Using first-principles methods, we investigate the effect of Al on the generalized stacking fault energy of face-centered cubic (fcc) CrMnFeCoNi high-entropy alloy as a function of temperature. Upon Al addition or temperature increase, the intrinsic and extrinsic stacking fault energies increase, whereas the unstable stacking fault and unstable twinning fault energies decrease monotonously. The thermodynamic expression for the intrinsic stacking fault energy in combination with the theoretical Gibbs energy difference between the hexagonal close packed (hcp) and fcc lattices allows one to determine the so-called hcp-fcc interfacial energy. The results show that the interfacial energy is small and only weakly dependent on temperature and Al content. Two parameters are adopted to measure the nano-twinning ability of the present high-entropy alloys (HEAs). Both measures indicate that the twinability decreases with increasing temperature or Al content. The present study provides systematic theoretical plasticity parameters for modeling and designing high entropy alloys with specific mechanical properties. High-entropy alloys (HEAs) have attracted significant attention in recent years ,4,5,6,7.In conventional alloys, it is often a challenge to improve the strength and ductility at the same time. Usually higher strength is achieved by sacrificing ductility and vice versa. On the other hand, the deformation twinning mechanism can be used to overcome the strength-ductility trade-off. The deformation twins are created by the dislocation gliding in the slip systems under external stress. The newly created twin boundaries hinder the dislocation motion, resulting in an increased work hardening rate . At the same time, twinning maintains the elongation of alloys during work hardening by delaying the onset of plastic instability by necking .γusf), the intrinsic stacking fault energy (γisf), the unstable twin fault energy (γutf), and the extrinsic stacking fault energy (γesf). γisf is the most widely used parameter to predict the twinning ability, twinning stress [γisf [b112 is the Burgers vector of partial dislocation. A lower γisf suggests that deformation twins are easier to form, and the twinning stress is relatively low. For example, the twinning easily happens in Cu but not in Al, which is attributed to the lower γisf of Cu (45 mJ/m2) than that of Al (122 mJ/m2) [γisf of many medium-entropy alloys (MEAs) and HEAs are as low as (or even lower than) those obtained for the twinning-induced plasticity (TWIP) steels [γisf of CrMnFeCoNi HEA is 25–35 mJ/m2 [2 [γisf decreases with lowering temperature. γisf of MEAs and HEAs were studied by theoretical methods as well. Both CrCoNi and CrMnFeCoNi have negative theoretical γisf [The generalized stacking fault energy (GSFE) plays an important role in understanding the deformation mechanism of fcc alloys ,11,12. Tg stress , and phag stress . Classicrgy γisf , i.e., τ2 mJ/m2) . The mea) steels , which i35 mJ/m2  and 22–3mJ/m2 [2  measuredcal γisf ,17,18, wcal γisf .y(CrMnFeCoNi)y100− was modeled within the disordered local magnetic moment approach [The ab initio calculations were performed using the exact muffin-tin orbitals (EMTO) method . The Perapproach . The EMTapproach  and the approach  of Al-doγGSFE = (Ffault − F0)/A, where Ffault and F0 are the free energies of supercell with and without the fault, respectively, and A is the area. The free energy is approximated as F = E − TSmag, where E is the total energy and T is the temperature. Within the mean-field approximation, the magnetic entropy is kB is the Boltzmann constant, ic is the concentration, and iμ the local magnetic moment of the ith alloying element, respectively. The total energy E at each temperature and Al concentration was calculated at the corresponding lattice constant. We started from the experimental lattice constants of fcc Aly(CrMnFeCoNi)y100−  alloys at room temperature [y(CrMnFeCoNi)y100− alloys as a function of temperature, i.e., we assumed that Al addition has a negligible influence on the thermal expansion coefficient. This assumption is supported by the fact that the Debye temperature of Al-doped fcc CrMnFeCoNi varies little with the amount of Al [According to the Mahajan–Chin model , the nucperature . Then weperature  of fcc Cnt of Al . Namely,nt of Al  as the Ant of Al , the corγusf, γisf, γutf, and γesf our predictions give 285, −6, 281, and 3 mJ/m2, respectively. We observe that γisf is negative, and γesf is also very small. On the other hand, the energy barriers γusf and γutf are relatively large as compared to the energy barriers obtained for pure metals with low γisf [γisf is negative, the universal scaling law remains valid, which suggests that our results are reasonable. Similar negative γisf was reported in previous works. For instance, Huang et al. [2 for γisf of PM fcc CrMnFeCoNi at room temperature. On the other hand, the present γisf at 300 K is smaller than the former EMTO result (21 mJ/m2) reported by Huang et al. [γisf, which was considered by Huang et al. [In low γisf , such aslow γisf , i.e., γg et al.  used a sg et al.  consider2 [2, respectively. The deviations between the present result and the above VASP values [At 0 K and for the ferromagnetic (collinear) state, calculations based on the Vienna ab initio simulation package (VASP) combined with the special quasi-random structure (SQS) approach for the intrinsic stacking fault energy of CrMnFeCoNi gave average values of −54  and −31 2  with scaP values ,34 can by(CrMnFeCoNi)y100−  alloys as a function of temperature and composition. In the considered temperature and Al concentration range, both γisf and γesf increase monotonously with increasing temperature and Al content. At the same time, γusf and γutf decrease with increasing temperature and Al addition. It is found that temperature has a large effect on the GSFE. The values of γisf and γesf for the Al-free alloy are negative when the temperature is below 400 and 200 K, respectively, as shown in γisf follows closely the one predicted by Huang et al. [In g et al.  in spiteFhcp and Ffcc are the free energies per atom for the hcp and fcc phase, respectively. The last term is the interfacial contribution describing the transition zone between the fcc matrix and the hcp embryo. The interfacial energy σ was estimated to be of the order of 7 mJ/m2 [γisf and the stacking fault energy γ0 obtained merely from the structural energy difference, viz. γ0 is very close to γisf for all Al concentrations and temperature. Thus, the free energy difference between hcp and fcc can reflect the value of γisf. The small difference between γisf and γ0 is equal to the double of the interfacial energy σ. In σ slightly decreases with increasing temperature and Al content, but it remains in the range of 4–7 mJ/m2. Thus, at least for the present alloy family, the composition and temperature dependence of σ is rather weak and could safely be omitted. Similar observation was made by Dong et al. using calculations based on floating spin and longitudinal spin fluctuations schemes [For elemental metals and homogeneous solid solutions, the intrinsic stacking fault energy can be approximated by the energy difference between the hexagonal close packed (hcp) and fcc lattices, viz. fcc)A+2σ ,35, wher 7 mJ/m2  for the  schemes .γisf and γesf shown in γisf in fcc CrCoNi and CrFeCoNi alloys originate from the thermodynamic stability of the hcp phase at low temperatures. Recently, Zhang et al. [Previous theoretical study on the PM CrMnFeCoNi system  found thg et al.  confirmeg et al. .γisf generally improves the twinning ability of alloys, the combined effects of all energy parameters determining the GSFE should be considered when studying the twinning affinity. That is because the intrinsic energy parameters in yCrMnFeCoNi system, we adopt two twinning ability parameters. The parameter Ttw proposed by Asaro et al. [twT > 1 a twin is more favorable than the dislocation slip and vice versa. We plot twT as a function of temperature and Al content in twT decrease with increasing temperature and Al content, suggesting that the Al addition and increasing temperature decrease the ability of twinning. However, the twinning parameter remains far above 1, meaning that the present alloys remain prone to twinning even when the Al level comes close to the solubility limit within the fcc phase and temperature increases up to 600 K. A second twinning parameter was introduced by Jo et al. [Despite the fact that low o et al.  is defino et al.  as(2)rdrd < −0.5 we have stacking fault only, for −0.5 < rd < 0 both stacking fault and full slip can be realized, for 0 < rd < 2 full slip is combined with twinning, and for rd > 2 we have full slip only. Within the range of 0 < rd < 2, rd = 0 corresponds to the maximum twinning ability. As shown in rd values are much lower than 2, indicating a strong twinning ability. We find that rd increases with increasing Al content and temperature, meaning that the twinning ability decreases, which is fully consistent with the prediction from Ttw. There is one exceptional case that the negative rd in Al-free CrMnFeCoNi HEA below 400 K predict that only stacking fault and full slip will happen. However, plenty of deformation twins are found in the CrMnFeCoNi HEA [In terms of this parameter, one can distinguish four regimes corresponding to different deformation mechanisms. Namely, for CoNi HEA ,42. The y(CrMnFeCoNi)y100−  alloys as a function of temperature. The present theoretical results show that the GSFE can be tuned by adding Al or changing the temperature. In particular, the intrinsic and extrinsic stacking fault energies increase, whereas the unstable stacking and twinning fault energies decrease with increasing temperature and Al doping. The thermodynamic phase stability can reflect γisf accurately due to the fact that γ0 is very close to γisf. The interfacial energy σ slightly decreases with increasing temperature and Al content, but the change within the present composition-temperature interval always remains below ~30% compared to its mean value. Furthermore, from two parameters for twinning ability, it is predicted that Al addition and temperature increase cause a small decrease of the ability of twinning, but the alloys still remain prone to twinning even at the largest temperature and the highest Al-level considered here. The present theoretical data is expected to serve as input for modeling and design of new HEAs with desired mechanical properties.Using first-principles alloy theory formulated within the EMTO method, we have calculated the GSFE of paramagnetic fcc Al


