Antifreeze Proteins (AFPs) inhibit the growth of an ice crystal by binding to it. The detailed binding mechanism is, however, still not fully understood. We investigated three AFPs using Molecular Dynamics simulations in combination with Grid Inhomogeneous Solvation Theory, exploring their hydration thermodynamics. The observed enthalpic and entropic differences between the ice-binding sites and the inactive surface reveal key properties essential for proteins in order to bind ice: While entropic contributions are similar for all sites, the enthalpic gain for all ice-binding sites is lower than for the rest of the protein surface. In contrast to most of the recently published studies, our analyses show that enthalpic interactions are as important as an ice-like pre-ordering. Based on these observations, we propose a new, thermodynamically more refined mechanism of the ice recognition process showing that the appropriate balance between entropy and enthalpy facilitates ice-binding of proteins. Especially, high enthalpic interactions between the protein surface and water can hinder the ice-binding activity. AFPs lower the freezing temperature and slightly increase the melting temperature of water13. Therefore, these proteins are called thermal hysteresis proteins. The cryo-protection ability of those proteins also makes them interesting for industrial use like cryopreservation15, ice cream production16, frozen food storage17, and deicing18. Their structural variety indicates different evolutionary origins, whereby the specific face of the protein binding to the ice crystal, the ice-binding site (IBS), is similar for most of these proteins. The IBS is usually a rather apolar surface19 formed typically by threonine residues and, to a smaller extent, by other apolar amino acids (AAs) like valine (VAL), glycine (GLY), and alanine (ALA).Antifreeze Proteins (AFPs) are a structurally diverse class of proteins helping a variety of organisms, 20, ice-etching studies20, as well as structure determination methods like X-ray crystallography22 and NMR23. These have resulted in the currently accepted theory, stating that AFPs act by binding to the growing ice crystal19. This is remarkable and unique, as the protein’s natural solvent as well as ligand is water itself: in the liquid state acting as solvent, in the frozen state as ligand. Consequently, the binding of AFPs to ice-nuclei is likely one of the most challenging recognition problems posed by nature24.In order to understand how AFPs are able to prevent freezing, a variety of experimental methods have been applied to this protein family. The techniques include mutation studies27. The second step of this process, the inhibition, can be explained quite well with the principle of the Gibbs-Thomson (Kelvin) effect and is very well described in the literature28. In essence, the attached proteins force the ice surface to grow in a highly curved surface, resulting in a freezing point depression. Unfortunately, the adsorption mechanism is still not understood in detail28.AFPs prevent freezing by adsorbing to the growing ice crystal and subsequently inhibiting further ice growth31. They highlighted that the distances between regularly spaced residues at the IBS, or “active” site of an AFP, are comparable with the distances found between oxygen atoms in ice crystals31. This was also confirmed by subsequent reports and is still believed to be one of the key properties of IBSs33. Experimental observations confirmed this behavior, as AFPs were found to preferably bind to one specific ice site matching these IBS criteria34.Computer investigations based on experimentally obtained, three-dimensional structures have been performed for an atomistic view on this problem. The first computational studies focused on the shape of the IBSvia hydrogen bonds as sketched in Fig. 36. The proposed mechanism was rejected soon, as experimental studies showed that the OH groups of the IBS only have a negligible role for ice-binding38.Nevertheless, not only the correct shape, but also the adequate interactions of the protein with ice and water play a significant role. Initial studies focused on the enthalpic part of the binding process and suggested that AFPs bind directly to the growing ice crystal 39. The enthalpy gain strongly depends on the positions of the hydrogen bond donors and acceptors. Still, for most IBSs the number of hydrogen bonds formed between the protein and liquid as well as between the protein and solid water is similar40. For this reason, a correct enthalpic fit of the protein surface might not be, as previously proposed, the only prerequisite to be fulfilled41. It was assumed that for AFPs the enthalpic interactions contributions for protein/ice and protein/water are similar43. This means no enthalpy is gained when the AFP binds to ice, and would render the concept of the enthalpy as the only driving force for ice recognition obsolete.Later on, several authors investigated the enthalpy gain upon binding of different AFPs to various crystallographic ice planes44. Therefore, simulations of AFPs already in contact with the ice surface might not reveal the full story of AFP binding. Sönnichsen et al. suggested that solvated AFPs contain entropically unfavorable water molecules bound to their surfaces. When the protein binds to ice, these water molecules are released into bulk, which results in an increase of entropy and therefore in a free energy gain , rather than the protein diffusing through the ice-water interface and then binding to the ice (diffusion controlled)33.Conversely, Molecular Dynamics (MD) simulations showed that the residence time of water molecules around the IBS is too long for them to be removed upon ice-binding. Instead, they mediate the binding between ice and proteinace Fig. 33,42. In49 and AFPs in liquid water51. Most of these more recent simulations focused on order and structure of the water molecules in the environment of this protein family52. It was shown that the pre-ordering of water in the first hydration layer is similar to structures found in various ice crystals50. Nevertheless, whether solely the first hydration layer is significant, or if ordering extends to higher layers, is still discussed controversially54. Typically, water molecules around AFP surfaces are less dynamic (higher ordering), compared to inactive surfaces46. Modig et al., however, found that the mobility of water molecules around AFPs is similar to proteins with no antifreezing activity55. The partial contradiction between these studies already suggests that the dynamics of the water molecules do not suffice to explain the mechanism of ice-binding for AFPs. Other properties like the hydrophobic or hydrophilic character of the surface might also be decisive47.The proposed mechanism of ice-like water molecules was further investigated and refined by analyzing the dynamic behavior of water from simulations of AFPs with growing ice crystals56.Although all these studies are partly contradictive, they sharpened our understanding of the general ice-binding mechanism. Nevertheless, a full, coherent explanation is still missing. Especially, the question whether or not the pre-ordering is the main and/or only driving force remains to be answered. Additionally, it is an open question why AFP surfaces do not consist of charged residues in a regular shape, as those AAs would increase the order of the water structure in comparison to the relatively apolar AAs often found in IBSsThis study combines the early idea of a significant enthalpy contribution with the more recent theory of the pre-ordering in the hydration shell, proclaiming an entropy gain upon binding to be the driving force for binding. We show that neither the pre-ordering nor the enthalpy alone can be used to explain the ice-binding ability of AFPs. Instead, we point towards the importance of balance between entropy, as indicator of the pre-ordering, and the enthalpy.43, they can influence the ability of ice-binding significantly.To achieve this, we investigated the mechanism of AFP ice-binding from a more thermodynamic angle. Entropic and enthalpic contributions in the hydration shell of three different AFPs (from winter flounder (wfAFP), spruce budworm (sbwAFP), and mealworm (mwAFP)) were analyzed. By investigating three proteins of this structurally diverse family, we identified properties typical for the hydration shell of ice-binding proteins and their active sites. As known from drug design, the solvation and desolvation of binding sites can play an important role. Although the protein’s hydration shell is not removed, the hydration still changes from liquid water to ice. The energetic difference between ice growing towards an AFP Fig. : bottom 57. Furthermore, the grid-based approach of GIST allows investigating thermodynamic properties of water molecules with a spatial resolution. This permits evaluating the thermodynamics of single protein sites, helping to reveal why AFPs are able to detect ice in an excess of water.MD simulations of three AFPs in combination with Grid Inhomogeneous Solvation Theory (GIST) were used to study the hydration of AFPs. Inhomogeneous Solvation Theory has already been proven to be a valid approach to study the thermodynamics of water molecules surrounding proteins and peptidesTo obtain an overview of the hydration thermodynamics around the three investigated AFPs, five representative, restrained conformations of every AFP were simulated and analyzed with GIST. To obtain free energy, entropy, and enthalpy values for the IBSs and the remaining protein surfaces, the contributions of all water molecules (grid points) in a rectangular layer with a thickness of 10 Å were summed up for three different AFPs (from winter flounder (wfAFP), spruce budworm (sbwAFP), and mealworm (mwAFP)), a cylindrical sector with a leg length of 10 Å was used. The acquired values describe the average thermodynamic contributions to the hydration pertaining to the respective protein surface. Mean values of the five conformations and the corresponding standard deviations for every protein site are given in Table cf. Table All IBSs show less negative values for the total free energy of solvation than the NIBSs  than those surrounding the NIBSs . For mwAFP, the total entropy values are similar for the IBS  and the NIBSs . This already indicates that entropy alone is likely not a good indicator of ice-binding activity. IBSs consist of relatively apolar AAs 19 in contrast to NIBSs. These AAs show higher hydration entropies (lower order) in free solution than charged and polar AAs56. This further supports our conclusion that besides the entropy other factors are of major importance for ice-binding activity, too, as otherwise IBSs should consist predominantly of the most apolar AAs e.g. PHE, TRP.The entropy of the water molecules can, in a first approximation, be correlated to their order within the hydration shell. As most of the more recent studies focused on the entropic part of solvation (pre-ordering of water molecules)In contrast to the entropic contributions, Table 60. While for the IBSs entropy/enthalpy