examples of the less reported pleiotropic loci in cattle are given in Fig. tL) Fig. . Variantion Fig. . To furtits Fig. . This ob31, including KRT9, KRT14, KRT15, KRT16, KRT19, KRT35, and KRT36. Again, cluster analysis indicated the existence of several QTL in this region. The joint analysis showed that selected top variants had a correlated pattern of effects on milk production traits. These same variants had a less correlated pattern of effects on raw traits of SCC, temperament and many raw linear type traits of the mammary gland  93,513 variants prioritised by pwm < 1e−6 alone and (3) a random set of 93,513 variants. Overall, both the EDME with pwm and pwm alone prioritised pleiotropic variants predicted that dairy cattle were genetically better than the beef cattle for dairy traits and the difference in predictions between beef and dairy was generally lowest in the Random set  prediction of the largest advantage in gEBV of dairy over beef cattle  to estimate the FDR and the number of true discoveries. This method does not depend on the exact calculation of p values which depends on a statistical model that may not describe the data exactly.In this paper, we focus on finding pleiotropic variants and identifying the traits that each variant affects using EDME. Our approach differing from other published studies in three respects. Firstly, we use individual animal data rather than GWAS summaries. This is partly out of necessity because few summary data are available for cattle and most non-human species, but also, because some information is lost in summaries, it is better to start with individual data when this is available. Secondly, we use uncorrelated traits by applying a Cholesky transformation to the 34 raw traits. The choice of Cholesky transformation maximises the amount of data used by ordering the traits from the trait with the most complete data to the trait with the least complete data. Each CT trait is the raw trait corrected for all traits before it in this order. Transformed traits are always difficult to interpret but some interpretation of the CT traits is still possible. For instance, survival corrected for milk production traits focusses on reasons for death or culling other than milk production. However, when the number of traits considered increases, CT traits ordered late in the list would have reduced interpretability, but this does not affect the estimation of the multi-trait 11, therefore, the power for detecting lead variants across 34 traits was different between these two populations, as shown in heritability estimates  and dissect pleiotropy. The two types of analysis serve different purposes and data availability in two species.EDME quantifies the number of traits associated with variants in general and with particular variants based on the agreement of variant effect-directions for multiple traits across two populations. This unique analysis provides additional quantities for pleiotropy which fills a gap in our previous methods where only the multi-trait p < 1e−6 in both sexes we estimate that the average number of traits affected per variant (TE) was 9.6 and this supports the conclusion that pleiotropic effects on uncorrelated traits are widespread. This conclusion is also reached by Jordan et al.7 using a different analysis in humans. Widespread pleiotropy was also found by analyses of GWAS of correlated traits in humans8. However, EDME showed that variants varied widely in the number of traits affected from 1 to 22. In general, variants with a large effect on one trait tended to have small effects on many traits  to inform trait biology which is supported by published data18 . Only those bulls’ phenotypes which were based on records from more than 15 progeny were included. Phenotype data of up to 11,923 bulls included 6569 CRV bulls  with phenotypes derived from their Interbull MACE breeding values (https://interbull.org/ib/interbullactivities) degressed on the Australian scale and converted to the scale of the daughter trait deviation. The remaining 5354 bulls and all 32,347 cows were from DataGene. All these animals included Holstein , Jersey (2059 ♂ / 6174 ♀), cross breed (0 ♂ / 2850 ♀) and Australian Red dairy breeds (125 ♂ / 424 ♀).No live animals were used in this study. Phenotype data was based on trait deviations for cows and daughter trait deviations for bulls . Cn was a K (number of traits)×1 vector of Cholesky scores for animal n; L was the K × K lower triangular matrix of the Cholesky factor which satisfied LLt = COV, the K × K covariance matrix of raw scores after standardisation