The El Niño-Southern Oscillation (ENSO) results from the instability of and also modulates the strength of the tropical-Pacific cold tongue. While climate models reproduce observed ENSO amplitude relatively well, the majority still simulates its asymmetry between warm (El Niño) and cold (La Niña) phases very poorly. The causes of this major deficiency and consequences thereof are so far not well understood. Analysing both reanalyses and climate models, we here show that simulated ENSO asymmetry is largely proportional to subsurface nonlinear dynamical heating (NDH) along the equatorial Pacific thermocline. Most climate models suffer from too-weak NDH and too-weak linear dynamical ocean-atmosphere coupling. Nevertheless, a sizeable subset (about 1/3) having relatively realistic NDH shows that El Niño-likeness of the equatorial-Pacific warming pattern is linearly related to ENSO amplitude change in response to greenhouse warming. Therefore, better simulating the dynamics of ENSO asymmetry potentially reduces uncertainty in future projections. The asymmetry between El Niño and La Niña episodes in the tropical Pacific is often not well represented in models. Here, the authors show that this asymmetry is related to subsurface nonlinear dynamical heating and that a realistic representation of this process can potentially improve tropical climate projections. Advances in ENSO theory and modeling have led to improved understanding of ENSO physics. Nevertheless, capturing ENSO’s spatio-temporal complexity, as well as the correct balance of coupled feedbacks, remains an outstanding challenge11. For instance, while most of state-of-the-art ocean-atmosphere coupled climate models simulate its overall spatial pattern and temporal evolution realistically, this seeming realism occurs often for the wrong reasons. Large error cancellations are evident in the majority of climate models between positive coupled dynamic- and negative thermodynamic feedback processes that determine ENSO dynamics15. Furthermore, most models still fail to reproduce ENSO nonlinearity such as the observed asymmetry of sea surface temperature (SST) anomalies in the eastern equatorial Pacific18. These deficiencies are likely able to explain discrepancies among previous studies investigating ENSO properties in response to a changing climate28. Thus, the important question of which key factors control the diversity in simulated ENSO asymmetry among climate models remains a subject of debate29.The El Niño-Southern Oscillation (ENSO) originates from ocean-atmosphere coupled feedbacks in the equatorial Pacific30. In the eastern Pacific, where the ENSO signal is the strongest, the observed SST (and subsurface ocean temperature) skewness is highly positive . It is caused by a mean zonal pressure gradient force that is maintained by the easterly trade winds and westward surface current39. It is observed that the EUC is weakened or halted by anomalous central-Pacific westerly winds during strong El Niño events5, generating the intense NDH along the equatorial Pacific thermocline  is a deterministic advective process that enhances ENSO asymmetryine Fig. . A recen40) and Phase 6 , we show that ENSO asymmetry in CMIP models is largely proportional to the intensity of simulated subsurface NDH. Our results suggest that simulating the dynamics associated with ENSO asymmetry correctly is a necessary condition to constrain the tropical warming pattern due to ENSO amplitude change in a changing climate.This study aims to evaluate the subsurface NDH and ENSO asymmetry as well as atmospheric nonlinearities associated with ENSO feedbacks in state-of-the-art climate model simulations and to detect consequences thereof for future climate projections through constraining a climate model ensemble. Using multiple reanalysis datasets and climate model outputs for the Coupled Model Intercomparison Project Phase 5  is very close to the observations on average, however, the multi-model mean of the skewness (γENSO) cannot be statistically distinguished from zero. Thus, CMIP climate models fail badly in simulating ENSO skewness that is about 1 in observations, indicating no improvement in CMIP6 compared to earlier CMIP phases31.The positive skewness of the eastern-Pacific temperature anomalies that characterizes ENSO asymmetry is poorly reproduced among 25 CMIP5 and 26 CMIP6 historical simulations  linearly increases with respect to the relative strength of subsurface NDH variability to ENSO amplitude  among the CMIP models with a correlation coefficient of 0.78  surface heat flux feedback, characterized by an east-west contrast pattern near the dateline in association with the location of the main convection region, is underestimated in most climate models. Thus, we examine the zonal contrast of equatorial Pacific SW anomalies  in terms of its regression coefficient difference for positive and negative Niño-3 SST anomalies (∆xSW feedback asymmetry) in Fig. xSW feedback asymmetry with a moderate correlation coefficient of 0.37 (p = 0.008). However, the simulated ENSO skewness is generally too low even in the climate models that have higher feedback asymmetry. We also confirm that the dynamic feedback asymmetry derived from the zonal wind stress anomalies in the central-Pacific region  is nearly zero in reanalysis datasets despite that most climate models simulate positive asymmetry in the dynamic feedback  and are thus closer to the observations (0.30 month−1). Seven group H models with an NDH efficiency even greater than 0.20 month−1 are further classified as a subset, group HH. The other 29 models are categorized as group L (low NDH efficiency). Figure 37. In contrast, the group L models fail to reproduce these key nonlinear properties  are improved Fig.  and also15, the errors in the SST-winds coupling tend to be compensated by errors in thermodynamic radiative feedbacks, resulting in a seemingly realistic growth rate and thus ENSO amplitude . Comparing the historical period to the future scenario simulations for 2051–2100 , we find that the future change in the long-term mean of the subsurface NDH linearly follows ENSO amplitude change in group H Fig. . However52. Here we show that the projected warming pattern is strongly related to ENSO amplitude change once climate models are conditioned by their fidelity in dynamics responsible for ENSO asymmetry (as reflected in the simulated NDH efficiency). A measure of El Niño-likeness of tropical Pacific warming, defined as the spatial correlation coefficient of the SST trend pattern in the scenario simulations with the ENSO-regressed SST anomaly pattern in the historical simulations over 90°E–60°W and 20°S–20˚N (see “Methods” section), is positive  in most CMIP models48 but highly uncertain ranging from −0.11 to 0.83 . This relationship is strengthened to a correlation coefficient of 0.89 (p = 0.0073) within the group HH models that have greater NDH efficiency. The El Niño-likeness in group L is positive, ranging from 0.33 to 0.73, and there exists no correlation with ENSO amplitude change (r = 0.00) as expected because a simulated ENSO without realistic NDH is not able to yield a noticeable rectification effect.What kind of surface warming pattern will emerge in the equatorial Pacific in response to greenhouse gas forcing is still a subject of active debate.83 Fig. . In grouHow the projected ENSO change affects future trends is detectable in the difference between the strengthening and weakening ENSO (sEN and wEN) simulations once the CMIP ensemble is conditioned by the fidelity to simulated ENSO nonlinear dynamics Fig. . In a CM50. This can be attributed to ENSO-independent processes such as reduced equatorial-Pacific mean upwelling due to a weakening of the Walker and Hadley circulations53, of which the latter is more prominent in group L  can lead to a more pronounced El Niño-like global-warming pattern, whereas suppressing the rectification effect leads to less eastern Pacific warming. Without simulating ENSO asymmetry and relevant dynamics realistically, however, climate models project an El Niño-like warming pattern onlyp L Fig. .50 and from winds to ocean currents39  and 26 CMIP6 models for 1850–2014 (ref. 41) for the monthly fields of SST (tos in the data archives), zonal wind stress (tauu), near-surface temperature (tas), surface heat fluxes , and precipitation (pr). The potential temperature (thetao) and three-dimensional ocean currents  were available for all the 25 CMIP5 models and for 18 out of the 26 CMIP6 models for the historical simulations. For the CMIP5 models and 3 of the CMIP6 models , the vertical velocity was not provided and thus yielded as the division of the vertical mass transport (wmo) by the horizontal area of a grid cell (areacello) and by the reference density (1035 kg m−3) (ref. 58). The horizontal current vectors of the MPI models were corrected following Shigemitsu et al.59 since these models have curved equatorial axes. We interpolated the surface variables to a regular 1° × 1° longitude-latitude grid and the ocean variables to a 1° × 0.5° grid. We also used two future scenario simulations with rising radiative forcing pathway leading to 8.5 W m−2 in 2100: a CMIP5 Representative Concentration Pathway (RCP8.5) for 2006–2100 and a CMIP6 Shared Socioeconomic Pathway 5 (SSP5-8.5) for 2015–2100. Since the greenhouse gas emission pathways are different between these two scenarios60 and the number of group H models available for the CMIP6 SSP5-8.5 scenario is limited to only 3 , the Ocean Reanalysis System 5 (ORAS5) for 1979–2017 (ref. 62), version 3.3.1 of the Simple Ocean Data Assimilation ocean/sea ice reanalysis (SODA331) for 1980–2015 (ref. 63), and the National Centers for Environmental Prediction Global Ocean Data Assimilation System (GODAS) for 1981–2017 (ref. 64). The SST was derived from the nearest-surface potential temperature of each reanalysis dataset.We used four reanalysis products for the potential temperature, three-dimensional ocean currents, wind stress, and net surface heat flux: The Ocean Reanalysis System 3 (ORAS3) for 1959–2011 (ref. 65), ERA5 for 1979–2018 (ref. 66), and TropFlux for 1979–2017 (ref. 67). The radiative surface heat flux components were also derived from OAFlux for 1984–2009 (ref. 68), CERES EBAF Ed4.0 for 2001–2017 (ref. 69), GEWEX SRB version 3 for 1984–2007 provided