ratios between 0.43 and 0.53  than for non active surfaces .In contrast to other studies suggesting that the long-range order is significantly higher for IBSs than for other proteinsSW) lower than −6.0 kcal/mol  plotted. Hence, a water molecule shown in both plots corresponds to a water molecule with low (unfavorable) entropic interaction but also with strong enthalpic contributions. While the number of entropically unfavored (ordered) water molecules is similar for all protein surfaces, the number of strongly bound water molecules is significantly lower for the IBS (#9) compared to the remaining surfaces (#17–18). Furthermore, the IBS has more water molecules with unfavorable entropy values without enthalpic compensation , whereas for the other surfaces fewer according water molecules can be found (#5–7). Similar trends are also observed for the other AFPs (sbwAFP and wfAFP). The orientations of the sidechains differ between the clusters, but have no significant influence on the obtained solvation thermodynamic results. However, a regular arrangement likely is an additional requirement for ice-binding activity61.Further insight can be gained when instead of the overall entropic or enthalpic contributions of all water molecules close to one protein site, the thermodynamic properties of single water molecules are investigated. Therefore, all water molecules with an entropy term (TΔS) lower than −2.5 kcal/mol Fig.  right tomol Fig.  left in 47. In accordance with results obtained for the three different, original AFPs, similar trends were found for the mutations as shown in Table To further confirm the observed trends, experimentally tested mutations of the AFP of the winter flounder were investigated. The four THR  were changed to four serine (SER) (Mutation SSSS), ALA , or VAL (VVVV) residues. The SSSS modification shows no antifreezing activity at all, whereas the mutants AAAA and VVVV show slightly decreased antifreezing ability compared to the naturally occurring form (TTTT)SW) cutoff was set to −3 kcal/mol/water molecule - as the protein is smaller and therefore allows for an inclusion of more water molecules. The entropic (TΔS) cutoff value is set to −2.5 kcal/mol/water molecule. Again, the number of strongly interacting water molecules is higher for SSSS (#20) than for all other forms (#16–17), whereas the number of entropically ordered water molecules is similar for all proteins (#10–13).Similar to the analyses for the three, naturally occurring AFPs, it is possible to examine the properties of single water molecules. Again, all enthalpically strongly interacting water molecules in close proximity to the two THR residues  are shown as red spheres Fig.  left, al62. Secondly, the water molecules need to form an ice-like structure around the protein, which has been discussed extensively in studies on the pre-ordering and dynamics of water50. As all interactions between the protein and the rigid ice surface can also be formed between the protein and the flexible water molecules of the liquid phase, the binding enthalpy cannot be the driving force for the ice-binding process. Therefore, the entropic gain upon binding and/or the enhanced ice formation between the ice-like surface of the protein and the ice-surface are responsible for the ice-binding process to be energetically favorable. Surprisingly, our study could not find lower entropy values (higher order) in the IBSs compared to NIBSs. In agreement with studies by Modig et al., we find that IBSs do not show more pronounced long range hydration effects compared to other protein surfaces55. This strongly suggests that other forces also play a significant role. As the free energy, consisting of enthalpy and entropy terms, is the driving force for all chemical processes, it seems obvious that enthalpic interactions, although they are similar for protein-water and protein-ice, can have an impact on the ice-binding ability. Enthalpic interactions were more recently paid less attention to in the analyses of AFPs, for it was found that interactions between protein and ice are similar to those found in IBSs and water40. We, however, reveal that the enthalpy gains are significantly lower for IBSs than for other protein sites. On one hand, this is not surprising as the IBSs are more apolar than other protein surfaces. On the other hand, typically not the most apolar AAs are found in IBSs. The necessity for a perfect match between enthalpy and entropy in combination with the correct geometry is thus indicated. Our studies focus on the hydration properties of the AFPs and derive conclusions from this pre-ice-binding state . The enthalpic interactions describe how strong a water molecule is bound to the protein surface. Therefore, if the protein-water interactions are strong, water molecules cannot leave their positions. One can imagine such a water molecule as being attached to the protein through a stiff, rigid spring. In contrast, when a molecule is only weakly bound, it is very likely able to move without a large enthalpic penalty . We can picture this as a water molecule attached to the protein surface with a flexible spring.The water molecules in the first hydration layer are bound to the surface of the solute This model can now be combined with the already established hypothesis of ice-like water molecules forming the first hydration shell, adding a more detailed explanation of the recognition and adsorption step. Water molecules in the first hydration layer form ice-like structures around the IBS. This ordering of water is not as perfect as in ice  are often found in AFPs.Our proposed mechanism also explains why at the NIBSs of AFPs very often charged residues are found. Instead of just increasing the hydrophilicity of the molecule, they also prevent further ice growing by the mechanism proposed and, therefore, prevent the protein from being completely coated by ice. Furthermore, our study explains why not the most hydrophobic residues are found in IBSs. These residues would have low solute water enthalpic interactions, favorable for the ice-binding, but they do not sufficiently pre-order water in their hydration shell. Therefore, we propose that the balance between entropy and enthalpy has to be within a precise range for an IBS. Very hydrophilic surfaces (e.g. charged amino acids) induce strong ordering in their surroundings, which is favorable for ice-binding, but also impose too strong enthalpic interactions hindering the process of ice-binding. Too hydrophobic surfaces on the other hand, show low enthalpic interactions with water but are not able to order the hydration layer ice-like64. Whereas ice-nucleation, at first glance, does not seem to be the best example to compare the AFPs’ behavior to, it is very likely that the mechanisms of these processes are very similar. Dolev et al. and Koop et al. already suggested that AFPs are very similar to ice-nucleation proteins (INPs), only differing in terms of protein size, or the size of the active site, respectively66. Small ice-binding proteins are good AFPs and show ice-nucleation activity only at very high concentrations67, whereas large INPs show nucleation activity at relatively high temperatures (−5 °C) but can also act partially as AFPs68. Additionally, Qiu et al. reported that the ice nucleation ability for alcohol monolayers is much better than for monolayers of acids of the same chain length, which agrees with our proposed mechanism. The interaction energies of acid functions are much higher than for alcohol groups and also the lattice mismatch is larger56. Interestingly, the group found that the ice nucleation ability increases with the interaction energy between the alcohol groups and the water molecules62. This might have multiple origins: Firstly, the optimal conditions, e.g., enthalpic interactions between water and solute, may be slightly different for AFPs, INPs and other ice nucleating agents, since AFPs could be more apolar than ice nucleating substances. Secondly, Qiu et al. only observed the increased nucleation ability at a perfectly matching surface; the effect may be different when the nucleus structures do not have a perfect ice-shape, such as the AFP surfaces investigated in this study. At these AFP surfaces, waters are only ice-like, their orientations differ from that of perfect ice and they have to rearrange to fit to the ice lattice. In nature, almost no materials are perfectly ice-shaped. For a perfect ice-shaped substrate these rearrangements are not required and mobility of the water molecules would hinder the ice nucleation ability of the material. Thirdly, we used an all atom force field in this study, which in general should describe the investigated structures in more detail.A similar observation for a related chemical substance was reported by Michaelides and coworkers: They found that the hydrophobicity of a surface has to be in the correct range to show ice-nucleation activityet al. for K-feldspar69. Due to thermal fluctuations, water can rearrange to form an ice-nucleus. Similar to AFPs, when the enthalpic interactions are too strong, these rearrangements are limited, whereupon no ice-nuclei can be formed  support ice-binding, whereas different coating might help to prevent freezing at critical surfaces.Contributing an additional piece of enthalpic interactions to the already proposed mechanism of the ice-like water and entropy gain hypothesis, we were able to fine-tune the hitherto given explanation of the mechanism. Most notably, we added a further step to the proposed path, explaining why amino acids with strong solute-water interactions, like charged residues, are not able to bind to ice surfaces. This is in concordance with the studies of Qui 73, ice-adhesion proteins74, and other ice-nucleating agents75. Our investigations thus help to understand the mechanism of ice-binding, an indispensable prerequisite for the design of antifreezing agents (e.g. lacquers for planes) and ice-nucleating materials (e.g. additives for snow cannons) but also for understanding processes during cloud formation.The results presented can also be applied to the mechanisms of other ice-binding proteins like ice-nucleation proteinsAMBER software package. X-ray single-crystal structures  were used as starting points. In the case of sbwAFP and mwAFP, two residues were not resolved in the crystal structures. Instead of these two AAs, capping groups  for sbwAFP and C-terminal N-methyl (NME) for mwAFP) were introduced. All mutations introduced to obtain the crystal structures were back-mutated to the naturally occurring form. wfAFP was, in addition to its naturally occurring form, also simulated in three mutated forms. For the mutants, the crystal structure 1WFA was used, too. Four THR residues  were transformed to VAL, ALA, and SER accordingly. All proteins were solvated in an octahedral box using the AmberTools package with a minimum distance between the box edge and the protein of 12 Å78. The protein force field ff14SB79 was used in combination with the TIP4P-200580 water model. TIP4P-2005 was chosen as it allows to reproduce properties of water molecules in the