as z-scores, gn was a K × 1 vector of traits for animal n. Cholesky transformation decorrelated all traits at once. However, as a result, the Kth Cholesky-transformed trait can be interpreted as the Kth original trait corrected for the preceding K − 1 traits and each Cholesky-transformed trait had a variance of close to 1 (Supplementary Data 9) and this would result in sample size for all traits being determined by the trait with the smallest number of records, i.e., 1439 bulls and 4086 cows. Another condition required to be met for the current Cholesky transformation was that the same descending order of the selected traits matches between the bull and the cow data sets. This allowed that CT traits were the same in bulls and cows such that the GWAS of one trait in two sexes were comparable.Phenotype decorrelation was conducted using Cholesky transformation, with the formula of mentclass2pt{minim37y = vector of phenotypes for bulls or cows, breed = three breeds for bulls, Holstein, Jersey and Australian Red and four breeds for cows ; bx = regression coefficient b on variant genotypes x; a = polygenic random effects ∼N where G = genomic relatedness matrix based on all variants. The above GWAS model was also applied to estimate the total genomic variance for heritability calculations for all traits, but without including the “bx” term in the model.The 34 decorrelated traits were analysed one trait at a time independently in each sex with linear mixed models using GCTAχ2 statistic for the ith variant was calculated based on its signed t values generated from each single-trait GWAS: 1). ti was a K (number of traits = 34) × 1 vector of the signed t values of varianti effects, i.e., b/se, for the K traits; ti′ was a transpose of vector ti(1 × K); and V−1 was an inverse of the K × K correlation matrix where the correlation was calculated over the all estimated variant effects  of all trait pairs. The χ2 value of each variant was examined for significance based on a χ2 distribution with k degrees of freedom to test against the null hypothesis that the variant had no significant effects on any one of the Kth traits. The conventional FDR of χ2 tests were calculated following1.The multi-trait t values of bull GWAS and cow GWAS results was performed using the formula12). Where tw was the weighted t value for bulls and cows accounting for the phenotypic error differences between bulls and cows11, calculated as the quotient of the weighted variant effects Bw and the weighted effect error sew; bbull and sebull were the variant effects and errors obtained from single-trait GWAS in bulls and bcow and secow were the variant effects and errors from cow GWAS. Once the tw of each trait was obtained, the multi-trait meta-analysis was performed using Eq. 9, where over 630,003 SNPs from the high-density SNP chip panel were used for GWAS with 25 traits in bulls and cows.To fully utilise the GWAS summary data obtained in bulls and cows separately, a weighted multi-trait meta-analysis of the signed p values adjusted (divided) by their functional-and-evolutionary trait heritability (FAETH) score13. Then, variants ranked within the top 10% within each sex were selected for LD pruning, using Plink 1.938 with r2 > 0.95 within 5 Mb windows. For pruned variants, in each 5 Mb window, with the overlapping size of 2.5 Mb, we calculated t values (beta/s.e. from GWAS described above) of 34 CT traits for varianti and variantj; r) measured as the correlation between the genotypes of varianti and variantj. These ρ values were clustered using graph based Random Walks determining densely connected subgraphs (clusters)39 implemented in igraph40. On average there were 12 variants per cluster in bulls and cows. The clustering of the variants aimed at finding groups of variants tagging the same QTL. Normally, variants with strong LD were considered as tagging the same QTL. However, variants tagging one QTL should also show similar effect patterns across multiple traits . Therefore, by adding the correlation of effect t value, i.e., ρij to better group variants tagging the same QTL than using rcor or rLD alone. After clustering, up to 50 clusters were retrieved within each window. To verify if identified clusters can represent local QTL, the top 100 variants from clusters based on their FAETH adjusted multi-trait p value were selected. These 100 top variants were used to conduct a conditional analysis of GWAS37 of 34 traits in each sex. A meta-analysis of the conditional GWAS results used Eq. The use of sequence variants led to a large number of variants in high