by the NASA Langley Research Center Atmospheric Sciences Data Center NASA/GEWEX SRB Project, and ISCCP-FH for 1984–2009 provided by ISCCP H-series cloud data from NOAA/NCEI. The precipitation was obtained from GPCP version 2.3 for 1979–2018 (ref. 70). To calculate the regression for these datasets, SST from NOAA ERSST version 5 (ref. 71) was used for each data period.We used three atmospheric reanalysis products together with four oceanic reanalysis datasets for the wind stress and each component of the surface heat flux: ERA-interim for 1979–2018 . The shortwave- and longwave radiative surface heat flux anomalies are averaged over the Niño-3 and Niño-4 regions . The zonal contrast of shortwave heat flux (∆xSW) used in Fig. T indicates the potential temperature; u, v, and w are the zonal, meridional, and vertical ocean currents; the overbar and prime denote the climatological monthly mean and the detrended anomaly. The residual term (res) includes thermodynamic and subgrid-scale processes, but the total advective terms are dominant for determining the subsurface temperature tendency at least in ocean reanalysis products37. Following Hayashi and Jin37, the subsurface NDH is defined as the NDH terms averaged for 100 W°–180°, 1°S–1°N and 50–150 m depth . The relative amplitude of the NDH variability to ENSO amplitude is called the NDH efficiency (unit: month−1), ranging from 0.24 to 0.38 with an average of 0.30 in four ocean reanalysis products  to assess the variability in the eastern Pacific region, where the SST variability is the most intense in observations and climate models Fig. . The asypth Fig. . Its moncts Fig. .24. Then, we defined El Niño-likeness as the spatial correlation between the linear SST trend in the scenario simulations and the detrended SST anomalies regressed to the detrended Niño-3 SST anomalies in the historical simulations over the tropical Pacific domain (90°E–60°W, 20°S–20°N; solid box in Fig. The future changes of the ENSO amplitude and the long-term mean of NDH are increments from the historical data periods to RCP8.5 or SSP5-8.5 scenario simulations for 2051–2100. Here, the period of the scenario simulations was selected given that the ENSO response to global warming is transient in earlier periodst-test for the composited fields and correlation values, except for the differences between two CMIP groups for which the Welch’s t-test was used (Fig. The statistical confidence levels were tested by a two-tailed Student’s sed Fig.  and 9c. Supplementary InformationPeer Review File


ITGA6 and ITGB4 can be useful biomarkers for CRC early detection in a non-invasive assay and as a prognostic factor, respectively. Integrin α6β4 is one of the main laminin receptors and is primarily expressed by epithelial cells as an active component of hemidesmosomes. In this article, after a brief summary about integrins in the gut epithelium in general, I review the knowledge and clinical potential of this receptor in human colorectal cancer (CRC) cells. Most CRC cells overexpress both α6 and β4 subunits, in situ in primary tumours as well as in established CRC cell lines. The mechanisms that lead to overexpression have not yet been elucidated but clearly involve specific transcription factors such as MYC. From a functional point of view, one key element affecting CRC cell behaviour is the relocalization of α6β4 to the actin cytoskeleton, favouring a more migratory and anoikis-resistant phenotype. Another major element is its expression under various molecular forms that have the distinct ability to interact with ligands (α6β4 ± ctd) or to promote pro- or anti-proliferative properties (α6Aβ4 vs. α6Bβ4). The integrin α6β4 is thus involved in most steps susceptible to participation with CRC progression. The potential clinical significance of this integrin has begun to be investigated and recent studies have shown that  Epithelial cells lie and attach to the basement membrane, a specialized network of extracellular matrix molecules that comprise specific collagens, proteoglycans and exclusive glycoproteins such as laminins as well as non-exclusive ones such as fibronectins. Cell adhesion is mediated by membrane receptors specific for these glycoproteins. In the intestine, there are a number of these receptors that have been identified for epithelial cells including dystroglycan and the 37/67 kDa laminin receptor  as well It is noteworthy that while some of these integrins are mostly associated with the differentiated state in the intestinal epithelium cells such as α3β1 and α7β1, many are predominantly expressed by the proliferative cells at the base of the epithelial cells of the crypts in both the small and large intestines ,3,6 and,ITGA6A) expression in neoplastic cells and its role in CRC progression will also be presented. Finally, as expected from these data, ITGA6A and ITGB4 expressions in CRC primary tumours have been explored as prognostic factors; l will also present rationale for using ITGA6 variants as biomarkers and data that confirm their validity for identifying patients with CRC lesions in a non-invasive mRNA-based stool test. In this review, I will first present studies reporting increased expression of the β4 integrin subunit in CRC lesions and potential mechanisms accounting for the regulation of its expression. Through its unusual long cytoplasmic domain, the β4 subunit is also subject to relatively complex inside out and outside in signalling regulation that can affect both cellular adhesion and migration. β4 can only dimerize with the α6 subunit. In epithelial cells, this association appears exclusive since most α6, if not all, is associated with β4. The α6 subunit is subject to alternative splicing, generating two potential variants called α6A and α6B. In contrast to other tissues that predominantly express one or the other, the two variants are expressed in the epithelium of the small and large intestines but in distinct compartments, α6B being restricted to the quiescent differentiated cells while α6A is predominant in the normal proliferative cells required for the renewal of the digestive epithelium as well as in cancer cells. Progress concerning the mechanisms leading to α6A   so that ITGB4 promoter since its cloning [ITGB4 transcription [ITGB4 expression has also been suggested after identification of microRNAs that may target the ITGB4 transcript such as miR-21 [ITGB4 promoter [Integrin β4 subunit expression appears to be mainly regulated at the transcript level but the mechanism of its overexpression in CRC cells is still incompletely understood. There have been a number of studies that have reported specific potential interactions of transcription factors with the  cloning  in a var cloning , JUN [29 cloning . In CRC cription  but rececription  and FOSLcription  that nees miR-21  and miR-s miR-21  as well promoter . In normal epithelial cells, the β4 subunit is one of the key components of hemidesmosomes, a specialized adhesive structure found in epithelia. Most integrin β subunits bear short cytoplasmic domains smaller than 50 amino acids able to interact with actin filaments through cytoplasmic linker proteins such as talin and vinculin that are also used as scaffolding for the recruitment and activation of intracellular signalling pathways . In contIn carcinoma cells, numerous studies have demonstrated that α6β4 promotes cell motility and invasive behaviour rather than stable anchoring to the extracellular matrix via a mechanism related to the one used for cell migration in wound healing in normal cells . Since tITGA6, as for ITGA3 and ITGA7 thought to have been derived from a common ancestor [As mentioned above, the integrin α6 subunit is the only possible dimerization partner for β4. ancestor , is subjancestor . Althougancestor , the relancestor . As for many other epithelial cell types, intestinal cells can express both variants . Closer ITGA6 transcripts was noted in CRC as compared to the corresponding resection margins and this increase was attributed to an up-regulation in ITGA6A expression, with total levels of ITGA6B remaining comparable to those of the resection margins [ITGA6A expression. Expression of the α6 variants was investigated in CRC in situ and in adenocarcinoma cell lines. In CRC primary tumours, although most carcinoma cells expressing both α6A and α6B a clear loss of α6A/α6B segregation was observed . Quantit margins . ConsistITGA6 expression is still limited. Among the consensus binding sites for the transcription factors SP1, NF-kB, AP1 and MYC identified on the ITGA6 promoter [ITGB4 [ITGA6 transcription. Pharmacological inhibition of MYC activity as well as molecular manipulations of intracellular MYC levels has shown a direct concordance between MYC levels and ITGA6 expression in intestinal cells while chromatin immunoprecipitation assays have confirmed the functionality of the MYC binding site on the ITGA6 promoter in the intestinal context [Information about transcriptional regulation of promoter , only SPpromoter . Considepromoter ,48 and tpromoter , which cr [ITGB4 , MYC rep context . ITGA6 is expressed under the form of ITGA6A in CRC cells [ITGA6 has been relatively well studied and at least 10 splicing factors have been identified under various contexts but not in CRC cells. Among the various factors tested, the epithelial splicing regulatory protein 2 (ESPR2) was identified to be the main splicing factor responsible for ITGA6A expression in CRC cells [ITGA6 splicing in breast cancer cells [ESPR2 that was found to be up-regulated by MYC, ESPR1 was not modulated in CRC cells by this factor [ESPR2 active transcription indicates that MYC regulates both ITGA6 and ESPR2 expression resulting in the specific up regulation of ITGA6A in CRC cells [Since neo RC cells , the mecRC cells . It is ner cells  but in cs factor . FurtherRC cells . ITGA6A [ITGA6A expression [ITGA6A is a phenomenon occurring in the normal intestine, which appears to be exploited throughout the neoplastic process. It is interesting to note that the cells of the crypt proliferative compartment, which predominantly express α6A/ITGA6A ,43, are ITGA6A . Experimpression . These dITGA6A and MYC that their normal counterparts [ITGA6A in various CRC cell lines was also accompanied by a reduction in the capacity of these cells to develop tumours [MYC is a Wnt/B-catenin target gene [Indeed, colorectal cancer cell lines express 5–10 times more terparts  while thterparts . Specifi tumours . Inciden tumours , a centr tumours . As