liquid as well as the solid state81. Furthermore, TIP4P-2005 shows a reasonable freezing point of 252 K, close to the experimentally measured value of 273 K. After solvation, the proteins were equilibrated according to a protocol developed by our group82. The protocol includes an intensive pre-equilibration of water, before the solute atoms can move. This prevents the artificial closing of protein pockets where no crystal water molecules are resolved. After equilibration, the proteins were simulated for 200 ns without restraints. A time step of 2 fs was used and coordinates were saved every 10 ps. To keep the pressure at 1 bar, an isotropic implementation of the Berendsen barostat was used83. To obtain more diverse structures, the temperature for the unrestrained simulations was set to 300 K for the AFPs from spruce budworm and mealworm via a Langevin thermostat84. For the winter flounder AFP, the temperature had to be set near the freezing point of the TIP4P-2005 water model (260 K), as otherwise the α-helical structure would have been degenerated.AFPs from the winter flounder (wfAFP), spruce budworm (sbwAFP) and mealworm (mwAFP) were simulated using the 85. Five clusters obtained thereby were chosen, for the investigated proteins are rigid , making a number of five adequate. The clusters were solvated and equilibrated, again according to the same protocol, but with coordinate restraints for the entire protein as required by GIST86. Every cluster was simulated for 100 ns; coordinates were saved every 100 ps for the GIST analysis. For the cluster simulations, a temperature of 260 K, close to the TIP4P-2005 freezing point, was chosen, as this is the temperature where the protein is active.Five representative conformations for each investigated AFP were obtained using a hierarchical agglomerative (bottom-up) clustering approach on these unrestrained MD simulations87.The concept of GIST is briefly outlined in this section. For a more detailed discussion of the theoretical background we refer to respective publications of Gilson and co-workersSolv(q). As restricting the solute to just one conformation is a rough simplification, multiple GIST calculations can be used to estimate the free energy of solvation of a flexible solute ΔGSolv by summation (eq. q) corresponds to the probability to find the solute in conformation q. In this report, multiple possible conformations of the solute were accounted for by running unrestrained simulations of the proteins. Afterwards, the trajectory was subsequently clustered in five representative conformations. The five clusters were then simulated individually with positional restraints as required by GIST.GIST aims at calculating the free energy of solvation for a fixed solute ΔGtion eq. .2\documeGIST allows to split the free energy in multiple enthalpic and entropic contributions as shown in eq. SW, and the interaction between the water molecules ΔEWW. The solvation entropy consists of a translational ΔStrans and an orientational part ΔSorient, covering the entropy of the water molecules. All terms depicted in eq. SW, ΔStrans, ΔSorient are zero.The free energy is divided into two enthalpic and two entropic terms. The enthalpic terms cover the interaction energy between the solute and the water molecules ΔEIn addition, GIST uses a grid-based approach, which allows to obtain a spatial resolution of the solvation properties around a solute. This permits the investigation of the thermodynamic contributions to different protein sites.The GIST output can be further processed to determine the structural properties of water on different protein surfaces. For further analysis, structural motifs of the different proteins were used. We made a distinction between the protein sites binding to ice and sites exposed to liquid solvent after binding, which are called “non ice-binding sites” in the following.α-helix only, making it a “quasi-cylindrical” system. Therefore, the surrounding water was divided in four regions . For all other regions, the radius was set so that the same number of water molecules was analyzed as for the IBS region . Similar approaches were used for sbwAFP and mwAFP, however, the minimum distance to the plane, defined by the backbone atoms of the AAs building the surface, was used instead of the minimum distance to the α-helix. Again, the number of water molecules within a 10 Å layer of the IBS was used as reference value for all other regions. For sbwAFP and mwAFP different combinations of length and width for the integrated regions were tested, whereby the qualitative results remained the same. The reported values correspond to a base area of 14 × 14 Å2 for sbwAFP and 20 × 10 Å2 for mwAFP.The water properties in the colored regions were analyzed for all three proteins. For the blue circle segment of the wfAFP, the radius was set to 10 Å (from the center of the 90.An approach based on highly occupied water positions was used to identify water sites of special interest close to the protein surface. Subsequently, the density of one water molecule was subtracted from the highest occupied grid point and its surrounding points and a water molecule was placed at this position. This results in a visualization of the most probable water positions and their corresponding thermodynamic values. A more detailed explanation of how these water positions were derived is given in our respective previous reportThe datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.


The West Antarctic ice sheet (WAIS) is highly vulnerable to collapsing because of increased ocean and surface temperatures. New evidence from ice core tephra shows that subglacial volcanism can breach the surface of the ice sheet and may pose a great threat to WAIS stability. Micro-CT analyses on englacial ice core tephra along with detailed shard morphology characterization and geochemical analysis suggest that two tephra layers were derived from subglacial to emergent volcanism that erupted through the WAIS. These tephra were erupted though the center of the ice sheet, deposited near WAIS Divide and preserved in the WDC06A ice core. The sources of these tephra layers were likely to be nearby subglacial volcanoes, Mt. Resnik, Mt. Thiel, and/or Mt. Casertz. A widespread increase in ice loss from WAIS could trigger positive feedback by decreasing ice mass and increasing decompression melting under the WAIS, increasing volcanism. Both tephra were erupted during the last glacial period and a widespread increase in subglacial volcanism in the future could have a considerable effect on the stability of the WAIS and resulting sea level rise. Understanding the link between glacial cycles and volcanism has been a topic of recent research focus9, but much remains to be learned on this topic. The delicate balance between ice loss of the WAIS and the potential increase in volcanism, due to increased decompression melting because of ice loss5 could cause a positive feedback mechanism that could increase sea level significantly in the future10. Subglacial volcanism could also produce a large amount of basal ice melt that would help lubricate the base of WAIS, causing an increase in ice flow, such has already been speculated to have occurred at Pine Island glacier in the past11.The West Antarctic ice sheet (WAIS), a large and unstable marine-based ice sheet, is highly vulnerable to accelerating ice loss caused by erosion of buttressing ice shelves by upwelling warm ocean water12, or are completely buried beneath the ice13  whereas the East Antarctic ice sheet is largely grounded above sea level. The WAIS overlies the volcanically active West Antarctic rift system (WARS) and a number of volcanoes protrude through the ice sheet2, young tephra layers have been observed using radar in the Hudson Mountains11 and an ice depression at subglacial Mt. Casertz15, where seismic activity has also been observed16 and has been interpreted to be related to subglacial volcanic activity. However, all of these studies rely on some type of remote sensing, and none were able to directly investigate the physical products of subglacial volcanism. Here, we present the first geochemical and volcanological evidence of subglacial volcanism occurring beneath WAIS obtained directly from associated tephra layers. Furthermore, X-ray micro-computed tomography (μCT) of in situ particles in ice-bound tephra layers allows a 3-dimensional view of the distribution and grain size of particles in three distinct and coarse tephra layers from the WAIS Divide ice core (WDC06A). This is the first time volcanic particles in ice have been imaged to see how particle shape and size vary with depth in the ice core, and this may prove to be a useful tool to help understand and characterize the eruptive history and tephra deposition processes. Based on geochemistry, as well as particle size and morphology, two of these layers, which have ice core ages of 22.3 and 44.8 ka  images were collected using an accelerating voltage of 15 kV, and a probe current of 0.5 nA. Glass analyses were carried out using a 15 kV accelerating voltage, 10 nA probe current, and defocused beam in order to avoid mobilization of Na during analysis. Details of quantitative analysis protocol can be found in Iverson, et al.17.At New Mexico Tech, tephra from the layers was recovered by melting the ice, filtering the meltwater and then mounting the samples for imaging and quantitative analysis using the methods of Iverson, Ice core samples (approximately 3 × 3 × 3 cm each) containing the same tephra layers were shipped at −20 °C to the Ice Research Laboratory at the Thayer School of Engineering at Dartmouth College, where they were stored at −30 °C until μCT analysis. Each sample was quartered  to allow for triplicate sub-sampling of the ash layers. Once cut, each subsample was scanned using a Bruker Skyscan 1172 desktop μCT housed in a −10 °C cold room. The Skyscan 1172 X-ray source produces a fixed conical, polychromatic beam with a <5 μm spot size, an accelerating voltage of 60 kV and a current of 167 μA. Samples were rotated 180° in 0.7° steps, while the X-ray attenuation images were captured by an 11Mp, 12-bit cooled CCD camera fiber-optically coupled to a scintillator.