LD. Consequently, a single QTL might be tagged by many sequence variants. To give an indication of the differentiation of pleiotropic QTL from sequence variants, a sliding-window (5 Mb) variant clustering was conducted. All calculations regarding this clustering were done separately in each sex. Firstly, variants were ranked by their multi-trait Meta-analysis of the conditional GWAS results showed that pleiotropic effects dramatically dropped, but only for those variants from the clusters with which the top 100 variants were selected  variants with ‘true negative’ effects on the trait, i.e., T− variants that truly decrease the trait value, (2) variants with ‘true positive’ effects on the trait, i.e., T+ variants that truly increase the trait value and (3) variants with ‘true zero’ effects on the trait, i.e., the T0 variants that had no effects on the trait. In practice, a GWAS conducted for the same trait in two different populations would have four categories of variant effect directions: (1) the ‘−−’ where the effect was consistently negative for the trait in two populations, e.g., bulls and cows in this study; (2) the ‘++’ where the effect was consistently positive for the trait in bulls and cows; (3) the ‘+−’ where the effect was positive for the trait in bulls but negative in cows; and (4) the ‘−+’ where the effect was negative for the trait in bulls but positive in cows.The R code of EDME can be downloaded from T0 variants which should have no TE, they were expected to be randomly distributed across the four observed categories  of variants. This meant that each one of the four categories of the ‘++’, ‘−−’, ‘+−’ and ‘−+’ variants contain an equal amount of the T0 variants . Therefore, the total number of ‘+−’ and ‘−+’ variants observed was equal to one-half of the total number of T0 variants expected. This then allowed the deduction of model Eq. T0. Once the number of T0 was known, the total number of T− and T+ variants can be determined by equating the expectation with the observed number of ‘++’ and ‘−−’ variants (n(B)) as described in the first and the third quadrant of the right panel of Fig. 2aT0 and Tr were determined, the false discovery rate by effect direction (FDRed) and true discovery rate by effect direction (TDRed) can be calculated based on the total number of variants entered the analysis in the two populations (n(A) + n(B)) as described in Eqs. If there were t values of bulls and cows with the same length of K, where K is the total number of traits. The idea was that the effect direction across multiple traits, i.e., the sign of the Π value, was not driven by the small trait effects which were more likely to arise from noise. Instead, the sign of the Π value was driven by relatively large trait effects which were likely to be robust. Then, the number of variants with negative Π values were used to calculate the multi-trait FDRed in Eq. For equation ti1⋅ti2T , the Π vn(B) that was equivalent to T0) and Tr). As K = 1), the multi-trait Eq. MTR was the multi-trait version of TDRed for Eq. For one variant analysed in K traits across the two populations, the single-trait Eq. R in Eq. , where \entclass1pt{miniman(variant) multiplied by the number of K traits, each one of the total X number  of variants would have K number  of t values. Then, for a total X number of variants by K number of traits, a X × K length  vector of t values can be obtained. If t value  in the X × K vector would be prioritised by Eq. For Eq. X × K TC of trait by variant was achieved, two additional pieces of information can be estimated. One was the count of the traits assigned to each variant in the X × K vector and this was the observed TE for each variant. The other was the count of the variants with positive Π assigned to each trait in the X × K vector and this was the identification of the pleiotropic variants related to each trait, variantstrait. See the online tutorial for using EDME to quantify pleiotropy and to do other related analyses at https://ruidongxiang.com/effect-direction-meta-analysis-edme-of-gwas/.Once a prioritised set of trait in overlaps between 34 CT trait sets were counted. The significance of overlaps were compared with the expected number using the hypergeometric test (p) using the variant-overlap matrices generated by GeneOverlap41 in R. This analysis required four types of counts: the size of overlap between set A  and set B , the size of set A, the size of set B and the size of background . The number of variants in the overlap and in the union of pleiotropic variantstrait between traits was obtained. The