MYC get gene , this suget gene , an effeget gene . In summary, while there is a clear segregation of α6β4 forms in the normal intestinal mucosa where α6Aβ4cdt- is expressed by the proliferative cells of the lower crypt and α6Bβ4ctd+ is mainly expressed by the quiescent and differentiated cells of the upper crypt and surface epithelium, cancer cells predominantly overexpress α6β4 under the α6Aβ4ctd+ hybrid form , which aIn light of the functional evidence described above indicating that α6β4 is directly involved in the various steps of CRC progression, there has been growing interest toward assessing its clinical significance as a biomarker for monitoring two critical phases of CRC development: early tumour detection and prognosis. ITGA6 and ITGB4 expression in CRC. Based on the large public datasets that store this information as well as software that allows efficient data mining, it is becoming more and more affordable to analyze these data to compare their expression with pathological features and patient survival. In a recent study, Li et al. [ITGB4 level expression in tumours with overall survival using four distinct NCBI GEO datasets as well as the TCGA dataset, selected on the basis of their size (more than 50 patients) and availability of overall survival information. Using the integrated data, high expression of ITGB4 in CRC was found to be significantly associated with an unfavorable overall survival rate indicating that it is a prognostic factor for colon cancer [ITGA6 has also been investigated but it was found that its expression did not influence the association of ITGB4 expression with prognosis in colorectal cancer [ITGA6A variant was not specifically considered making the result difficult to interpret. Incidentally, based on the use of genetically modified mouse Itga6 mutant models, De Archangelis et al. concluded that the α6β4 integrin could be classified as a tumour suppressor in the colon based on their observations that depletion of the α6 subunit in intestinal epithelial cells leads to a chronic inflammation that drives the subsequent development of tumors [ITGA6A and ITGA6B separately in future studies should help to clarify these issues.There have been a number of studies that have investigated i et al.  analyzedn cancer . ITGA6 hl cancer . Howeverf tumors , albeit f tumors , as summDetection of CRC at early stages is a key factor for reducing mortality because this cancer can be treated with high success rates before the occurrence of metastasis ,56. AdvaITGA6 in cancer cells, notably under its ITGA6A form, our group has also evaluated this target in the stools of patients with colorectal lesions, based on the rationale that exfoliated cancer cells express higher levels of ITGA6 and are resistant to anchorage-dependent apoptosis, increasing the likelihood of detecting it in the stools  vs. FIT alone . In a ree stools .ITGA6 and ITGA6A confirmed the usefulness and reliability of the approach [ITGA6 levels were found to be increased in stool samples of AA and CRC at all stages while receiver operating characteristic (ROC) curves revealed that ITGA6 as a single marker can predict 75% of the AA and 81% of the CRC, with a 88% specificity [ITGA6A levels were only found in samples from patients with CRC, consistent with previous observations in primary tumours [ITGA6 in algorithm-based analyses should strengthen this approach toward the development of a new tool for CRC screening.Using a relatively straightforward protocol for RNA extraction from the stools of patients with AA (24), CRC (91) and controls (60) , TaqMan-approach . Indeed,cificity . Comparacificity . Interes tumours ,44. CombITGA6 and ITGB4 have clinical relevance as biomarkers for a stool-based non-invasive CRC screening test and as indicators of overall survival, respectively. Further studies should contribute to implementing these data in the clinical care area, ITGA6 and ITGB4 representing potential therapeutic targets as well as biomarkers for assessing therapeutic therapies. Since its discovery as being predominantly expressed in primary CRC, integrin α6β4 has been the subject of various studies that have shown that this laminin receptor can mediate pro-migratory, pro-proliferative and pro-survival properties to cancer cells, three characteristics associated with CRC progression. Incidentally, new studies have shown that


Due to the combination of exotic features, this material offers great potential as a material platform for novel quantum effects.Time reversal symmetric (TRS) invariant topological insulators (TIs) fullfil a paradigmatic role in the field of topological materials, standing at the origin of its development. Apart from TRS protected strong TIs, it was realized early on that more confounding weak topological insulators (WTI) exist. WTIs depend on translational symmetry and exhibit topological surface states only in certain directions making it significantly more difficult to match the experimental success of strong TIs. We here report on the discovery of a WTI state in RhBi 2, where the topological surface states with saddle points result in a van Hove singularity along the (100) direction near Fermi energy.Weak topological insulators (WTI) remain difficult to be observed in experiments. Here, the authors discover a WTI state in RhBi Z2 topological invariants, . The case ν0 = 1 is referred to as a strong topological insulator (STI) 2. A characteristic feature of a STI is the existence of gapless topological surface state (TSS) on all surfaces, which have been observed experimentally in many materials such as Bix1−Sbx, Bi2Se3, and Bi2Te3 3. In contrast to 2D TIs, even when ν0 = 0 the system can have non-trivial νi, resulting in a weak topological insulator (WTI). Reported WTI states are rather rare as gapless TSS can be detected only on particular surfaces, which may not be natural cleaving planes in many 3D materials. For instance, Bi14Rh3I9 was predicted to be a WTI with Z2 = . However, direct experimental verification of the TSS has remained elusive since the cleaving plane is (001), which is a topologically trivial side 4 and hence forces reverting to indirect signals on e.g., step edges5. The recent development of nano-ARPES has reinvigorated the search for WTIs. For instance, a first WTI TSS was only recently measured by isolating a ~2 μm size side facet and using nano-ARPES in quasi-one-dimensional bismuth iodide β-Bi4I46.From the perspective of considering solely TRS, 3D topological insulators are classified by a series of 2 as an exciting candidate material. To minimize potential degeneracies in reciprocal space, we decided to start with the lowest possible symmetry unit cell: triclinic. To maximize spin-orbit coupling we chose the heaviest  stable element, Bi as a majority component. For simplicity we chose to start by limiting our search to binary compounds. As a result of this cascade of physically inspired constraints we rapidly identified RhBi2 as a promising candidate material with clear van der Waals-like bonding along the crystallographic a-axis . RhBi2 is the only known compound to this specific, very low symmetry, structure. Here, we provide theoretical understanding and experimental evidence of the simplest WTI state in triclinic crystal RhBi2 with clear TSS at the natural cleaving surface. As we will discuss below, the WTI classification of RhBi2 maximally profits from its space group. As 7. Moreover, due to the absence of additional symmetries none of these high symmetry momenta are related and a WTI can exist in every stacking direction8. In fact, this carefully selected, simple structure makes this the only space group in which the symmetry eigenvalues at TRIM points convey all topological invariants one-to-one12. Rather surprisingly, we find that this freedom of choosing the stacking direction culminates in an index, , that is perpendicular to the layering of the material, creating the possibility of a TSS preserving cleavage plane.As part of an effort to design and discover materials with novel, intrinsically non-trivial, topological properties we identified RhBixis Fig. b. RhBi2 2 allows the system to have a saddle points, where the curvature of a band has opposite sign in two perpendicular direction in momentum space. A saddle point is closely related to a VHS, leading to a divergence in the density of states. Previously, VHSs have been reported in a variety of materials; graphene14, cuprate superconductors17, Pt2HgSe3 18, Pbx1−SnxSe(Te)19. The proximity of EF to a VHS is expected to significantly enhance the impact of electronic correlations and drive quantum many body instabilities toward superconductivity22 ferromagnetism26 or antiferromagnetism27, depending on band structure and many-body interactions. In addition, the subtle interplay of protected and correlated surface states with the bulk is predicted to lead to unusual surface quantum criticality28. As we show, this is expected to result in an order of magnitude enhancement of superconducting Tc, and generally increases the tendency toward development of electronic order. Partial substitution of Rh with Ru or electrostatic gating offer a possible path for lowering the EF in RhBi2. Owing to the simplest topological classification and VHS in the vicinity of EF, triclinic crystal RhBi2 offers unique advantages for exploring exotic quantum phenomena in a weak topological insulator.The lack of symmetries, especially the absence of rotational symmetry, in triclinic RhBi2 by using ARPES, DFT calculations and an effective model. Our result reveals two surface Dirac points, which are protected by time-reversal symmetry at the 2 along (100) has a WTI phase, which is characterized by Z2 = .We present a study of triclinic RhBi2 is an interesting case in terms of both band structure and topology. The bulk band structure of RhBi2 calculated from density functional theory30 (DFT) using PBE exchange correlation functional with spin-orbit coupling (SOC) is plotted in Fig. EF is shown in Fig. d and Bi p orbitals. From the small but finite density of states (DOS) at EF in Fig. 2 is a metal exhibiting non-overlapping pockets. There are no crossings between the top valence and bottom conduction bands anywhere in the BZ. The two bands crossing the EF give multiple electron and hole pockets. The electron and hole pockets are near BZ boundaries, while there is a large band gap around the BZ center Γ point. Notable are the electron pockets around X and near L points and the hole pockets