® software that uses a modified Feldkamp cone-beam algorithm to produce a vertical stack of gray-scale cross-section images. The resulting images had a spatial resolution of 15 μm, and selected an internal volume of interest measuring 12 mm × 12 mm in the horizontal plane, with vertical heights varying dependent upon the thickness of the ash layer. Image post-processing was performed using a thermal drift correction of the X-ray source, ring artifact reduction, post-alignment correction, beam hardening correction, and a two-pixel Gaussian kernel smoothing to reduce noise.Reconstruction of the resulting radiographs was completed using a Bruker Skyscan’s NRECONA histogram shape-based approach was used to set critical thresholds, enabling us to segment the tephra particles from the gray-scale images. Particles smaller than 27 voxels (cube measuring ~45 microns on edge) were considered noise and excluded from further analysis. Individual three-dimensional analysis was performed on the resulting particles. Statistics were measured on both particle size and particle shape .18, whereas a minority of the large shards are very fluidal, indicative of eruptions driven by magmatic volatiles, and not impacted by external water  are interpreted to be from local volcanoes, probably within a few hundred km from the drill site, based on the large, blocky particle size and their unique chemical composition30, whereas the mossy and blocky particles would be more typical of phreatomagmatic eruption style31. In comparison, observations of many other tephra layers found in the WDC06A core are fine grained (<50 μm) and comprised mostly irregular shards 20–30 μm in diameter17. Phreatomagmatic eruptions can produce co-erupted magmatic and phreatomagmatic tephra32, but if that were the case for these tephra layers, there would be large irregular shards throughout the entire deposit. Instead, there are bands of large irregular shards mixed with smaller blocky fragment followed by band of primarily smaller blocky fragments , which is consistent with observations made at Icelandic volcanoes that have undergone both magmatic and phreatomagmatic phases during a single eruption  concentration in the glass. Sulfur is a volatile component that fractionates into the Hion Fig. 38. The v39. Based on this information, a tephra load of .01 g/cm2, which would represent a fine dusting of tephra, was calculated to be present 30 km from vent. At the other end of the explosivity spectrum, the 1875 rhyolitic eruption of Askja Volcano produced around 2 km3 of tephra in a series of eruptions with Plinian, subplinian, and phreatoplinian characteristics40. Based on detailed mapping, 5 mm of tephra was present 150 km from the vent, along the maximum dispersal axis for the phreatoplinian part of the event35. Given that Tephra A and C in the WDC06A core are likely to be derived from eruptions intermediate in explosivity between these two end members, it is unlikely that the deposition site sampled by the WDC06A core was no more than around 200 km from the eruptive vents. In comparison, the 2010 eruption of Eyjafjallajökull, deposition thickness of >1 cm were found only within 100 km of the edifice41.Finding an exact analog to use to understand tephra dispersal for the eruptions that produced the two tephra layers found in the WDC06A ice core that we argue may have a begun as subglacial events, is challenging. However, two well-studied Icelandic analogs are presented here. The first is the 2004 subglacial to emergent eruption of the Grimsvotn volcano. Because the Grimsvotn eruption was basaltic, it is likely to have been somewhat less explosive than the eruptions that produced the two subglacial to emergent WDC06A tephra layers. Albedo changes in the ice cap surface, measured by MODIS, were attributed to tephra deposited on the ice sheet from the Grimsvotn eruption13. Mt. Thiel is the closest subglacial volcano to WDC06A but is 1.5 km below the ice surface. Mt. Resnik is a tall peak, with the summit only 300 m below the ice surface, <100 km away from WDC06A. However, Mt. Resnik has an overall negative magnetic signature suggesting the edifice is older than 760 ka, the last magnetic reversal13. Mt. Casertz is the only subglacial volcano with a current ice depression over the top of the edifice15. However, the volcanic peak is 1.4 km below the surface and ~250 km from WDC06A. Because there are two different tephra with distinct chemical compositions it is likely that more than one subglacial volcano has erupted through the ice sheet. All things considered, the best candidate is Mt. Resnik because of the close proximity and low ice burden. Ice sheet elevation models suggest that WAIS was >200 m lower during the last glacial period42 reducing the ice burden significantly. It is possible that recent volcanic activity at Mt. Resnik during a time of normal polarity may not be large enough to offset the overall reversed polarity of the edifice. Mt. Resnik may also be the source of both tephra but this is difficult to support without geochemical characterization of material from the Mt. Resnik edifice, which cannot be obtained without drilling.Three subglacial volcanoes near the WDC06A drill site have been identified by aeromagnetic surveys, and are potential sources for Tephra A and C. These are Mt. Thiel, Mt. Resnik and Mt. Casertzin situ ice core tephra allowing for the spatial distribution of tephra particles to be observed on a scale not seen before.Evidence from tephra layers in the WDC06A ice core suggests that two subglacial eruptions have breached the WAIS in the past 45 ka. A basanitic eruption occurred at 44.5 ka and deposited >1 cm of tephra on the local ice sheet. A second, trachyandesite to trachydacite tephra deposited 2 cm of tephra, with some shards greater than 200 μm in diameter, at 22.3 ka. Micro-CT analysis performed on these tephra show a complicated eruption history with a mixed magmatic and phreatomagmatic phase punctuating the predominantly phreatomagmatic eruptions. This is the first time that μCT has been used on Continuing ice loss from WAIS will eventually lower the ice sheet elevation and may cause a positive feedback by increasing volcanism in West Antarctic. Although there is no supporting evidence linking enhanced volcanism with collapse of WAIS in the Quaternary, increased volcanism could produce more basal melt water, increasing ice flow and ice loss thus perpetuating positive feedback. The delicate balance between deglaciation and volcanism may have a profound effect on the stability of WAIS and the subsequent sea level rise.Supplemental InformationSupplementary Data


The driven-dissipative Bose-Hubbard model can be experimentally realized with either negative or positive onsite detunings, inter-site hopping energies, and onsite interaction energies. Here we use one-dimensional matrix product density operators to perform a fully quantum investigation of the dependence of the non-equilibrium steady states of this model on the signs of these parameters. Due to a symmetry in the Lindblad master equation, we find that simultaneously changing the sign of the interaction energies, hopping energies, and chemical potentials leaves the local boson number distribution and inter-site number correlations invariant, and the steady-state complex conjugated. This shows that all driven-dissipative phenomena of interacting bosons described by the Lindblad master equation, such as “fermionization” and “superbunching”, can equivalently occur with attractive or repulsive interactions. However, to our knowledge the dependence of the non-equilibrium physics of the Bose-Hubbard model (BHM) on the signs of the hopping and interaction energies has yet to be explored. In superconducting circuits, which are a natural setting for studying the non-equilibrium physics of driven-dissipative many-body systems11, strong interactions are more accessible with attractive interaction energies than with repulsive interaction energies13. On the other hand, theoretical studies of the driven-dissipative BHM (DDBHM) have focused on the case of repulsive interactions. Finding a theoretical link between the attractive and repulsive interaction regimes of the DDBHM would therefore be of practical experimental benefit.The non-equilibrium behaviour of Bose-Hubbard systems has received considerable theoretical attention recentlyin situ (within a limited range) in both magnitude and sign15.In this work we point out a symmetry in the Lindbladian equation of motion for the DDBHM that implies that the driven-dissipative physics of repulsive interactions can be replicated with attractive interactions, irrespective of the magnitude of the interaction strength. To illustrate this, we employ a fully quantum (i.e. non-mean-field) numerical treatment of a DDBHM trimer. We show that simultaneously changing the signs of the interaction, hopping, and detuning while keeping their magnitudes fixed changes the non-equilibrium steady state (NESS) but does not change the three-site number correlator nor the statistics of the on-site boson number. We also demonstrate that this observable symmetry persists even in the presence of strong disorder in all of the sign-flipped parameters. This symmetry can be experimentally tested with existing superconducting circuit technology, which has the potential to realize the BHM such that the chemical potential, on-site interaction energy, and inter-site hopping energy are all tunable ħ = 1):Jl,l+1 denotes the hopping amplitude between the lth and (l + 1)th site, Ul denotes the boson interaction energy on the lth site, γ is the local dissipation rate, Ω denotes the drive amplitude , and Δl = ωl − ωd, which plays the role of a chemical potential, is the site-dependent drive detuning when ωl is the bare frequency of the lth site and ωd is the drive frequency.We investigate the open boundary dissipative Bose-Hubbard chain under homogeneous coherent driving in a frame rotating at the drive frequency. With on-site dissipation to a Markovian bath, the effective equation of motion (EOM) (see Appendix for derivation) is given by the following Lindblad master equation . Therefore the NESS attained by evolving with H is equal to the complex conjugate of the NESS attained by evolving with −H. However, the transformation ρ → ρ* does not change the observable statistics of the state. The observables of the NESS are therefore invariant under negation of the Hamiltonian. We note that this symmetry applies not just to the DDBHM, but to any model described by the Lindblad master equation where the dissipation operators are invariant under complex conjugation. This is discussed and demonstrated further in16, an independent work whose findings overlap with the ones presented here.The NESS of the DDBHM, denoted equation , \documementclass2pt{minimH → −H entails Ω → −Ω, which is equivalent to bl → −bl. However, bl → −bl itself does not change the boson number statistics. To see this, note that if b → −b, thenFor the DDBHM there is a further simplification of the symmetry. The transformation Ul → −Ul, Jl,l+1 → −Jl,l+1, and Δl → −Δl. We note that a dimer system is a special case, where the sign of J also need not change (see ref.16).We therefore conclude that Ω → −Ω is unnecessary to preserve the boson number statistics in the NESS; the invariance only requires ρ18, which amounts to a quantum mechanical treatment characterized by a refinement parameter χ that designates the maximum size of the tensors that represent each site, and therefore the maximum amount of total correlations  between bipartitions of the chain that can be captured by the MPDO. Linking each site tensor with its neighbor in the MPDO is a diagonal matrix of χ “singular values” that represents these correlations.The numerical simulation is performed by employing a matrix product density operator (MPDO) representation of ρ becomes a vector, denoted |ρ〉, and the superoperator ρ∞ under a given set of system parameters Ul, Jl, Δl, Ω, and γ, we first use the hybrid evolution method of Ref.19 to evolve the