Treatment of wounds in special areas is challenging due to inevitable movements and difficult fixation. Common cotton gauze suffers from incomplete joint surface coverage, confinement of joint movement, lack of antibacterial function, and frequent replacements. Hydrogels have been considered as good candidates for wound dressing because of their good flexibility and biocompatibility. Nevertheless, the adhesive, mechanical, and antibacterial properties of conventional hydrogels are not satisfactory. Herein, cationic polyelectrolyte brushes grafted from bacterial cellulose (BC) nanofibers are introduced into polydopamine/polyacrylamide hydrogels. The 1D polymer brushes have rigid BC backbones to enhance mechanical property of hydrogels, realizing high tensile strength (21–51 kPa), large tensile strain (899–1047%), and ideal compressive property. Positively charged quaternary ammonium groups of tethered polymer brushes provide long‐lasting antibacterial property to hydrogels and promote crawling and proliferation of negatively charged epidermis cells. Moreover, the hydrogels are rich in catechol groups and capable of adhering to various surfaces, meeting adhesive demand of large movement for special areas. With the above merits, the hydrogels demonstrate less inflammatory response and faster healing speed for in vivo wound healing on rats. Therefore, the multifunctional hydrogels show stable covering, little displacement, long‐lasting antibacteria, and fast wound healing, demonstrating promise in wound dressing. A new class of highly stretchable, adhesive, biocompatible, and antibacterial hydrogel dressing is designed and prepared by synergizing biocompatible polyacrylamide hydrogel scaffold, biological adhesive polydopamine, and antibacterial polymer brush grafted from bacterial cellulose nanofibers. Compared with the wounds at flat areas of human body, it is still challenging to treat the wounds at special areas such as joints, popliteal fossae, axillae, and muscle folds. Poor adhesive performance, difficult fixation, and incomplete coverage are the main reasons. Moreover, in clinic, most wounds are sterilized with 75% alcohol or iodine, followed by covering with cotton gauzes. Therefore, regular disinfection and dressing replacement are necessary due to lack of antibacterial property of cotton gauze. In addition, fixed cotton gauze dressing needs to be taped, and sometimes, the skin is allergic to tape material. To this end, designing a stretchable, adhesive, antibacterial, and biocompatible dressing is of great clinical significance.Wound dressing has been an important branch of biomedical materials research.1 Skin Because of their superior biocompatibility, controllable physical properties, natural drug‐loading structure, and abundant functional groups, hydrogels have gradually become a hotspot of medical wound dressing. To date, hydrogels have been successfully applied to treat skin defects, infected wounds, burn wounds, diabetic feet, and wet wounds inside the body. Based on the healing requirements of different wounds, one or more functions such as good tissue adhesion, excellent mechanical property, antibacterial capability, cell crawling promotion, physical contraction, local immune regulation, and antitumor property have been implanted in the hydrogel dressings, such as Cur‐QCS/PF, QCSP/PEGS‐FA , OSA‐DA‐PAM, PDA@AgNPs/CPHs, NPs‐P‐PAA, and STP hydrogels. However, the existing hydrogel dressings were difficult to achieve a satisfactory balance among the multiple functions. For example, due to the presence of quaternary ammonium salt, both Cur‐QCS/PF and QCSP/PEGS‐FA hydrogels showed excellent antibacterial property, but their tensile strain (below 100%) and adhesion strength (less than 8 kPa) were not satisfactory. OSA‐DA‐PAM and STP hydrogel dressings had good adhesion and stretching performances, but no antibacterial property. With the catechol structure and nanosilver, PDA@AgNPs/CPHs and NPs‐P‐PAA hydrogels exhibited excellent tissue adhesion and antibacterial properties, but use of silver‐functionalized biomedical materials could give rise to cumulative toxic effect of heavy metal in organisms. Therefore, it is still highly challenging in preparing a hydrogel dressing with ideal tissue adhesion, good stretchability, broad‐band antibacterial capability, cell crawling promotion, and bio‐compatibility by a facile and efficient material design.Hydrogels are a class of 3D network gels formed by chemical and/or physical crosslinking.3 Becag‐pDADMAC, BCD) into polydopamine/polyacrylamide (PDA/PAM) hydrogels. For the as‐prepared multifunctional BCD/PDA/PAM hydrogels, the PAM component has good biocompatibility and stable crosslinking structure, and is thus used as the hydrogel scaffold. Inspired by the biological adhesion of dopamine from mussel, the PDA component has abundant catechol groups and thus can adhere to various surfaces, especially