near the Y point. There are also two small hole pockets totally inside the BZ. Although the structure is stacked on the bc plane along the b1 direction, a large electron pocket is on the b1 = 0.5 plane around the X point. In contrast, there is band gap on the b3 = 0.5 plane around the Z point.Due to the symmetry group hosting only an inversion center, the layered triclinic RhBi7. In fact, from the perspective of the recent advancements in classifying band structures using constraints in symmetry eigenvalues10 and comparing them to atomic configurations12, the space group at hand, number 2 or 9, as there are no symmetry constraints between high symmetry momenta8. The topological indices, apart from TRS invariant ν0 that we find to be zero, comprise three Z2 invariants corresponding to the weak indices and a Z4 index31 that comes from promoting ν0 to the inversion symmetric context. The latter corresponds to the twice the value of the inversion invariant δi, Z4 = 2δi, here9. The calculated Z4 index is 2, indicating that RhBi2 is topologically non-trivial, but indeed not a strong topological insulator. The calculated parity eigenvalue products are (+1) at Γ and Z points, and (-1) at all the other TRIMs, which gives the Fu-Kane index of , determining the three Z2 invariants. This can also be confirmed by Wannier charge center (WCC) evolution or Wilson loop on k3 = 0.0 and 0.5 planes in Fig. Z2 = 1 on these planes34. In contrast, 2D Z2 = 0 on the other k1,2 = 0.0 or 0.5 planes. Interestingly, although the layered structure is stacked along the b1 direction, the weak TI can be seen as a stacking of quantum spin Hall (QSH) layers along the b3 direction.Topological analysis. With inversion being the only symmetry in the system besides time-reversal symmetry, the topological features are determined by the parity eigenvalues of the occupied bands at TRIM points1 or perpendicular to the bc plane, i.e., (100). On the (100) surface, the Γ and X points are projected to EF, the area near the 35, parity eigenvalue products can also be projected onto surface as in πa = δa1δa2, where TRIM a1 and a2 projected into a on surface. The result is (−1) for 2 is a topologically non-trivial 2D material as a layered compensating semimetal hosting the simplest WTI possible as the underlying space group has minimal symmetry.In Fig. 2, we performed ARPES measurements and DFT calculations to identify relevant features in the electronic structure. Fig. 2 measured using laser-based APRES, where dashed lines mark main crystallographic directions in the BZ. The experimental data in Fig. 2 possesses TSS arising from weak topological insulating phase in (100) direction. In addition, we observed twofold rotational symmetry at the FS from the DFT calculations, although the crystal structure is triclinic. This is because three-dimensional inversion symmetry reduces to effectively two-dimensional rotation symmetry upon projection of all transverse momenta. To understand this phenomenon, we carefully studied different projections of each layer in the unit cell. Supplementary Note k1(kx) values on (100) surface. Red looped curves represent electron pockets. Based on the calculation, only projections from k1= 0 and 0.5 planes show twofold rotational symmetry and the k1 = 0 plane shows large electron pocket around the center of the BZ. Therefore, the large electron pocket around k1 = 0 plane and addition of all planes in the BZ will give us the effective twofold rotational symmetry on the 2D FS.In order to verify the nontrivial topological nature of triclinic RhBiTo demonstrate surface state origin of the measured band dispersion, we plot data along a entclass1pt{minimaentclass1pt{minimaentclass1pt{minimaentclass1pt{minima36, it shows a strong warping effect along the energy axis making saddle points in the lower band. k ⋅ p model band dispersion in Fig. #4) which are marked as dashed lines in Fig. kz), Fig. z ~ 0.45 Å−1 while the horizontal cut , Fig. ky direction. On the other hand, band dispersion in the horizontal direction significantly deviates from the vertical directions as shown in Fig. Out of the two surface Dirac points present, the Dirac point around the d0(k) is even in k and d1,2,3(k) are odd in k. Expanding our energy to second order then givesE0 is the energy at the crossing points of the surface bands, {Ai}, {Bi} and {Ci} are all real parameters and momenta are measured relative to the H(k) to third order, giving:To qualitatively address the observed saddle points in vicinity of the entclass1pt{minimaentclass1pt{minimaεk = 0, are called van Hove points and lead to singularities in the density of states (DOS): gs denotes spin degeneracy). In two dimensions, d = 2, saddle points of the dispersion lead to a logarithmically divergent DOS. If this divergence occurs close to the Fermi energy, electronic correlations are strongly amplified, which can drive the system toward various electronically ordered states such as superconductivity, spin or charge density waves. In contrast, nodal points of the dispersion, where the Fermi surface shrinks to a point are characterized by a vanishing DOS.Extrema of the energy dispersion, ∇ 2 that occur in close proximity to each other. To further underpin this observation, we here study in detail the properties of a low-energy k ⋅ p model , the DOS is large and almost constant, corresponding to an effective mass of about m* ≈ 0.4me. This is an average of the almost-flat character of the lower band along As described above, our ARPES measurements indicate the presence of both van Hove and nodal points in the surface bands of RhBi(see Eq. ) that deTc close to the van Hove point. This provides an explicit and quantitative prediction on the expected boost of correlation effects in RhBi2 arising from the surface saddle points, stimulating further experimental efforts to tune the Fermi energy close to the saddle points. Such tuning can be accomplished by chemical substitution  or electrostatic gating. For concreteness, we consider a fully gapped s-wave superconducting state stabilized on the surface of RhBi2. We calculate the ratio Tc/Tc,0 as the system is tuned across the van Hove singularity, where Tc,0 refers to the transition temperature away from the van Hove point. A discussion of the microscopic origin of superconductivity and possible other pairing channels is left for future work. Note that similar enhancements are expected in other interaction channels such as for density wave states. At weak coupling, Tc can be calculated from the standard BCS expressiong is a momentum-independent superconducting coupling and Λ corresponds to the Debye frequency in case of phonon-mediated superconductivity. At the saddle points the DOS diverges as ρ0 ≈ 3.2 × 10−3 Å−2eV−1 and D ≈ 16.5 meV [see Fig. 37  for several reasons. First, the photon energy and polarization of photon source may influence intensity of ARPES data. Second, the collected data always include signals from both surface and bulk states.Our results identify RhBi2 also hosts potential for other future pursuits. For example, the material could host intriguing new physical phenomena and new topological phase transitions when stress or strain are applied. On a related note, being a WTI in simplest form, RhBi2 could also spark interest in making it a material platform to examine the role of defects. Indeed, growing a dislocation in different directions will ensure the binding of topologically protected modes when the weak index vector is parallel to the defect’s Burger vector42. This pursuit is further underpinned by the unusual nature of the stacking vector  that is perpendicular to layering of the material and thus poses new relative orientations between the two, directly affecting the possibility of growing defects.Apart from the discussed implications, RhBi2 crystals were grown using the high temperature solution growth method out of excess Bi43. An initial concentration, Rh20Bi80, of elemental Rh and Bi was placed into a fritted alumina crucible44 and sealed in fused silica ampoule under a partial pressure of argon. The ampoule was then heated up to 900 ∘C over 4 h, held there for 3 h and cooled down to 480 ∘C over 200 h. At this temperature the excess solution was separated from the RhBi2 crystals using a centrifuge43.The crystal structure is confirmed by X-ray diffraction (XRD) measurement.Sample growth. RhBi45. Data from the laser based ARPES were collected with 6.7 eV photon energy. Angular resolution was set at ~0.1∘ and 1∘, along and perpendicular to the direction of the analyser slit respectively, and the energy resolution was set at 2 meV. The size of the photon beam on the sample was ~30 μm in the laser system and ~0.5 mm in the helium lamp system. Samples were cleaved in-situ at a base pressure lower than 1 × 10−10 Torr, 40 K and kept at the cleaving temperature throughout the measurement.ARPES experiments. Helium discharge lamp ARPES consists of a helium discharge lamp and a Scienta R8000 analyzer. The Helium discharge lamp ARPES data were collected wtih 21.2 eV photon energy. The laser ARPES system consists of a Scienta DA30 electron analyzer, picosecond Ti:Sapphire oscillator and fourth-harmonic generator30 (DFT) have been calculated with PBE46 exchange-correlation functional, a plane-wave basis set and projected augmented wave method47 as implemented in VAS49. The experimental lattice parameters in the triclinic unit cell are used. A Monkhorst-Pack50 (7 × 7 × 7) k-point mesh with a Gaussian smearing of 0.05 eV including the Γ point and a kinetic energy cutoff of 229 eV have been used. To calculate topological properties, a tight-binding model based on maximally localized Wannier functions53 was constructed to reproduce closely the bulk band structure including SOC in the range of EF ± 1eV with Rh sd and Bi p orbitals. Then the spectral functions and Fermi surface of a semi-infinite RhBi2 (100) surface were calculated with the surface Green’s function methods57 as implemented in WannierTools58.Ab initio Calculations. Band structure with spin-orbit coupling (SOC) in density functional theorySupplementary InformationPeer Review File