MPDO representation of a random initial state ρ under a desired choice of parameters until convergence in achieved. We then sweep the value of Ω in increments, converging the MPDO with real time evolution at each increment. Convergence is considered complete when χ = 15 and a timestep size of 10−1 is sufficient to achieve this for all of the cases that we consider. We verify uniqueness of the NESS by performing the sweep of Ω in both directions. We truncate the Hilbert space on each site at four quanta, and always choose γ = 1.In the MPDO picture the system density matrix 16 for results with a uniform dimer system). We first test the boson number symmetry when the parameters are uniform across the trimer. We specifically look at two cases: Case 1 examines the change in the NESS under the number-conserving transformation argued above ; Case 2 examines the change in the NESS under a transformation that is different from the number-conserving transformation discussed in the previous section: the sign of J is kept fixed while the sign of U and Δ are changed. The simulation parameters are summarized in Table To test the arguments set forth above, we perform numerical investigations on a DDBHM trimer system  the number statistics of the NESS of the DDBHM can exhibit a strong dependence on the sign of the hopping energy, and (2) it is possible for the number statistics of the NESS to be exactly the same for opposite signs of the interaction energy with the same magnitude.These theoretical predictions are experimentally testable with existing superconducting circuit technology, and the symmetry is applicable beyond the DDBHM to any situation where the Lindbladian jump operators are real.attractive interactions are more readily accessible13 rather than strong repulsive interactions. Therefore, the equivalence between attractive and repulsive interactions that we have shown here for driven-dissipative bosonic phenomena indicates that superconducting circuits with strong attractive interactions are a viable platform for investigating predictions made for driven-disspative bosonic phenomena involving strong repulsive interactions, such as repulsively induced photon superbunching3, fermionized photons1, polariton crystalization2, photon transport resonances5, first-order dissipative quantum phase transitions6, and diffusive-insulator transport phase transitions8.For self-interactions of bosons in superconducting circuits, strong 16.Our findings confirm and complement the results in the recent independent work by Li and Kochħ = 1):The open boundary Bose-Hubbard chain under homogeneous coherent driving is described by the following Hamiltonian th site, Ul denotes the boson interaction energy on the lth site, Ω denotes the drive amplitude, and ωd denotes the drive frequency. With on-site dissipation to a Markovian bath, the density matrix ρ of the chain is governed by the following Lindblad master equation: γ is the local dissipation rate. To eliminate the time dependence, the master equation is multiplied from the left by U and from the right by U†, where l = ωl − ωd is the site-dependent drive detuning, which plays the role of a chemical potential. For simplicity, in the main text we write ρ and H.ρ18, which amounts to a quantum mechanical treatment characterized by a refinement parameter χ that designates the maximum size of the tensors that represent each site, and therefore the maximum amount of total correlations  between bipartitions of the chain that can be captured by the MPDO. Linking each site tensor with its neighbor in the MPDO is a diagonal matrix of χ “singular values” that represents these correlations.The numerical simulation is performed by employing a matrix product density operator (MPDO) representation of ρ becomes a vector, denoted |ρ〉, and the superoperator ρ∞ under a given set of system parameters Ul, Jl, Δl, Ω, and γ, we first use the hybrid evolution method of ref.19 to evolve the MPDO representation of a random initial state ρ under a desired choice of parameters until convergence in achieved. We then sweep the value of Ω in increments, converging the MPDO with real time evolution at each increment. Convergence is considered complete when χ = 15 and a timestep size of 10−1 is sufficient to achieve this for all of the cases that we consider. We verify uniqueness of the NESS by performing the sweep of Ω in both directions. We truncate the Hilbert space on each site at four quanta, and always choose γ = 1.In the MPDO picture the system density matrix


From 2012 to 2016, California experienced one of the worst droughts since the start of observational records. As in previous dry periods, precipitation-inducing winter storms were steered away from California by a persistent atmospheric ridging system in the North Pacific. Here we identify a new link between Arctic sea-ice loss and the North Pacific geopotential ridge development. In a two-step teleconnection, sea-ice changes lead to reorganization of tropical convection that in turn triggers an anticyclonic response over the North Pacific, resulting in significant drying over California. These findings suggest that the ability of climate models to accurately estimate future precipitation changes over California is also linked to the fidelity with which future sea-ice changes are simulated. We conclude that sea-ice loss of the magnitude expected in the next decades could substantially impact California’s precipitation, thus highlighting another mechanism by which human-caused climate change could exacerbate future California droughts. Persistent atmospheric ridging in the North Pacific steered storms away and led to the California drought of 2012-16. Here the authors use simulations to show that sea-ice changes trigger reorganization of tropical convection resulting in drying over California. These uncertainties are largely a consequence of the sensitivity of Californian rainfall to both tropical and mid-latitude atmospheric circulation changes, such as variability in the El Niño/Southern Oscillation (ENSO) and shifts in the Pacific jet stream4. California’s winter precipitation has decreased over the past two decades, and between 2012 and 2016 California has entered into one of the most severe droughts on record9. The impacts of reduced rainfall have been intensified by anomalously high temperatures that have enhanced potential evapotranspiration5. Several studies posit that California’s drought has an anthropogenic component arising from increased temperatures, with the likelihood of such warming-enhanced droughts expected to increase in the future11.There is considerable uncertainty in model projections of twenty-first century precipitation changes over California6. A La Niña event in 2011/12 and anomalously warm sea-surface temperatures (SST) over the west tropical Pacific in 2012/13 and 2013/14 may have helped sustain the North Pacific geopotential ridge8. Climate model simulations forced with observed SSTs alone were unable to capture all the important features of the recent precipitation decline, suggesting that California’s recent precipitation deficit may in part be attributable to other factors, such as internal atmospheric variability8.The exceptionally dry conditions during the winters of 2012–2015 were accompanied by a prominent dynamical feature: a persistent geopotential ridge located in the North Pacific. This ridge pushed storm tracks further north, resulting in wetter than normal conditions over the northwest and substantial drying over the southwest of the United States12. Most of the existing literature points to anomalous tropical SSTs and convection as dynamical drivers of the geopotential changes in the North Pacific14. However, at least one study has implicated Arctic sea-ice loss as a possible cause of the drier winters over the American southwest18. One proposed physical mechanism involves surface warming and geopotential height increase over the newly open ocean areas in the Arctic, which in turn drives anomalous ridging over the North Pacific by perturbing high-latitude planetary wave patterns15. Although this mechanism is not considered to be a primary driver of California’s precipitation variability, scientific interest in the “sea-ice hypothesis” has been heightened by the pronounced Arctic sea-ice loss over the satellite era and the dramatic sea-ice retreat expected by the end of the twenty-first century19. Motivated by this, we focus on elucidating the possible mechanisms by which large-scale sea-ice cover changes could affect precipitation over California.A positive geopotential anomaly in the North Pacific is not unique to the recent drought. Similar anomalies are known to be associated with precipitation decline across the American southwest20), thereby obtaining an ensemble of simulations with a seasonally ice-free Arctic (“low Arctic ice” simulations). These are compared to control simulations representative of sea-ice conditions at the end of the twentieth century. A comparison between “low Arctic ice” and control simulations allows us to isolate the atmospheric response that is solely associated with changes in sea-ice cover. Neither the SSTs nor the sea-ice cover are prescribed in our model simulations. We are therefore able to account for atmosphere–surface ocean interactions and SST changes necessary for propagation of high-to-low latitude atmospheric teleconnections23. Unlike previous studies that impose artificial energy fluxes to achieve sea-ice loss25, our sea-ice parameter perturbations allow for energy budget conservation.A novel feature of our approach is that we sample the uncertainties in selected sea-ice physics parameters  coupled to a mixed-layer ocean model. We do not investigate how this initial atmosphere–surface ocean response may become modulated by the slower deep-ocean response over longer  time periods as in refs. 25. We verify that at the short timescales of interest here (<50 years after the sea-ice loss), an AGCM coupled to a slab ocean yields a qualitatively similar short-term response to that produced by the same AGCM coupled to a full ocean model (AOGCM) (see Supplementary Discussion). Our results show that the consequences of Arctic sea-ice decline are not restricted to the Arctic region alone. Loss of Arctic sea-ice cover of the magnitude expected in the next few decades, could induce large-scale atmospheric circulation changes across the Northern hemisphere, resulting in significant drying over California.Our primary interest is in the fast atmospheric response to sea-ice changes in the first decades after the sea-ice loss has occurred. This fast response is mediated by the surface ocean, and typically dominates the overall response during the first years or decades after the initial high-latitude perturbation2 threshold used to define a nearly ice-free Arctic19. By comparison, CMIP-5 simulations of twenty-first century climate and extrapolations of observed changes in ice volume place the time horizon for a nearly ice-free Arctic roughly between 2020 and 204019. The smallest and largest differences between the “low Arctic ice” and control Arctic sea-ice area  