special areas needing large movements. More importantly, the BCD component not only has rigid BC backbones to enhance the mechanical property of hydrogels, but also has pDADMAC brushes with broad spectrum and low toxic positively charged quaternary ammonium groups for providing high‐efficiency and long‐lasting antibacterial performance. Moreover, the positively charged pDADMAC brushes could help attract negatively charged epidermis cells and thus promote cell crawling and proliferation. Therefore, our BCD/PDA/PAM hydrogels have superior mechanical behaviors with high tensile strength (21–51 kPa), large tensile strain (899–1047%) and ideal compressive performance, and demonstrate stable covering, little displacement, long‐lasting antibacteria and fast wound healing.Herein, a new class of highly stretchable, adhesive, biocompatible, and antibacterial hydrogel dressings is designed and prepared by introducing poly (pDADMAC) brushes grafted from bacterial cellulose (BC) nanofibers  is a highly efficient active/controllable polymerization system and can be used in surface functionalization of BC with abundant hydroxyl groups. pDADMAC chains were grafted from nanofibers of BC via SI‐ATRP, leading to formation of BCD  and C1s (287.1 eV) peaks ; peaks at 287.9, 286.3, and 284.7 eV of the deconvoluted high resolution C1s spectrum were mainly attributed to bonds of O—C—O, C—O, and C—C/C—H of BC, respectively . After grafting pDADMAC, new peaks appeared at 197.1, 268.0, and 402.1 eV, which were assigned to Cl2p, Cl2s, and N1s, respectively ; peak at 286.2 eV was mainly attributed to C—N/C—O bonds of BCD . Fourier transform infrared (FT‐IR) was also used to study the structure evolution of BC, initiator‐functionalized BC (BC‐Br) and BCD . Compared to BC, a new peak appeared at 1735 cm−1 for BC‐Br, which was attributed to carbonyl (C=O) stretching vibration; new peaks at 848 and 1479 cm−1 for BCD were ascribed to the characteristic bands of C—N and methyl (—CH3) groups of quaternized ammonium, indicating pDADMAC was successfully grafted.BC has a natural nanofiber network structure with good hydrophilicity, mechanical property, and biocompatibility, which has a broad application prospect in biomedical dressings.16 Sur which could affect the stability of acidic reactants. Here, BCD was firstly dispersed in the aqueous dopamine solution. Considering dopamine could prepolymerize under the action of oxidants, ammonium persulfate (APS) was used for prepolymerization of dopamine in our study . Due to presence of positively charges, the zeta potential of BCD/PDA/PAM hydrogel was measured to be 1.42–3.78 mV (pH = 6.5) or 1.64–3.35 mV (pH = 7.2), and became higher with increasing the BCD content . The positive charges would endow the hydrogel with antibacterial performance  environment,22 whiy Figure , Step 2,y Figure , Step 3.y Figure . With a s Figure . The rice Figure  and prom−1 was ascribed to C=O stretching of PAM; the peak at 1620 cm−1 was the N—H deformation peak for primary amine deriving from PDA, demonstrating the successful polymerization of dopamine in the system; the C—N stretching peak at 1402 cm−1 was from primary amide of both PDA and PAM in the hydrogel; the —NH2 in‐plane rocking peak at 1124 cm−1 mainly derived from PAM; the characteristic peak of BC at 619 cm−1 in the fingerprint region proved the existence of BCD.10‰BCD/PDA/PAM hydrogel was transparent light brown Figure , which we of BCD.22e2.2 The cut 10‰BCD/PDA/PAM hydrogel was healed within 30 min and could be stretched without cracking after 2 h healing . Meanwhile, the sample with 30 min healing showed a good healing effect and no re‐fracture was observed when attached to the left index finger with the movement of joints . As a result, the self‐healed hydrogel would be enough to meet the requirements of dressing.The network of BCD/PDA/PAM hydrogels was maintained by both noncovalent bonding  and covalent bonding of crosslinked polymers. Due to the existence of noncovalent bonds, 10‰BCD/PDA/PAM hydrogel showed a valuable self‐healing performance .29 TheFigure  The good resilience to withstand large deformation and high compressive strength made it qualified to meet the demand of toughness as hydrogel dressing.With a network system of physical and chemical crosslinking, BCD/PDA/PAM hydrogels have good elasticity and toughness. Under compressive loading, 10‰BCD/PDA/PAM hydrogel could withstand 60% of compressive strain under a stress of 45 kPa and recover to its original shape after removal of the load Figure . TherefoFigure 22a Th Addition of BCD enhanced the degree of crosslinking, which slightly decreased the strain compared with PDA/PAM hydrogel (1207%), but improved the toughness of hydrogel. The tensile strength of BCD/PDA/PAM hydrogels increased with an increase of BCD content, indicating that BCD had a reinforcing effect. The fracture tensile strength greatly increased from 21 