Biomechanical measurements were then conducted to determine the functional integrity of the samples. NIR spectral variations resulting from different damage types were investigated and the samples classified using partial least squares discriminant analysis (PLS-DA). Partial least squares regression (PLSR) was then employed to investigate the relationship between the NIR spectra and biomechanical properties of the samples. Results of the study demonstrate that substantial spectral changes occur in the region of 1700–2200 nm due to tissue damages, while differences between enzymatically and mechanically induced damages can be observed mainly in the region of 1780–1810 nm. We conclude that NIR spectroscopy, combined with multivariate analysis, is capable of discriminating between cartilage injuries that mimic idiopathic OA and traumatic injuries based on specific spectral features. This information could be useful in determining the optimal treatment strategy during cartilage repair in arthroscopy.This study evaluates the feasibility of near infrared (NIR) spectroscopy to distinguish between different cartilage injury types associated with post-traumatic osteoarthritis and idiopathic osteoarthritis (OA) induced by mechanical and enzymatic damages. Bovine osteochondral samples ( The condition is mainly characterized by severe pain, restricted joint movement and erosion of articular cartilage, the layered tissue covering the ends of bones in articulating joints. This highly specialized, avascular and aneural tissue is responsible for load transmission and lubrication in the joint. Cartilage is comprised primarily of a framework of collagen fibers and entrapped proteoglycan macromolecules, the extracellular matrix (ECM) components of the tissue 20–35%), and water 65–80%).–35%, and5–80%.–35in vitro and in vivo injury models have been used,et al.et al.et al.et al.11Cartilage injuries differ in extent and type of tissue damage and the response of the tissue to the injury.Cartilage damage can be assessed and repaired during arthroscopic surgery. However, traditional arthroscopic examination of cartilage injuries is subjective and has poor intra- and inter-observer reliability.34et al.et al.et al.Optical spectroscopy is an effective, non-destructive method for determining the structure and composition of materials, including those of biological origins. In particular, NIR spectroscopy is among the most useful optical methods for qualitative and quantitative arthroscopic assessment and characterization of the properties of articular cartilage.in vivo evaluation of cartilage structure, composition and integrity,Although NIR spectroscopy has been shown to be a promising technique for The aim of this study is to evaluate the capacity of NIR spectroscopy to distinguish between different cartilage injury types associated with PTOA and idiopathic OA induced by respective mechanical and enzymatic damages in bovine cartilage.n = 10) with visually normal cartilage surface were extracted from bovine (age 14–22 months) knee joints obtained from a local abattoir. Osteochondral samples (n = 72) were harvested by using biopsy punch (diameter = 7 mm) from different anatomical locations of medial and/or lateral sides of patellae , mechanical damage (n = 24), and enzymatic damage (n = 36). Cylindrical osteochondral plugs with 7 mm diameter were prepared for intact control and mechanical damage groups. In case of enzymatic damage, to avoid lateral penetration of the enzyme into the tissue, larger rectangular samples (10 × 15 mm) were enzymatically treated followed by extraction of 7 mm cylindrical plugs from the center of the degraded tissue.Patellae n = 0 with vin = 12) was subjected to mechanical injury via impact loading using a custom-made drop tower  at the end was dropped onto the sample from a height of 7.5 cm. The impactor dropping height, and thus energy delivered to the cartilage surface, was determined based on preliminary assessments to create minor chondral cracks on the cartilage surface.The samples in this group were further divided into two subgroups. The first subgroup M1, , n = 12 n = 12) was subjected to mechanical abrasion surface damage using P80 sandpaper (corresponding to particle size of 200 µm). Using a custom-made grinding tool , collagenase 90 min  and trypsin 30 min . The prewarmed samples were incubated at 37 °C and 5% CO2 in PBS solution containing the respective enzymes  and supplemented with antibiotics, including Penicillin–Streptomycin–Amphotericin B  for the different times specified previously. The incubation times of 30 min for trypsin and 90 min for collagenase were applied to induce mild cartilage degradation that mimic early OA. In order to induce severe damage, long incubation time of 24 h in collagenase was applied.Two enzymes were used for degradation of the samples in group 2. Collagenase D (Sigma Aldrich) was used for the degradation of the collagen network,in vivo arthroscopy. Each spectral measurement is the average of 50 acquisitions, with integration time of 16 ms. The NIR system consisted of a spectrometer , light source  and a custom diffuse reflectance arthroscopic fiber optic probe.d = 3.25 mm) resembles the shape of a traditional arthroscopic hook. The probe tip window (d = 2 mm) contains 114 optical fibers (d = 100 µm), with 100 fibers emitting and 14 fibers (7 + 7) collecting light to the spectrometers. Avasoft software  was used for spectral data acquisition.32NIR spectral measurements of each sample were obtained before (Pre) and after (Post) degradation. NIR measurements (3 spectra per sample) were carried out before and after injury at the center of samples immersed in PBS mimicking nippy (https://github.com/uef-bbc/nippy), an open source spectral preprocessing toolbox.Spectral preprocessing was conducted using To investigate differences between “Pre” vs. “Post” damage groups and for classification of “Mechanical” vs. “Enzymatic” damage groups, multivariate classification analysis based on partial least squares discriminant analysis (PLS-DA) was employed using classification toolbox (version 5.3)R2) between the actual and predicted values.The partial least squares regression (PLSR) technique was employed in MATLAB to investigate correlation between articular cartilage spectral data of different damage groups and reference measurements of biomechanical properties. PLSR models were validated using test set (15% of data) similar to PLS-DA. Model performance was evaluated using root mean square error of prediction (RMSEP), cross-validation (RMSECV) and the coefficient of determination Eeq). A three-step testing protocol (5% of remaining cartilage thickness at each step with 100%/s ramp rate) was applied with the relaxation time between each step being 900 s. Before mechanical indentation, the samples were preconditioned using a cyclic 2% strain (4 full cycles). The stress–relaxation protocol was followed by measurement of the dynamic modulus (Edyn), for which a sinusoidal dynamic test was performed with frequencies of 0.1, 0.5, 1, and 2 Hz . The values of equilibrium and dynamic moduli were calculated by assuming the cartilage to be a mechanically elastic and isotropic material.18Biomechanical indentation tests were performed after sample degradation and NIR measurements. The instrument used for biomechanical measurements consisted of a custom made high-precision material testing device . The data was expressed as mean Table  and compp < 0.05) after data pre-processing.Mean NIR spectra of enzymatic and mechanical damage groups, with respective control group, are presented in Fig. The results of two PLS-DA classification models are presented in Fig. Training set (85% of samples) was used for creating the first model (“Pre” vs. “Post”), and the model was validated using an independent test set (15% of samples). A confusion matrix, showing the model performance on the test set is presented in Table p < 0.05)  were observed between the enzymatically and mechanically damaged samples.Significant variation in cartilage biomechanical properties was observed between control and damaged cartilage (5) Figs. a and 4b.R2= 78–95%) were obtained with the optimal models for prediction of the biomechanical parameters  of the samples from their NIR spectral data.rs Table .Table 6Pin vitro. The experimentally induced damages, mechanical and enzymatic injuries, are associated with trauma related structural injury and osteoarthritis related changes in tissue composition, respectively. The findings presented here could prove useful in detecting compromised cartilage prior to visible signs of matrix structural and compositional degeneration.In the present study, we investigated for the first time the ability of NIR spectroscopy, conducted using a custom fiber-optic arthroscopic probe, to detect differences between enzymatically and mechanically induced damages of articular cartilage Classification based on PLS-DA provides an insight into the relationship between the optical response of articular cartilage and the state of its matrix. The high PLS-DA classification accuracy for “Pre” vs. “Post” group classification  suggests significant changes in the tissue structure and/or composition following degeneration. This indicates that NIR spectroscopy is sensitive to overall degenerative changes in the cartilage matrix.in vivo adaptation, a two-model approach would be required; in the first stage a model that distinguishes between healthy and damaged cartilage will be evaluated, while the second stage model (if the tissue is classified as damaged) will determine the nature of damage .It is a well-known fact that enzymes modify the chemical bonds of molecules,The depth-dependent interactions of NIR light with articular cartilage are related to chemical bonds of the matrix constituents, i.e., water, PG, and collagen, particularly molecules containing OH, CH, NH, and SH bonds.Biomechanical testing showed a significant decrease equilibrium and dynamic moduli of the enzymatically and mechanically damaged cartilage samples when compared to the control group. The lower values of equilibrium and dynamic moduli in all damaged groups can be attributed to significant loss of the superficial proteoglycans.The capacity of NIR arthroscopy to distinguish between different cartilage injury types that mimic PTOA and idiopathic OA via mechanical and enzymatic damages, respectively, was evaluated in this study. We conclude that NIR spectroscopy, based on specific spectral features and combined with multivariate classification analysis, has the potential to distinguish between idiopathic and trauma-related degeneration of cartilage, as well as structural injuries with and without PG or collagen losses. This information could be useful in determining the optimal treatment strategy during arthroscopic cartilage repair.