number of overlapping dividing the number of the union was used to calculate the sharing index for each trait pair. For each trait, its sharing indices with the other 33 traits (excluding self-pair) were averaged and the averaged sharing index was then used to rank each trait.The number of pleiotropic variantst values  for those 93,513 variants prioritised by p value and multi-trait EDME were used as variant input for GSMR. Settings of MR followed the default options of GSMR, including the threshold of HEIDI outlier test being p < 0.01. Both forward and reverse analysis were conducted. GSMR generated MR p values were corrected for multi-testing by the Bonferroni method. A putative causal relationship was defined as the forward MR was significant and the reverse MR was not significant at Bonferroni corrected p < 0.05 level.This analysis was conducted using GSMRtrait identified by the multi-trait analysis, their single-trait GWAS from bulls and cows were mapped and were analysed for single-trait FDRed using Eq. 18 and their enrichment in each set of variantstrait was tested using the hypergeometric test. The p value of enrichment was adjusted for multi-testing.For each set of variants37 function. The model for the joint analysis was the same as Eq. t value was re-calculated based on the beta (‘bJ’) and se (‘seJ’) generated from the joint analysis for each trait using Eq. t values were presented in Fig. The joint analysis was conducted using GCTA-COJO35) contained the whole genome sequence of cattle independent of the Australian data with no phenotype but with breed information. To perform a validation test without phenotype in the validation population, we used the genotypes of selected variants and 37 raw traits  prioritised by EDME and p value, (2) prioritised by p value alone and (3) a random set of variants with the matching variant number. These 3 sets of genomic prediction equations were generated for each of the 37 original traits  in both the bull and cow data sets. The summary statistics of these 37 raw traits were given in Supplementary Data N = 2334).The genomic best linear unbiased prediction (gBLUP) implemented in MTG2N = 567), Jersey (N = 66), Brown Swiss (N = 148), Finnish Ayrshire (N = 25), Normandy (N = 44), Norwegian Red (N = 24), Swedish Red (N = 16). The 1000-bull beef cattle included Angus (N = 272), Beef Booster (N = 29), Belgian Blue (N = 16), Blonde d’Aquitaine (N = 26), Braunvieh Beef (N = 4), Charolais (N = 128), Hereford (N = 75), Limousin (N = 82), Maine Anjou (N = 5) and Simmental (N = 225). The mean of gEBV of the 1000-bull dairy and beef cattle were compared using a t test. For the t test of each trait between dairy and beef cattle, a t value was calculated as the mean difference (with reference level set to beef cattle) divided by the standard error and this t value was presented in Fig. The dairy cattle in the 1000-bull genome included Holstein N = 56, Jersey Further information on research design is available in the Peer Review FileReporting SummarySupplementary Data 1-12Description of Additional Supplementary FilesSupplementary Information


The nanoparticles are embedded in a dielectric matrix (SiN) which improves the antireflection property of SiN (Herein, we report a theoretical investigation of large photocurrent density enhancement in a GaAs absorber layer due to non-absorbing spherical dielectric (SiO This is caused by suppression of light reflection via high refractive index substrate (famously known as Kerker effect)7. Nanostructures such as NPs with size greater than and/or of the order of incident sunlight wavelength show Mie scattering. Additionally, metal NPs also show plasmonic scattering due to the oscillation of free electrons at metal-dielectric interface8. However, metal NPs face high absorption at the resonance wavelength. On the other hand, dielectric NPs do not show this behavior in a narrow band range9. This have captured the attention of scientific community recently and being investigated widely. Dielectric NPs at the front of solar cells have been demonstrated experimentally15 and theoretically19 with improved device performance. Wan et al.’s TiO2 NPs coated solar cell exhibited ca. 30% enhancement in photocurrent13. Whereas, Ha et al. demonstrated experimentally more than 30% efficiency gain by using SiO2 NPs on a GaAs solar cell14. These NPs were closely packed and worked as an antireflection coating (ARC). The wide-angle improvement was also noticed for the entire visible spectrum. Huang et al. measured the normalized current density of with/without sub