to 51 kPa as an increase of the BCD ratio from 5‰ to 15‰, compared with PDA/PAM hydrogel (11 kPa). During cyclic tensile tests, a small degree of stress reduction was observed after the first cycle, which was attributed to the toughness of BCD network  formed at the hydrogel‐skin interfaces, indicating strong bonding . Although sticky fibrils formed during the separation, no residual hydrogel remained on the skin and no allergy was observed after a 24 h adhesion , indicating that 10‰BCD/PDA/PAM hydrogel had good biocompatibility. To evaluate the potential utilization of BCD/PDA/PAM hydrogels as medical adhesives, in vitro lap shear testing was performed using porcine skin . The tissue adhesive mechanism of our hydrogels was attributed to catechol groups of PDA component that had high binding affinity to amines, thiols, and imidazoles in peptides and proteins of tissue Figure .[24, n Figure .[8, a Figure , higher l Figure .[14, n Figure . The adh2.3 Advantages of quaternary ammonium salt antibacterial agents lie in low bactericidal concentration, low toxicity, low irritation, broad‐spectrum, and long‐lasting effects. The principle of sterilization is mainly from the positive charges, which could adsorb the negatively charged bacteria by electrostatic force, and accumulate on their bacterial walls, thus causing growth inhibition and death of bacteria. In this study, highly positive charged pDADMAC brushes of BCD were introduced to provide BCD/PDA/PAM hydrogels with antibacterial property  and Escherichia coli (E. coli) culture solutions to assess antibacterial property. The experimental groups were BCD/PDA/PAM hydrogels with different BCD ratios immersed in culture solutions containing bacteria, while the control group was only a culture solution containing bacteria. Optical density (OD600) values of bacteria cultured at different times were measured. As shown in Figure 600 values of S. aureus and E. coli in the control group increased significantly at the 8th and 6th hours, respectively, and reached a peak at the 12th hour. In the experimental groups, the OD600 values of S. aureus and E. coli for 10‰BCD/PDA/PAM and 15‰BCD/PDA/PAM hydrogels did not increase within measurement time of 96 h, indicating that the bacteria were completely killed. For 5‰BCD/PDA/PAM hydrogel, the OD600 value of S. aureus began to increase after 24 h and reached a peak value at the 48th hour, and the OD600 value of E. coli started to increase after 12 h and also reached a peak value after 48 h. This showed that the higher the BCD ratio, the better the antibacterial performance, and the longer was the antibacterial duration. The degree of turbidity of bacterial culture solutions was related to the number of bacteria. It was observed that the culture solutions of 10‰BCD/PDA/PAM and 15‰BCD/PDA/PAM hydrogels were clear after 48 h, while the culture solutions of 5‰BCD/ PDA/PAM hydrogel and the control group were still cloudy after 48 h, which was consistent with the bacterial growth curves , and presence of viable cells was assessed by cell counting kit‐8 reagent (CCK‐8) assay. BMSCs were planted on hydrogels and co‐cultured for 5 days. OD450 values showed that the proliferation activity of BMSCs on the experimental groups of BCD/PDA/PAM hydrogels and the control group increased gradually with increasing the cultural time   and cell nuclei (blue) morphologies on all the hydrogels. For the hydrogels, the cells were distributed in a spindle‐like shape and formed a higher density of homogeneous cell layer, demonstrating better cell attachment, spreading and retention performances than the control group  Figure . The cel) Figure . The resp Figure . This re2.5 As shown in Figure S14 (Supporting Information), we evaluated the healing‐promoting property of BCD/PDA/PAM hydrogel in a rat's infected wound model and further evaluated the in‐vivo biocompatibility. 10‰BCD/PDA/PAM hydrogel and BC/PDA/PAM hydrogel were chosen as the experimental groups, while the control group received no hydrogel dressing treatment. Considering the wound in normal rats recovered in 2 weeks, the wound healing was evaluated on day 0, 5, 10, and 15. After hydrogel implantation, wounds covered by hydrogels were observed to heal faster than wound in the control group, and redness and swelling of new tissues became less , respectively, indicating a faster healing ratio of wounds treated by 10‰BCD/PDA/PAM hydrogel. On day 10, 10‰BCD/PDA/PAM hydrogel remained ≈13% (BC/PDA/PAM hydrogel) and 30% (the control group) advantages in wound area ratio (p < 0.001). Furthermore, on day 15, wound treated by 10‰BCD/PDA/PAM hydrogel showed a complete closure, but BC/PDA/PAM hydrogel group and the control group still had wound area ratios of ≈8% and 14% (p < 0.01), respectively. These results clearly indicated that 10‰BCD/PDA/PAM hydrogel had much better wound healing effect than BC/PDA/PAM hydrogel and the control group. The