in response to sea-ice changes. Experimental configurations that impose artificial surface energy fluxes in order to remove sea-ice cover necessarily yield a substantially larger surface energy imbalance than the one described here.In the first step of this teleconnection, sea-ice loss alters the high-latitude energy budget  can provide a compensation for energy budget perturbations elsewhere23. This is not dissimilar to the observed changes in tropical TOA fluxes during ENSO-related convection changes that are also capable of affecting the global energy budget32.Tropical compensation of high-latitude energy budget perturbations has been noted in other studies employing AGCMs coupled to a slab ocean model23. Specifically, over the northern tropics, in the region of the northeasterly trades, the progression of cold (warm) SST anomalies will lead to an increase (decrease) in the surface wind strengths. This results in increased (decreased) evaporative cooling, thus allowing for further propagation of cold (warm) anomalies toward the equator. Over the southern tropics, the response is the opposite, due to the background southeasterly flow. Negative (positive) wind strength and latent heat flux anomalies over the northern (southern) tropics in response to Arctic sea-ice loss are shown in Supplementary Fig. The mechanism by which high-latitude changes propagate into the tropics and induce tropical convection responses involves two processes: (i) a southward advection of the initial high-latitude temperature perturbation over the mid-latitudes through transport and mixing; and (ii) a wind/evaporation/sea-surface temperature feedback in the region of the northeasterly trades. The tropical response to high-latitude sea-ice loss in our model simulations is consistent with these findings  in the equatorial Pacific initiates a northward-propagating Rossby wavetrain. The characteristics of this wavetrain are positive stream function and geopotential anomalies immediately outside the region of increased convection (anticyclonic flow), and negative anomalies in the extratropical Pacific (cyclonic flow). We find that this mechanism also operates in our simulations.We suggest that the tropical Pacific convection changes described above play a key role in driving the North Pacific circulation changes. Linkages between the equatorial Pacific convection anomalies and extratropical (North Pacific) atmospheric circulation changes are found in both observational and modeling studiesDuring the DJF season, the area of strongest decrease in high cloud cover is located over the central tropical Pacific  California Fig. . Arctic 13. While such tropical and subtropical convection changes could be a consequence of natural variability, our analysis indicates that they can also be forced from the high latitudes by substantial sea-ice loss. Our simulations imply that two hitherto separate hypotheses—that Californian rainfall is primarily influenced by tropical convection changes 11 and that Arctic sea-ice loss can drive precipitation changes over California (“Arctic sea-ice loss hypothesis”)30—are not easily separable. Our study demonstrates that the impacts of Arctic sea-ice changes require understanding complex atmospheric teleconnections that can propagate back and forth between the extratropics and the tropics.The schematic in Fig. 40. This is the opposite to the precipitation response accompanying Arctic sea-ice loss. In accord with previous studies36 and the mechanism advanced here, increased convection should in turn drive a northward-propagating Rossby wavetrain consisting of an anticyclonic anomaly in the tropical Pacific and a cyclonic anomaly in the North Pacific. This cyclonic flow is associated with negative geopotential height anomalies over the North Pacific  leading to wetter conditions over California. Simulations in which the sea-ice physics parameter perturbations are prescribed in the Southern hemisphere only  and no high northern latitude changes, it provides additional support for our conjecture that the sea-ice changes can influence North Pacific geopotential height through tropical convection changes. More generally, any high-latitude perturbation (northern or southern hemispheric warming or cooling) that impacts the position of the tropical Pacific ITCZ, will have an impact on California’s rainfall.Many aspects of the observed mean state of the atmosphere during the recent 2012–2016 California drought are qualitatively consistent with our simulated response to Arctic sea-ice changes. ERA-Interim estimates of the precipitation, geopotential, and OLR anomalies between 2012 and 2015 (relative to the period 1979–2010) are shown in Supplementary Fig. 41. Another important factor may be the 2014 phase shift of the Pacific Decadal Oscillation from negative to positive. However, this shift would be expected to alleviate drought conditions over California—not intensify them42. Finally, we note that other hemispherically asymmetric forcings may also trigger—via the same physical pathways described here—tropical convection changes and teleconnections affecting California’s precipitation. Possible examples include asymmetric forcing by anthropogenic aerosols, volcanic eruptions, and solar irradiance variations. All of these forcings can alter the inter-hemispheric temperature gradient43, thereby causing shifts in the location of tropical convection and initiating “far-field” precipitation changes over California.This consistency does not, however, constitute compelling evidence that the 2012–2016 California drought is attributable to Arctic sea-ice changes. Rather, it illustrates that some of the atmospheric features of the droughts driven by Arctic sea-ice loss may resemble those of the most recent California drought. The intensification of dry conditions over California since late 2012 may have also been affected by several other factors not discussed in this study, such as the appearance of a large warm SST anomaly off the west coast of North America—though this appears to be a consequence rather than a cause of the altered atmospheric circulations causing the drought44. Abrupt high-latitude temperature increase during the last interglacial (the Dansgaard–Oeschger and Bølling–Allerød warmings) are manifest in the tropics through a northward shift in the position of the ITCZ47. Conversely, the signature of cold stadials and Younger Dryas cooling in the Arctic is matched by a southward shift of tropical precipitation across all ocean basins48. These ITCZ shifts are consistent with precipitation changes inferred from high-resolution, precisely dated speleothem records: speleothems across the southwestern United States indicate shifts to drier conditions during the Dansgaard–Oeschger warmings50, the Bølling–Allerød warming, and the termination of the Younger Dryas cooling51. Similarly, during the Heinrich 1 and Younger Dryas cold periods, wetter conditions are indicated by lake-level high stands in the Great Basin and glaciation in central and southern California53, while at least one modeling study has implicated North Atlantic cooling and a corresponding southward ITCZ shift as a possible cause of increased precipitation over the western United States54.It is of interest to consider whether paleoclimatic evidence provides support for our model-inferred two-step teleconnection Fig. . We focu55. In addition, volcanic activity may have also had an impact on tropical precipitation during this time56. However, proxy data for the last millennium does yield information regarding the second teleconnection step—the link between the ITCZ location and southwestern rainfall. The southward shift of the ITCZ in the transition from the medieval climate anomaly (MCA) to the little ice age (LIA) is well documented58. The effect of this shift is apparent in the contrast between the dry MCA and the wet LIA in the western US lake levels59, from trees growing on lake beds exposed by low lake levels61, and in pollen records62. Interestingly, a brief southward shift in the ITCZ position between ~AD 1050 and 125057 is clearly recorded in the American southwest as a wet interval in the midst of the dry MCA. Great Basin lakes expanded briefly during this period64, concurrent with drowning of trees growing below modern water levels61 and increased soil moisture in southern California (as inferred from pollen records)62. Such periods during the MCA and LIA provide some support for the second teleconnection step. In the absence of more reliable sea-ice data sets, however, we cannot confirm if such covariance relationships between the ITCZ location and southwestern rainfall are directly attributable to sea-ice changes, or could instead be due to other factors .The timing, magnitude, and drivers of sea-ice changes during the last millennium are less well understood30. Additional analysis of the short-term (first 50 years) response of an AOGCM response to sea-ice changes in a complementary, energy-conserving setup confirms our AGCM/slab ocean findings  the different timescales of the response; and (ii) studies that attempt to isolate the impacts of sea-ice changes by imposing large artificial energy perturbations in order to achieve the sea-ice loss25, and investigations that achieve sea-ice changes in an energy-conserving manner (ref. 30 and the current study).Finally, we address the suitability of our experimental configuration (an AGCM coupled to a slab ocean) for studying the fast atmosphere–surface ocean-mediated response to sea-ice changes. In our simulations, key response features are manifest within the first two decades  response to Arctic sea-ice loss described in our study is consistent with the response found in previous AOGCM studies that allow for ocean dynamics and deep-ocean changes. The long-term centennial climate response to sea-ice changes may, however, differ from the fast response described here. While investigations with other climate models are necessary to further confirm these findings, our results strongly suggest that what happens in the Arctic does not stay in the Arctic and provide a physically plausible pathway by which high-latitude sea-ice forcing may mediate tropical climate, and thereby influence California’s rainfall.68. Our study thus identifies yet another pathway by which human activities could affect the occurrence of future droughts over California—through human-induced Arctic sea-ice decline.As a final remark, we note that the pronounced Arctic sea-ice loss over the satellite era is likely human-induced, arising from anthropogenic warming caused by greenhouse gas increases69. The model configuration incorporates the Community Atmosphere Model version 4 (CAM4)70, Community Land Model version 4 (CLM4)71, and Los Alamos Sea Ice Model version 4 (Community Ice CodeE 4—CICE4)72 coupled to a mixed-layer (slab) ocean. The atmosphere and land models are run on a 1.9° × 2.5° (latitude × longitude) finite volume grid with 26 atmospheric levels in the vertical dimension. The ice and ocean models use a 1° displaced pole grid. The greenhouse gas concentrations, solar insolation, and orbital parameters