micrometer silica (SiO2) spheres coated amorphous silicon (a-Si) solar cells and noticed the enhancement after 40° angle of incidence (AOI)20.Nanoparticles (NPs) are being used extensively in solar cell applications due to its high forward to backward scattering2 NPs are embedded in a dielectric ARC (SiN), also called 21. However, the specular behavior of SiN ARC layer is characterized by Abelès’ famous transfer matrix method (TMM)22. The analytical model is presented in detail elsewhere23. The hybrid ARC made of two-dimensional (2D) array of the SiO2 NPs of equal period in the dielectric SiN matrix bounded with air and a GaAs absorber layer was investigated, as shown in Fig. 24. AOI varies from normal incidence (0°) to 85°. NPs’ surface filling density In this manuscript, we perform an analytical modelling on a structure in which SiOmentclass2pt{minim25. Thin film SiN ARC layer shows high transmittance for the thickness 60–80 nm over a wide range of AOI  because dielectric NPs do not absorb the sunlight in a narrow band spectrum as discussed in the beginning. The weighted solar power transmittance from hybrid ARC (SiO2 NPs + SiN) is shown in Fig. 2 NPs + SiN) show nearly the same behavior for ARC thickness interval 60–80 nm at AOI 0°–40°. Furthermore, the improvement in transmittance from hybrid ARC (SiO2 NPs + SiN) is omnidirectional. For comparison, we also calculated the transmittance for 100% SiO2 thin film layer as ARC which shows a decrease in the transmittance at higher AOI .The ARCs in solar cells are designed to minimize the reflectance and maximize the transmittance across the wavelength range of interest. Figure entclass1pt{minimaentclass1pt{minimaentclass1pt{minimaentclass1pt{minimaentclass1pt{minimaentclass1pt{minima27. Operating wavelength is taken from 300 to 870 nm because GaAs absorbs the sunlight in this wavelength range. We assumed that all the photons which reaches to the GaAs layer, got absorbed; hence 2 NPs + SiN) at the surface filling density 2 NPs + SiN) structure till 45° AOI, and after that the curves split  structure comparing to the SiN ARC. We also plotted 2 NPs + SiN) at 2 NPs + SiN) at In the solar cell application, photocurrent density mentclass2pt{minim28. The GaAs layer is assumed to face due south in the Northern Hemisphere, or due north in the Southern Hemisphere. We compared the normalized photocurrent density at two different tilt angles cases for the given location: optimum tilt angle29 and 45°. The sun position calculation was done with a freely available MATALB code30. The improvement in hybrid ARC is clearly noticed at every location. The change due to hybrid ARC is more when the tilt angle is far from the optimum tilt angle  at normal and non-normal AOI. In our device structure, the vicinity is filled with dielectric SiN host medium. At normal incidence, both the thin film SiN ARC and SiO2 NPs show approximately equal 23. As a result, enhancement in 2 NPs + SiN) case  improves the photocurrent density in a GaAs layer at higher AOI. We obtained more than 100% enhancement in the photocurrent density at 85° AOI. Sunrise to sunset calculation of the normalized photocurrent density have also shown improvement in the hybrid ARC case. In future, solar cells integrated into buildings, cars, etc. might become more important. In these cases, the panels are typically not oriented toward the sun and they have to deal with AOI far from the normal incidence. Conventional In summary, we performed an analytical study which suggests that a combination of 23 which is a combination of Transfer matrix method (TMM), Dipole model and Mie theory. A self-generated MATLAB code is used to solve Mie theory for the scattering efficiency of metal and dielectric NPs. Using the dipole model, an angular distribution of dipole radiation by a NP in the neighboring substrate is obtained which is later used to calculate the total diffuse scattering (reflected and transmitted) by a NP. The total transmittance is calculated with a linear summation of specular transmittance and diffuse transmittance in which the specular transmittance is calculated with the TMM method and the diffuse transmittance is calculated by the diffuse scattering of NPs.The simulation study is performed using an analytical model30.Assuming a perfect absorber layer (IQE = 1) based solar cell device, the transmittance obtained from the analytical model is used to calculate the photogenerated current density. For the angle of incidence (AOI) of the sunlight on a solar cell surface, the sun’s position is calculated by a freely available MATLAB code