reason was that the 10‰BCD/PDA/PAM hydrogel had abundant positive charge, which killed the bacteria in time and reduced the inflammatory response. In addition, under the continuous stimulation of positive charges, it could promote crawling and proliferation of fibroblastic cells.The ideal wound dressing should have the advantages of promoting healing, anti‐infection, and less irritation.30 As s Figure . The wou2.6 Histological analysis was used to assess the quality of the regenerated epidermis in defects for the experimental groups of 10‰BCD/PDA/PAM and BC/PDA/PAM hydrogels and the control group without hydrogel dressing treatment on days 5, 10, and 15  for 30 min, followed by addition of 3.2 mL triethylamine. The mixture was stirred in an ice bath, and 4 mL 2‐bromisobutyryl bromide was added in drops within 30 min. The mixture was further kept at 0 °C for 15 min and then stirred at room temperature for 24 h. The targeted BC‐Br was obtained by washing thoroughly with ethanol and deionized (DI) water to remove residual reactants. The final BC‐Br was stored in a 4 °C refrigerator for later use.The water in BC water‐dispersion was fully replaced by dimethylformamide (DMF) by centrifugation. BC solution (520 mg in 60 mL DMF) was purged with nitrogen (N BC‐Br (150 mg) and DADMAC (10 mL) were dissolved in water–methanol mixtures  in a Schlenk flask. The solution was purged with N2 for 30 min and then CuBr (20.2 mg) and N,N,N,N,N‐pentamethyldiethylenetriamine (62 µL) were added immediately. The mixture was still stirred with protection of N2 for another 10 min and the reaction was carried out at 60 °C for 24 h with stirring. The final BCD was obtained by washing thoroughly with DI water and ethanol, and then stored in a 4 °C refrigerator for later use.According to the literature,36 BC‐N,N‐methylene bisacrylamide and tetramethylethylenediamine were added to BCD/PDA solution under stirring for 10 min. The final mixture was poured into a mold and kept at 60 °C for 3 h to form hydrogel. Finally, the obtained hydrogel was soaked in DI water and 75% ethanol to remove the excess monomers and dried at room temperature for later use. The weight percentages of all chemicals for various BCD/PDA/PAM hydrogels were listed in Table S1 (Supporting Information).The BCD/PDA/PAM hydrogels were prepared via a two‐step process: 1) BCD was firstly dispersed in the aqueous dopamine solution. Then, APS was added into the solution to initiate prepolymerization of dopamine. The mixture was stirred at room temperature for 25 min as the BCD/PDA solution turns brown. 2) Acrylamide, FT‐IR spectra were obtained by an FT‐IR spectrometer . Zeta potential of hydrogels was measured by using a Zetasizer Nano‐ZS PN3702 system . Surface morphology, internal structure, and element mapping of hydrogels were analyzed by using a field emission scanning electron microscope  after lyophilization. XPS (Thermo‐VG Scientific ESCALAB 250Xi) with a standard Al Ka X‐ray source (1486.8 eV) was used to analyze the chemical structure. Self‐healing test was done by using a simple cut‐link model. Compressive, tensile, and adhesive tests were performed on a universal mechanical testing machine . The adhesion performance of BCD/PDA/PAM hydrogels were proven by covering on human skin. The cell compatibility of the hydrogels was confirmed before the experiments. These experiments were carried out with the full, informed consent from human subjects.S. aureus and E. coli were used for the tests. Bacterial growth curve, colonies forming units (CFU) test and live/dead bacteria assay were evaluated. Details were provided in the Supporting Information.To investigate the antibacterial activity of BCD/PDA/PAM hydrogels, The BMSCs (SCSP‐405) were used to evaluate the cytotoxicity and cell attachment of BCD/PDA/PAM hydrogels. Details were provided in the Supporting Information.The BC/PDA/PAM and 10‰BCD/PDA/PAM hydrogels were implanted into full‐thickness wounds of a rat model to evaluate their wound healing performances. Details were provided in the Supporting Information.th, 10th, and 15th day postsurgery, the wounds with surrounding tissue were collected carefully, fixed in 10% paraformaldehyde solution, and embedded in paraffin for routine histological processing. According to the standard protocols, tissues with 5 mm thickness were prepared. HE staining was used to assess the morphology and tissue regeneration. Masson staining was used to assess collagen deposition.On 5p < 0.05, **p < 0.01, and ***p < 0.001.Statistical analysis was performed using SPSS software . Data was expressed as mean ± standard deviation (SD). Statistical differences were determined using one‐way analysis of variance (ANOVA) followed by a Bonferroni post hoc test for multiple comparisons. The levels of significance were labeled with *The authors declare no conflict of interest.Supporting InformationClick here for additional data file.