are representative of the year 2000 values for all simulations. The prescribed ocean heat flux (“q-flux”), salinity, temperature, and velocity fields required for the mixed-layer ocean model simulations are derived from a fully coupled CCSM simulation using the full-depth ocean.We use the Community Climate System Model (CCSM) version 4In order to isolate the atmospheric impacts of sea-ice loss, we compare two sets of experiments that differ only in the amount of sea-ice cover. For this purpose, we have developed a novel experimental configuration in which we alter the sea-ice cover without imposing artificial energy fluxes in the high latitudes as done in the previous studies. When sea-ice loss is achieved by imposing non-physical heat flux perturbations, energy is not conserved. This makes it difficult to determine if the observed atmospheric response originates solely from the sea-ice changes or if it is also impacted by the imposed energy flux perturbations. Analyzed response represents cumulative effect of sea-ice extent and thickness changes.20. The selected sea-ice physics parameters are shown in Supplementary Table Sea-ice loss in our model simulations is achieved through sea-ice physics parameter perturbations. We use an ensemble of 70 Latin hypercube simulations to select the sea-ice physics parameters that have the strongest impact on the resulting sea-ice extentt-test in order to account for different sample size and variances between the control and “low Arctic ice” simulations. Prior to t-test calculations, the equivalent sample size is determined at each grid point .Statistical significance is estimated using Welch’s https://esgf-node.llnl.gov/projects/psipps/. Provided are monthly means of the following CAM4 variables: ice fraction (ICEFRAC), surface pressure (PS), surface temperature (TS), upper tropospheric temperature (TROP_T), total precipitation (PRECT), geopotential (Z3), horizontal and meridional wind speed components (U and V), vertical (pressure) velocity (OMEGA), net longwave flux at the atmosphere top (FLNT), and high cloud cover (CLDHGH); all for years 20–40 of model integration. Additional data can be made available on request.Simulation output processed for the purpose of this study has been made public and can be obtained at Perturbed sea-ice physics parameter simulations require changes to the following parameters: snow grain radius tuning parameter, thermal conductivity of snow, and snow melt maximum radius. Their respective values are given in Supplementary Table Peer Review FileSupplementary Information


The aim of this proof-of-concept study is to introduce new high-dynamic ECG technique with potential to detect temporal-spatial distribution of ventricular electrical depolarization and to assess the level of ventricular dyssynchrony.5-kHz 12-lead ECG data was collected. The amplitude envelopes of the QRS were computed in an ultra-high frequency band of 500–1000 Hz and were averaged (UHFQRS). UHFQRS V lead maps were compiled, and numerical descriptor identifying ventricular dyssynchrony (UHFDYS) was detected.An electrical UHFQRS maps describe the ventricular dyssynchrony distribution in resolution of milliseconds and correlate with strain rate results obtained by speckle tracking echocardiography. The effect of biventricular stimulation is demonstrated by the UHFQRS morphology and by the UHFDYS descriptor in selected examples.UHFQRS offers a new and simple technique for assessing electrical activation patterns in ventricular dyssynchrony with a temporal-spatial resolution that cannot be obtained by processing standard surface ECG. The main clinical potential of UHFQRS lies in the identification of differences in electrical activation among CRT candidates and detection of improvements in electrical synchrony in patients with biventricular pacing.The online version of this article (doi:10.1007/s10840-017-0268-0) contains supplementary material, which is available to authorized users. Pathological changes in the structure of cardiac ventricles often manifest themselves in electrical activity. The clinical 12-lead ECG-based criteria for left ventricle (LV) dyssynchrony quantification and cardiac resynchronization therapy (CRT) implementation are based primarily on the duration and morphology of the QRS complex . UnfortuConventional ECG diagnostic information is usually limited to 100 Hz. Most QRS parameters including QRS duration or morphology use frequency band below 30 Hz. Broad-band ECG measured by high-frequency and high-resolution monitors provide more precise QRS morphology  and infoHere, we introduce an ultra-high frequency electrocardiogram (UHF-ECG) technique. The higher frequency and the dynamic range allow for more accurate identification of the temporal distribution of electrical depolarization in a single lead. The mutual comparison of depolarization activation patterns in different ventricular segments (leads) and computation of depolarization inter-lead delays can be potentially interpreted as ventricular dyssynchrony.The acquisition system BioSDA09  was used to record ECG signals at 5-kHz with a dynamic range of 26 bits (3 nV resolution) and a frequency range of 2-kHz. Measurements were performed at the International Clinical Research Center at St. Anne’s University Hospital, Brno, Czech Republic. The UHF-ECG data was collected over 5–15 min in the resting supine position with a standard 12-lead ECG setup.The UHF Solver and SignalPlant   softwareThe shapes of averaged QRS complexes Fig. a of V leDetailed description of UHF-ECG signal processing including comparison of different frequency ranges is available in the Electronic Supplementary Material.Initially, we have studied seven patients with characteristic QRS complex shape. Table All subjects gave their informed consent to the investigation. This study was approved by the local ethics committee—The Ethics Committee at St. Anne’s Hospital, Brno, Czech Republic.Fig. The main aim of cardiac resynchronization therapy is to improve mechanical synchrony . STE wasThe STE analysis software depicted the color-coded strain rate map from the basal, middle, and apical segments of the septum and left lateral wall Fig. c. The onFigure Table Figure Figure Figure Figure The gold standard for detailed assessment of RV or LV dyssynchrony is still being discussed . SurfaceWe compared ten patients Table  before CPatients 15–17, classified as non-responders, have small UHFQRS dyssynchrony (<50 ms) and narrow QRSd (<151 ms) prior to CRT. Biventricular pacing has no effect on QRSd and LV ESV. CRT reduces electrical dyssynchrony, though significantly less than in responders.Our preliminary results of ten consecutive patients who completed 6-month follow-up suggest the potential of UHF-ECG derived dyssynchrony to correctly define responders or non-responders to CRT. Thus, UHF-ECG derived dyssynchrony deserves attention and, considering also advantages of UHF-ECG mentioned in the text of our paper, it may have the potential to be one of the most significant predictors of responsiveness to CRT.Mechanical cardiac activity can be assessed primarily by echocardiography or magnetic resonance imaging (MRI). Several echocardiographic methods have been clinically utilized for the quantification of mechanical (contractile) myocardial dyssynchrony, including M-mode echocardiography, Doppler tissue imaging, Doppler-derived strain, and strain rate analysis or, more recently, STE. Each of these methods has limitations leading to modest accuracy to predict CRT response , 23. LowHigh UHFQRS temporal resolution, resulting from the frequency band, is coupled with superior reproducibility. Sufficient signal-to-noise ratio is obtained by averaging. The averaging technique cannot be used in echocardiography. Moreover, the analysis may be conducted with various types of QRS complexes, and even irregular beats can be independently analyzed.If the premise that UHFQRS measures the activity of depolarizing action potentials of myocardial contractile cells (Phase 0 of AP) is accepted, the electrical and mechanical activity of the ventricles can also be put into context Figs.  and 7. LHere, we present a new technique based on limited examples. We are aware that these preliminary results serve rather as a demonstration of the potential of the UHFQRS method.UHF-ECG measures and evaluates very weak voltage potentials far below the level of microvolts. The lower signal-to-noise ratio must be eliminated by prolongation of the measurement time to obtain more QRS patterns to average .Technical limitations: We demonstrate UHFQRS in a frequency range of 500–1000 Hz. To validate the presented results, ECG monitors with internal sampling higher than 2 kHz and minimal 16-bit or higher analog-digital converters are needed. Conventional 1 kHz ECG and frequency range 150–350 Hz seems to be sufficient to obtain basic information about ventricular dyssynchrony.UHFQRS is a deterministic method. In this proof-of-concept study, the clinical operator had no access to the UHFQRS maps and UHFQRS morphology computation.A significant advantage of the UHFQRS method is simplicity in application: Standard 12-lead ECG electrode placements can be used. The UHFQRS amplitude shape and multi-lead amplitude overlap can be identified and parametrized, unlike the morphology of the QRS complex which is not always clear


Protein phosphorylation is catalyzed by kinases which regulate many aspects that control death, movement, and cell growth. Identification of the phosphorylation site-specific kinase-substrate relationships (ssKSRs) is important for understanding cellular dynamics and provides a fundamental basis for further disease-related research and drug design. Although several computational methods have been developed, most of these methods mainly use local sequence of phosphorylation sites and protein-protein interactions (PPIs) to construct the prediction model. While phosphorylation presents very complicated processes and is usually involved in various biological mechanisms, the aforementioned information is not sufficient for accurate prediction. In this study, we propose a new and powerful computational approach named KSRPred for ssKSRs prediction, by introducing a novel phosphorylation site-kinase network (pSKN) profiles that can efficiently incorporate the relationships between various protein kinases and phosphorylation sites. The experimental results show that the pSKN profiles can efficiently improve the prediction performance in collaboration with local sequence and PPI information. Furthermore, we compare our method with the existing ssKSRs prediction tools and the results demonstrate that KSRPred can significantly improve the prediction performance compared with existing tools. As one of the most common posttranslational modifications (PTMs) , 2, phosTo this end, several experimental methods, including low-throughput , 10 and So far, several computational methods –19 have Although these methods have achieved success, phosphorylation presents very complicated processes, it is usually involved in various biological mechanisms. In consequence, the aforementioned