Orcinus orca) are distributed widely in all oceans, although they are most common in coastal waters of temperate and high-latitude regions. The species’ distribution has not been fully described in the northwest Atlantic (NWA), where killer whales move into seasonally ice-free waters of the eastern Canadian Arctic (ECA) and occur year-round off the coast of Newfoundland and Labrador farther south. We measured stable oxygen and carbon isotope ratios in dentine phosphate (δ18OP) and structural carbonate  of whole teeth and annual growth layers from killer whales that stranded in the ECA (n = 11) and NWA (n = 7). Source δ18O of marine water (δ18Omarine) at location of origin was estimated from dentine δ18OP values, and then compared with predicted isoscape values to assign individual distributions. Dentine δ18OP values were also assessed against those of other known-origin North Atlantic odontocetes for spatial reference. Most ECA and NWA killer whales had mean δ18OP and estimated δ18Omarine values consistent with 18O-depleted, high-latitude waters north of the Gulf Stream, above which a marked decrease in baseline δ18O values occurs. Several individuals, however, had relatively high values that reflected origins in 18O-enriched, low-latitude waters below this boundary. Within-tooth δ18OSC ranges on the order of 1–2‰ indicated interannual variation in distribution. Different distributions inferred from oxygen isotopes suggest there is not a single killer whale population distributed across the northwest Atlantic, and corroborate dietary and morphological differences of purported ecotypes in the region.Killer whales ( Orcinus orca) indicate they are most abundant in coastal, high-latitude waters of both hemispheres, with lower densities occurring in less productive tropical and offshore waters1. In the northwest Atlantic (NWA), where there has been almost no directed research on killer whale distribution, incidental sightings and whaling records reflect a similar general pattern of decreasing abundance from the Arctic to the Gulf of Mexico and Caribbean Sea4. Over the past several decades, killer whales have been observed more frequently in both the eastern Canadian Arctic (ECA)5 and off the coast of Newfoundland and Labrador (NL)6, potentially reflecting shifting distributions and/or increasing abundance in response to declining sea ice5 or recovery from commercial whaling and culls7. Assessment of potential explanatory factors within the broader context of the NWA , however, has been limited by existing observational data, which is largely qualitative and includes temporal and spatial biases.Global distribution patterns of killer whales  affecting dissolved inorganic carbon (DIC) concentrations and associated 13C fractionation leads to pronounced latitudinal δ13C gradients in marine surface water carbon species and phytoplankton20. Baseline isotopic variation is incorporated into animal tissues via food and water , thus serving as a marker of their geographic origins18. Although not commonly used in this context, the oxygen isotope composition (δ18O) of biogenic apatite is an effective marker of cetacean distributions across isotopically distinct regions of the ocean22. Marine surface water δ18O is governed by relative rates of evaporation and precipitation, resulting in a latitudinal gradient of several per mil in both hemispheres23. Cetacean body water closely tracks marine δ18O, as their dominant oxygen fluxes  are not strongly fractionating26. Biogenic apatite in dentine and bone, in turn, precipitates in oxygen isotope equilibrium with a constant offset from body water in homeothermic mammals28, such that the δ18O of phosphate (δ18OP) and structural carbonate (δ18OSC) ultimately vary linearly with that of source marine water29.One of the earliest ecological applications of stable isotope analysis has been the assignment of animal distributions through matching tissue isotope composition with underlying geographic isotope variationδ18O occurs in the North Atlantic, where a latitudinal δ18O gradient spanning several per mil exists between the Arctic, which is characterized by 18O-depleted marine surface waters typical of high latitude regions, and the mid North Atlantic, which is characterized by 18O-enriched Gulf Stream waters23. The δ13C of DIC and phytoplankton also vary systematically across the North Atlantic, decreasing by up to 10 per mil moving northeast from the Caribbean to the Norwegian Sea20. These two elements together can thus provide complementary discriminatory power for evaluating North Atlantic whale distributions31. To that end, we measured δ18OP, δ18OSC, and δ13C of structural carbonate (δ13CSC) in biogenic apatite of dentine from killer whales that stranded in the ECA and NWA. Source marine water δ18O (δ18Omarine) was estimated from dentine δ18OP values using a published calibration22, and then compared to the North Atlantic δ18O isoscape23 to infer individual killer whale distributions. Our objectives were to evaluate whether ECA and NWA killer whale distributions (1) overlap within the broader North Atlantic, and (2) encompass the relatively 18O-enriched waters of the mid North Atlantic, as earlier hypothesised2 and recently demonstrated using satellite telemetry10. The δ18O values of most ECA and NWA killer whales indicated their distributions were restricted to the 18O-depleted, high-latitude waters surrounding the ECA, NL, and Greenland, although several individuals originated from a broader area encompassing 18O-enriched, low-latitude waters. These findings are discussed within the contexts of population structure and purported killer whale ecotypes in the ECA and NWA.The most pronounced variation in global marine Teeth from killer whales that stranded in ECA  and NWA (n = 7)  from a subset of ECA (n = 2) and all NWA (n = 7) whales to assess within-tooth δ18OSC variation. Mandibular bone was sampled from skulls lacking teeth using a handheld rotary tool. Bone should be directly comparable to dentine because the δ18OP of both tissues varies linearly with δ18O of environmental water with similar intercepts and slopes22, and any effect of cooler ambient temperatures of narrow jaws on 18O fractionation should be similar for teeth and mandibles29. Both whole-tooth and bone samples also integrate long-term isotopic composition, with the caveat that bone is subject to remodelling and dentine generally is not34.Dentine was collected for δ18OP and δ18OSC were analyzed following procedures described in Matthews et al.22. Briefly, for isotopic analysis of phosphate oxygen, powdered samples (25 to 35 mg) were dissolved in 3 M acetic acid, and silver phosphate (Ag3PO4) was then precipitated following the ammonia volatilization method36. Aliquots of powdered Ag3PO4 (~ 0.2 mg) were then weighed into silver capsules and introduced into a Thermo Scientific™ High Temperature Conversion Elemental Analyzer (TC/EA). The resulting carbon monoxide (CO) gas was purified on a GC column packed with a 5 Å molecular sieve and swept in a continuous flow of helium to a Thermo Scientific™ DeltaPLUSXL™ isotope-ratio mass spectrometer (IRMS) for isotopic analysis.All stable isotope analyses were performed at the Laboratory for Stable Isotope Science (LSIS) at the University of Western Ontario, London, Ontario, Canada. Dentine and bone δ-notation relative to Vienna Standard Mean Ocean Water (VSMOW), calibrated using accepted values for standards IAEA-CH-6 (+ 36.40‰)37 and Aldrich Silver Phosphate–98%, Batch 03610EH (+ 11.2‰)38. The precision (SD) of these standard analyses ranged from 0.33‰  to 0.42‰ , respectively. The accuracy of this calibration curve was tested using NBS 120c phosphate rock; 11 analyses returned an average δ18OP =  + 21.57 ± 0.29‰, which compares well with its accepted value of + 21.7‰39. The average reproducibility for replicate δ18OP analyses of samples was ± 0.22‰ (n = 13).Phosphate oxygen isotope ratios are reported in 41. Powdered samples (~ 0.8 mg) were dried overnight at 80 °C in a reaction vial, which was then septa-sealed, capped, and evacuated using an automated sampler (Micromass MultiPrep). Ortho-phosphoric acid was then added to generate carbon dioxide gas (CO2) by reaction at 90 °C for 20 min. The evolved CO2 was cryogenically scrubbed and transferred to an IRMS (Fisons Optima) for analysis in dual-inlet mode.Structural carbonate oxygen and stable carbon isotopes were measured in untreated dentine since the effects of treatment to remove secondary carbonate and organic matter can be inconsistentδ18OSC values were calibrated relative to VSMOW using accepted values for NBS 19  and NBS 18 , with a precision (SD) of 0.05‰ (n = 51) and 0.12‰ (n = 27), respectively. Accuracy and precision (SD) were assessed using laboratory reference materials not included in the calibration curve: WS-1 , and Suprapur . δ13CSC values were calibrated relative to VPDB using accepted values for NBS 19  and LSVEC , with a precision (SD) of 0.05‰ (n = 51) and 0.13‰ (n = 24), respectively. Accuracy and precision (SD) were assessed using international and laboratory reference materials not included in the calibration curve: NBS 18 ; WS-1 , and Suprapur . The average reproducibility for replicate analyses of samples was ± 0.14‰ (n = 16) for δ18OSC and ± 0.07‰ (n = 16) for δ13CSC.43) since specimens were collected over an ~ 70-year timespan. Whale ages were estimated from counts of GLGs observed under reflected light, and the median of three counts conducted by one reader (CJDM) over several weeks was taken as the age estimate  was similar in direction and magnitude to declines in North Atlantic δ13C attributed to the Suess effect43. δ13CSC values were therefore adjusted to the most recent sample year (2013) by subtracting 0.023‰ year−1 to remove temporal bias.We first tested for temporal baseline isotope shifts  dolphins22  of dentine/bone δ18O of a large number of cetacean species from linear relationships with environmental δ18O22. Although the two GoM dolphin species, common bottlenose dolphins (Tursiops truncatus) and Atlantic spotted dolphins , exhibit nearshore-offshore habitat partitioning along a gradient in surface water δ18O values23, their δ18OP were statistically indistinguishable22 and therefore grouped in our analyses. Greenland and Denmark killer whales were excluded from these analyses given their small sample sizes. Significant Kruskal–Wallis tests were followed by Dunn’s multiple comparison post-hoc test with Benjamini–Hochberg adjustment of p-values44. All analyses were done using R version 4.0.032 and its associated package ‘FSA’45.Differences in 22 Table  as δ18O δ18OP based on a Euclidean distances and average linkage was performed on all killer whales (including Greenland and Denmark samples) using the R packages ‘cluster’46 and ‘dendextend’47.Hierarchical cluster analysis of δ18Omarine from each individual killer whale’s dentine δ18OP by rearranging the following published calibration:0, 18.73 ± 0.30‰) and slope  estimates are based largely on dentine δ18OP measurements of cetaceans from the North Atlantic and associated basins with heterogenous δ18Omarine22. Intercept and slope standard deviations and δ18OP measurement error were propagated through to final δ18Omarine estimates using first-order Taylor series expansion in the R package ‘propagate’48. δ18Omarine values encompassed by the estimated 95% CI for each individual killer whale were then extracted from modelled North Atlantic gridded surface δ18O data23 downloaded from Global Seawater Oxygen-18 Database49. Marine δ13C isoscapes20 were not used in this manner because confounding dietary and metabolic influences on dentine δ13CSC values50 could not be constrained to allow for direct comparison with baseline DIC or phytoplankton values.Geographic distributions were assigned by first estimating source δ18OSC measurements was calculated as an index of within-tooth variation for each of the 9 teeth that were measured.Finally, the standard deviation of individual GLG Ethics approval was not required for museum specimens used in this study. Destructive sampling was formally approved through museum protocols.