Glacier response to ice-shelf thinning is driven largely by the total melt rather than its spatial distribution. The spatial distribution of ocean-induced melting beneath buttressing ice shelves is often cited as an important factor controlling Antarctica’s sea-level contribution. Using numerical simulations, we investigate the relative sensitivity of grounded-ice loss to the spatial distribution and overall volume of ice-shelf melt over two centuries. Contrary to earlier work, we find only minor sensitivity to melt distribution (<6%), with a linear dependence of ice loss on the total melt. Thus, less complex models that need not reproduce the detailed melt distribution may simplify the projection of future sea level. The linear sensitivity suggests a contribution of up to 5.1 cm from Pine Island Glacier over the next two centuries given anticipated levels of ocean warming, provided its ice shelf does not collapse because of other causes. Glaciers that discharge ice to Antarctica’s Amundsen Sea Embayment (ASE)  are losiAlthough observations We simulated PIG with a shallow-shelf, ice-flow model initialized with velocity from 2017 /year] each applied to 30 randomly generated melt distributions e.g., . Figure To examine temporal melt variability, we simulated behavior with the same 200-year melt averages, but with a ±50% sinusoidal modulation (10-year period) to emulate observed decadal-scale variation , inset.To investigate sensitivity to the basal friction model, we repeated the steady-melt experiments with Weertman instead of RCF sliding (r2 ≥ 0.98), indicating that melt paces ice loss. Linear fits to the ensemble members .Across all simulations, the sensitivity of ice loss to individual distributions is minor (2.8 to 5.8%), as indicated by the ratios of the 30-realization SDs (σ) to means μ; see  increaseAs hypothesized above and confirmed by our simulations, a buttressed glacier only sustains increased discharge if its ice shelf sheds the excess mass through melting and calving. To further demonstrate, In all steady-melt cases, ice-shelf thinning declines over the course of the simulation to relatively low rates (<~10 Gt/year), representing a small fraction of the melt. Although small, these losses are critical for sustaining grounding-line retreat by consuming newly ungrounded ice.The simulations indicate that losses should decline by 2020 for melt in the range of 57 to 75 Gt/year, with 100 Gt/year of melt needed to sustain 2017 losses  over theTo investigate its effect, we simulated the recent shelf retreat as an instantaneous calving event by regridding the 2017 initial conditions to match the 2020 geometry . With this shelf reduction included, the 57 and 75 Gt/year cases produce speeds consistent with 2020 observations. When propagated forward 200 years, this model projects an additional ~5 mm sle loss for all melt levels .Contrary to earlier results using idealized one-dimensional (1D) models . Last, bThe simulations indicate that cyclic melt variability at decadal through centurial time scales has little effect , suggestAlthough our experiments were designed as sensitivity experiments, they can help assess PIG’s 200-year melt-related sea-level contribution. First, we consider how melt might evolve over this period. In the decades before 2009, PIG’s grounding line retreated from a bathymetric high  to its tAt decadal time scales, ocean heat content variability appears associated with changes in shelf-break wind anomalies emanating from the tropics . SimulatThe linearity evident in r2 values for the ISMIP6 data are not as high as for our single-model results, which is not surprising given the variance likely introduced by the variety of models and forcings used to generate the results. The relatively high r2 values, however, suggest that the spread in the projections from these models is largely driven by differences in the way they each simulate melt, rather than by their respective implementations of the ice dynamics  parts of the model domain, while producing more traditional Weertman-like behavior for the slower moving areas.An RCF function was used in an earlier study .Over most of the model domain, the value of hT, that best reproduces recent behavior. Although the earlier study used a different implementation of the shallow-shelf equations  above the grounding line, we solved for both A and C to smooth out any discontinuities between the forward and inverse solutions for A. As is common practice, the model actually solves for C = β2 and A = eθ.We initialized the model to 2017 conditions by solving for the friction-law coefficient C in  and 3 onA and C are iterative and interleaved at each