information adopted in the existing methods may not fully determine the corresponding protein kinase. It is well known that one protein kinase can catalyze multiple phosphorylation sites and one phosphorylation site can also be phosphorylated by multiple protein kinases –24. For Inspired by this information, we propose a novel computational method in this study, namely, KSRPred, for ssKSRs prediction by introducing a phosphorylation site-kinase network (pSKN) profiles that can efficiently incorporate the relationships between various protein kinases and phosphorylation sites. This method is based on the framework of kernel ridge regression , 30, whihttps://doi.org/10.1155/2017/1826496).In this study, we employ an experimentally verified human phosphorylation sites with corresponding kinases dataset, which include 6,839 verified sites and 389 kinases with 9,480 known ssKSRs extracted from Phospho.ELM  and the si and sj is calculated as follows:si(k), sj(k)) is the similarity score between the kth amino acid of si and the kth amino acid of sj given by BLOSUM62 matrix. Applying this operation to all phosphorylation sites pairs, we construct a similarity matrix denoted as Sseq. To ensure that the value of Sseq is distributed in the range of , normalization is performed subsequently, and the formula is defined as Kseq =  − minSseq)/(maxSseq − minSseq). The similarity matrix Kseq is considered as kernel similarity matrix of phosphorylation sites calculated from sequence level.A local sequence with a length of 15 amino acids is extracted from the phosphorylation site, which contains 7 upstream and 7 downstream residues. We compute the sequence similarities of two phosphorylation sites using BLOSUM62 matrix, which is an amino acid substitution matrix that shows the similarities among 20 types of amino acids and usually used to calculate the sequence similarity . The simpi and pj is calculated as Sppi = |Jpi∩Jpj|/|Jpi ∪ Jpj|, where Jpi and Jpj represent the PPI information of corresponding substrate, respectively. Applying this operation to all substrate pairs, we construct a similarity matrix denoted as Sppi. However, some substrates have more than one phosphorylation sites; these sites have same substrates and share the same PPI information [Kppi of phosphorylation sites can be obtained by directly extracting the similarity of substrates. The similarity matrix Kppi is considered as kernel similarity matrix of phosphorylation sites calculated from substrate level.The PPI information of substrates is extracted from STRING , which iormation . The simXs = {s1, s2,…, sns} and the kinase set as Xk = {k1, k2,…, knk}; the relationships between various kinases and phosphorylation sites can be described as a bipartite network G, where E = {eij : si ∈ Xs, kj ∈ Xk}. A link is drawn between si and kj when the phosphorylation site si has relationship with the kinase kj. This bipartite network can be presented by an ns × nk adjacent matrix Y, where yij = 1 if si and kj are linked, while all other unknown phosphorylation site-kinase pairs are labeled as 0. Afterwards, to incorporate pSKN profiles for prediction, we construct a kernel similarity matrix from the pSKN profiles using Gaussian kernel function . The similarity between two phosphorylation sites si and sj is calculated as follows:ysi and ysj represent the ith and jth row of the adjacency matrix Y, respectively. The kernel bandwidth is controlled by the parameter γs. It is normally defined as a new bandwidth parameter γs′ normalized by the average number of relationships with phosphorylation site per kinase. The formula for the calculation of γs isKnet. The similarity matrix Knet is considered as kernel similarity matrix of phosphorylation sites calculated from relationship level.The relationships between various kinases and phosphorylation sites can be expressed as a bipartite network , from whTo our knowledge, kernel ridge regression (KRR) is widely used in the field of bioinformatics –45, and T = {,…, }, where xi ∈ Rm and yi ∈ {0,1}, the basic idea of KRR relies on mapping the data into a higher dimensional space ℋ  according to a mapping Φ and then finding a linear regression function with the new training set T = {(Φ(x1), y1),…, (Φ(xn), yn), }, which represents a nonlinear regression in the original input space [λ is a regularization parameter used to control the trade-off between the bias and variance of the estimate. By calculating the derivative of this cost function [ω∗ = ϕ(ϕTϕ + λIn)−1Y. Therefore, for a new unlabeled sample x, the predicted label y ) can be calculated by the following formula:Y is the vector of values yi and K = Φ(xi)TΦ(xj) is the kernel function.Formally, given a training dataset ut space . The linfunction , we can ηφ = 1/3, φ ∈ {seq, ppi, net}. Using ( scikit-learn library (version 0.18) [ Python environment.In this study, we develop three similarity kernels, namely, sequence similarity kernel, PPI similarity kernel, and pSKN similarity kernel, from different data sources. In order to make full use of these kernels, we follow van Laarhoven et al.  and defi}. Using  and 6),,(6)Kxi,xon 0.18)  in the PF-Measure (F1), and Precision (Pre). The formula is defined as follows:Following previous works , 51, we In this study, we employ a novel pSKN profiles to predict ssKSRs. To confirm the effectiveness of pSKN profiles, we compare the proposed method with and without pSKN profiles on the basis of local sequence information. The prediction performances of these two methods are evaluated on the training dataset using 10-fold cross-validation. Here, we take kinase GSK3B, PLK1, P38A (MAPK14), and CDK2 as an example to illustrate the predictive performance, as shown in F1, Pre, and MCC are also adopted to ensure the reliability of performance evaluation. The measurements are evaluated at medium (Sp = 90.0%) and high (Sp = 95.0%) stringency levels, respectively. F1, Pre, and MCC values of different kinases at medium stringency level. It is indicated that the proposed method with pSKN profiles achieves the best predictive performance in almost all cases. For example, for PKCA, the Sn, MCC, F1, and Pre values are 69.5%, 39.8%, 40.5%, and 28.6%, which are improved by 11.6%, 7.1%, 5.6%, and 3.6% compared with the method using local sequences only. Moreover, Table S2 displays the high stringency level of Sn, MCC, F1, and Pre values, from which we can draw a consistent conclusion. In all, these results show that pSKN profiles can significantly improve the prediction performance of different kinases.Additionally, by following previous works , 20, 52,F1, and Pre values at medium stringency level (Sp = 90.0%) are improved by 6.1%, 2.8%, 1.9%, and 1.1%, respectively. We also display the performance of other kinases in Table S3.Recently, several studies , 19 use In the previous section, we have verified the effectiveness of pSKN profiles. In this section, we use the independent test dataset to compare KSRPred with four widely used ssKSRs prediction tools, namely, NetPhosK , iGPS 1, NetworKF1, Pre, and MCC) at medium and high stringency levels are also adopted to evaluate the performance. We draw the Sn-MCC-F1-Pre bar chart of the five methods based on the high and medium stringency levels, as shown in F1, and Pre values of KSRPred are increased by 42.9%, 28.1%, 24.0%, and 14.8% compared with iGPS and have an improvement of 50.0%, 33.4%, 28.9%, and 18.3% compared with PKIS, respectively. Similarly, compared with NetPhosK and NetworKIN, the Sn, MCC, F1, and Pre values of KSRPred are also improved 42.9%, 28.1%, 24.0%, and 14.8% and 87.5%, 66.5%, 60.5%, and 45.2%, respectively. We further analyze the results of this kinase and find that at the high stringency level some phosphorylation sites can be correctly assigned by KSRPred, yet not by the existing tools. For example, Y53 of AKAP8 (O43823) is catalyzed by SRC and can be correctly assigned by our method but cannot be predicted by the existing tools. In summary, these results suggest that KSRPred achieves a better or comparable performance as compared with the existing ssKSRs prediction tools. In addition, in Figure S2, we also compare the performance of the proposed method without pSKN profile with NetPhosK and iGPS. The result shows that, compared with these two tools, KSRPred without pSKN profile can also get a better performance. Taken P38A as an example, the AUC achieved by KSRPred without pSKN profile is 7.8% and 14.1% higher than NetPhosK and iGPS, respectively.In addition to the AUC values, the measurements . These discoveries suggest that KSRPred has not only a lower false positive rate but also the ability to discover unknown ssKSRs, which could be helpful for the subsequent experimental verification.In addition, due to the difficulty of experimental verification, computational method is also required to have the ability to detect unknown ssKSRs . In viewPhosphorylation plays a significant role in a wide range of cellular processes, which is catalyzed by protein kinases and many phosphorylation-related diseases are closely related to kinases. Prediction of ssKSRs is important for understanding phosphorylation process and provides a fundamental basis for further cell dynamics studies and drug design. However, traditional experimental methods are high-cost and time-consuming, and it is important to develop effective computational methods to predict ssKSRs. Although several computational methods for ssKSRs prediction have been proposed, these methods usually use the local sequence and PPI information, which are not sufficient for accurate prediction. In this study, we present the pSKN profiles that can efficiently incorporate the relationships between various kinases and phosphorylation sites. Using these pSKN profiles, the performance of our proposed method has been significantly improved. Meanwhile, we use PPIs extracted from STRING database as the substrate feature, and the experimental results show that our proposed method could make better use of this information compared with the existing method . Furthermore, through the analysis of potential phosphorylation sites, we find that some highly ranked results have been confirmed as phosphorylation sites catalyzed by kinases, suggesting its efficiency in discovering new potential ssKSRs for experimental validations and elucidating the molecular mechanism of protein phosphorylation.Although the proposed method has shown the good ability for ssKSRs prediction, there is still much room for improvement. It is well known that the quantity of training data plays crucial roles in mastering the performance of machine learning methods , 56, andFigure S1. Comparison of ROC curves using different information. Figure S2. Compare the ROC curves of three methods: KSRPred without pSKN profile, NetPhosK and iGPS. Table S1. The number of known phosphorylation sites of 103 kinases. Table S2. Comparison of prediction performance using different information at the high strategic level (Sp = 95.0%). Table S3. The predictive performance of all kinases. Table S4. Comparison of prediction performance of different methods at the high and medium strategy levels.