δ18OP values ranged from + 15.94 to + 22.40‰ , although pairwise comparisons indicated whales that stranded in the ECA (+ 17.21 ± 1.11‰) and NWA (+ 18.45 ± 1.81‰) were not significantly different (p = 0.087). ECA killer whale δ18OP did not differ from ECA belugas  but was significantly lower than GoM dolphins   or GoM dolphins (p = 0.23). Mean bone δ18OP values of the Greenland and Denmark killer whales were + 17.4 ± 0.3‰ and + 17.4 ± 0.4‰, respectively  Table . The δ18δ18OP produced groupings that were not consistent with stranding location. The most distant clusters comprised five killer whales from both the ECA and NWA with the highest δ18OP values ; the exception was the three whales that stranded together in Cumberland Sound in 1977 (the ECA-CS-1977 series) , however, had inferred distributions that largely excluded high-latitude coastal areas and encompassed a broader band of the North Atlantic, including the relatively 18O-enriched waters south of the Gulf Stream  and highest in whale NWA-SC-1975-1 (2.61‰) , as observational effort has been limited primarily to nearshore areas when killer whales are seasonally abundant , and photo-ID catalogues have not been developed for most regions. Our assessment of killer whale distributions using dentine oxygen isotopes integrated over long timeframes has revealed patterns in the species’ distribution in the North Atlantic that have been suggested, but not resolved, by previous sightings compilations across the region60. The ranges of most whales were restricted to high-latitude 18O-depleted waters; however, the broader ranges of a smaller number of whales encompassing lower latitude 18O-enriched waters in the North Atlantic indicates a considerable degree of spatial structure among killer whales in the ECA and NWA that has not been reported previously.Distribution patterns have not been fully described for even the best-studied killer whale populations , while variance in predicted isoscape values was not. The much greater discrepancy observed for whale NWA-BP-1998, for which only the lower limits of the 99% CI of its predicted source δ18Omarine corresponded to isoscape values in lower latitudes of the North Atlantic (not shown), could reflect extremely sparse sample coverage informing modeled values in that region23.Isoscapes have been used routinely to infer distributions and movements of terrestrial animalsδ18OP values and estimated δ18Omarine values, which encompass both sides of the sharp boundary in marine δ18O values demarcated by the Gulf Stream23. The inferred high-latitude distributions of most killer whales above this boundary is consistent with global patterns that show killer whale density increases by 1–2 orders of magnitude from tropical to polar regions1, including in the NWA, where comparatively few killer whale records exist from the eastern seaboard of the U.S.A. south to the equator4. However, inferred distributions of several killer whales that stranded in both the ECA and NWA encompassed relatively 18O-enriched, lower latitude waters across a broader area of the North Atlantic. We can rule out passive transport of carcasses from distant locations via currents as a source of variation for these five whales, which either live-stranded  or were found in inland Arctic waters in minimal state of decomposition (ECA-RB-2009). Whales observed seasonally in the ECA have been hypothesized to range possibly as far south as the Caribbean during winter2, and recent studies have demonstrated10 or inferred17 movements of ECA killer whales into temperate and perhaps tropical waters. Killer whales are observed year-round in low numbers throughout the Caribbean65, and large numbers of killer whales were observed by whalers in the 1800s in a widespread offshore area known to them as the Western Ground, which stretched from Bermuda to the Azores14. Limited data preclude interpretations of killer whale residence patterns in either region65, although Katona et al.4 suggested there could be resident and migratory populations stretching from the Bay of Fundy to the equator.The most obvious pattern in our data is the spread in 2. However, the ~ 2‰ range of individual δ18OP values among these whales exceeds the degree of variability expected for cetacean populations with similar distributions within waters with homogenous δ18O. Clementz and Koch66 reported δ18O ranges of ~ 0.5 to 1‰ in tooth enamel of cetacean populations from the isotopically homogenous Californian coast. For comparison with other North Atlantic cetaceans, bone carbonate δ18O differed by just 0.4‰ between fin whales  from western Iceland and northwestern Spain31, and dentine carbonate δ18O differed by a similar amount between sperm whales  from northwestern Spain and Denmark30. While groupings based on stranding location did not differ significantly, spatial differences among individuals inferred from δ18OP are largely consistent with previous bulk and amino acid-specific δ15N analyses that suggested some degree of spatial separation among these same killer whales51.The largely similar inferred distributions of most of the killer whales in the high-latitude waters surrounding the ECA, NL, and Greenland could reflect a continuous distribution across the region, as has been hypothesized68. Carbonate in biogenic apatite precipitates from blood bicarbonate and δ13CSC thus reflects the bulk isotopic composition of respired carbohydrates, lipids and proteins70. Despite advances in modelling spatial variation in DIC and phytoplankton δ13C across the North Atlantic20, calibration of killer whale dentine δ13CSC values to the predicted δ13C isoscape would therefore require knowledge not only of trophic position, but also the fraction of carbon from dietary lipids and proteins routed to δ13CSC (see ref.66). However, the ~ 4‰ range in δ13CSC among killer whales exceeds that expected from trophic factors alone, particularly since most of the killer whales in our sample fed at a similar tropic position52. With more detailed dietary information to allow for partitioning of trophic and spatial influences on δ13CSC, relative δ13CSC differences among killer whales with similar δ18OP values could offer additional discriminatory power, particularly in areas of uniformly 18O-depleted coastal, high latitude waters.Geographic assignments can be refined by using multiple isotopes to narrow potential distributions to areas where tissue values correspond with intersecting isoscape values71 demonstrated a constant rate of dentine deposition across all months in a captive killer whale, which we assume is also true of wild killer whales. However, dentine deposition rates vary seasonally in many odontocete species in response to seasonal food availability or environmental variation, with more material typically laid down from spring to fall73. If this deposition pattern occurs in wild killer whales, then our analysis of whole-tooth samples and subsequent inferences about distributions would be biased towards summer months. Bone, however, is slowly and continually remodelled34; as such, bone δ18OP of the five whales from Greenland and Denmark reflect a long-term average distribution within high-latitude, 18O-depleted waters. That being said, temporally crude whole-tooth and bone samples would obscure any seasonal movements10 or interannual variation in distribution. Within-tooth variation in δ18OSC on the order of 1–2‰ suggests interannual variation in ECA and NWA killer whale distributions. By comparison, dentine carbonate δ18O declines of ~ 2‰ across male North Atlantic sperm whale teeth were linked possibly to large-scale latitudinal migrations at sexual maturity30. Large-scale movements of killer whales have now been documented globally, including the North Atlantic10. However, their ranging patterns remain poorly understood, and fine-scale spatial resolution  afforded by in situ microbeam sampling techniques74 could help resolve seasonal and interannual variation in movements and distribution.Myrick et al.75, using samples not included in this study, showed NWA whales formed a different clade than other North Atlantic killer whales. In a more recent analysis that sequenced whole genomes, Lefort76 differentiated two clusters among ECA and NWA killer whales: one that comprised animals from northern Baffin Island and Newfoundland, and another that comprised animals from Hudson Bay and Baffin Island. There was also high covariance among killer whales from the low Arctic (Hudson Bay) and those from the eastern North Atlantic 76, which is consistent with isotope clusters that comprised animals from the ECA and Greenland and Denmark. We note, however, that the Hudson Bay whale included in Lefort76, ECA-RB-2009, was relatively distant from the five Greenland and Denmark specimens based on δ18OP values. Of the four animals included in both studies, low genetic variation was observed between whales ECA-AB-1948 and ECA-RB-2009 and between whales NWA-CB-1971-2 and NWA-BB-200276. Neither of these pairings, however, clustered tightly together based on δ18OP  have amino acid-specific δ15N patterns indicative of dietary differences from the other whales, coupled with morphological differences in tooth wear52. These whales appear to be ecologically and morphologically similar to the North Atlantic Type 1 killer whales that range from NL to Norway77, and morphologically similar to a single killer whale specimen from the Caribbean65. We assume that distribution, and not dietary, differences are the primary driver of observed δ18OP variation among these whales, as ingestion of water via food and metabolic water formed via oxidation of food are thought to be relatively minor oxygen fluxes compared to diffusion of water across cetacean skin25. This assumption is supported by similar dentine δ18OP values of fish-eating and mammal-eating killer whale ecotypes from the eastern North Pacific 22. It is also supported more generally by relatively small deviations (< 1‰) of dentine/bone δ18O of whale species with varied diets from linear relationships with environmental δ18O22. Vertical variation in δ18Omarine could potentially confound our interpretations, if, for example, higher killer whale oxygen isotope compositions were acquired while spending significant amounts of time foraging in deep-water on species such as Greenland shark . Greenland sharks from northern Baffin Island have relatively 18O-enriched tooth phosphate that corresponds to δ18Omarine at depths exceeding 300 to 500 m78. While this depth is within the dive range of killer whales79, the ~ 6‰ range in δ18OP separating the sampled killer whales  to > 250 m depths (~ − 0.5‰) in Baffin Bay62.Oxygen isotope data are consistent with purported killer whale ecotypes in the ECA and NWAδ18OP values among individuals of three of the four groups of animals that stranded together indicate they likely comprised stable, long-term associations with similar distribution and movement history, consistent with research indicating offspring generally do not disperse from killer whale matrilines80. However, the close to 4‰ spread in δ18OP among the group of three killer whales that stranded together in Cumberland Sound in 1977 suggests they were not part of a cohesive group. The different ages (and thus sizes) of these whales does not appear to be a factor. While there is some suggestion of a decline in δ18OP with age in some of the older NWA whales, no such pattern was observed for the ECA whales (Fig. δ18OP despite having a similar age range (Tables 2. Temporary associations between small, stable groups of killer whales have been observed in other locations where prey resources are highly localized81, a possibility in Cumberland Sound where belugas are seasonally aggregated in a relatively small area.The oxygen isotope compositions of groups of killer whales that stranded together also allow for some inference on the nature of their associations. Similar les Fig. . Moreovee Tables . The thr82. Distribution shifts in response to changing environmental variables such as declining sea ice extent and duration can be rapid, as exhibited across various taxa in Arctic regions83. We therefore recommend further study of factors that drive current killer whale distribution and population structure throughout the North Atlantic, using a range of complementary approaches such as long-term, coarse-scale data reported here versus short-term high-resolution telemetry data10.The high-latitude distributions inferred for most of the sampled whales is relevant for understanding potential killer whale range expansions and/or population increases with reductions in sea ice extent and duration. However, with half of the ECA specimens and most of the NWA specimens in our sample coming from the 1970s or earlier, much of our sample does not encompass the approximately five-decade period over which sightings have increased dramatically in both the ECA and off NLSupplementary Information 1.Supplementary Information 2.