step. Specifically, the first step in the solution is for C and that value is used to obtain a new solution for A and so forth until the model converges . We used a similar approach for A but selected a little more regularization than we might have otherwise to avoid unrealistically enhanced values of A in the shear margins, which increased the residual misfit by ~4 m/year (22 to 26 m/year).The solutions for A and C from the inversion. At each time step, the diagnostic equations are solved to determine ice-flow velocity, followed by a prognostic solve for thickness. After thickness is determined, regions that are afloat are determined by evaluating where surface elevation is at or below the height above flotation.We initialized the forward model with the solutions for A time step of 0.05 years was used for the lower melt (57 and 75 Gt/year) simulations, and a value of 0.025 years was used for the high-melt, faster-flow cases (100 and 125 Gt/year). We used a fully implicit Lax-Wendroff time-stepping scheme, which guarantees second-order convergence in time (The finite element mesh (fig. S3) consists of 107,480 triangular elements, with 54,123 vertices  derived from airborne radar observations with constraints from ice cores  and (650 to 1050) m, respectively. The ranges for α1, α2, and α3 were (−0.1 to −0.3), (−4 to −0.5), and (−4 to −0.5) year−1, respectively. The intercept, β1, randomly varied from 0 to −8 m/year. The other two intercepts, β2 and β3, were solved for such that the melt function is piecewise continuous. The smoothing function uses a randomly selected smoothing length, γ, which ranges from 200 to 4000 m. There are two smoothing modes, which are equally likely to be applied. The first continues the melt function, with thickness data inland of the grounding line, and smooths the data across the grounding line, which tends to maximize melt at the grounding line. The second mode imposes zero melt at the grounding line, which forces the maximum melt to be higher in the water column (see examples of each in M(t), which, in our simulations, could be a constant , sinusoidally varying about a mean or a linear function of time.A uniform distribution was used to generate all randomly selected parameters. The ranges for The simulations are referenced to 2017 before a series of calving events reduced the length of the ice shelf by nearly 20 km . We then regridded the 2017 initial solution to this mesh. As a result, the simulation starts up as though there was an abrupt calving event that removed nearly 20 km of the shelf (20% reduction in area), rather than the more phased retreat that actually occurred over a 3-year period. Three years after the shelf removal, the simulated speeds near the grounding line agree well with the late 2020 speeds for both the 57 and 75 Gt/year melt scenarios (ISMIP6 performed numerous simulations for Antarctica for which they broke out the losses by drainage basin for the years 2015 to 2100 as a function of sub–ice-shelf melt (For comparison, we performed a similar regression for our 85-year losses and found a similar sensitivity (black line in


We question the necessity of both the interference screw and EndoButton™ in the fixation of the distal bicep tendon and recommend that securing the interference tenodesis screw with an additional FiberWire® may provide a more secure fixation of the screw as compared to traditional approaches.Distal bicep tendon rupture is an uncommon form of bicep rupture which is typically seen in middle-aged men. We identified two cases in which the distal bicep tendon rupture was repaired with an EndoButton™  and interference screw with preservation of the EndoButton™ but a failure of the interference screw. This report highlights the addition of a FiberWire Innovation in surgical approach and fixation after distal biceps tendon ruptures has been prevalent in the past two decades with the development of a modified two-incision technique, suture anchors, cortical buttons, and interference screws . BiomechCase 1A 51-year-old man with a past medical history significant for hypertension and coronary artery disease presented with left elbow pain after forcefully shutting a car door. He described hearing and feeling a “snap” like a rubber band. Physical examination revealed proximal migration of the left biceps muscle mass, ecchymosis around the elbow, abnormal biceps hook maneuver, and inability to palpate the distal biceps tendon. He had increased discomfort with resisted forearm supination. X-ray evaluation was normal.The patient elected for surgery, and an anterior single incision distal biceps tendon repair utilizing a BicepsButton™  and 7 mm x 10 mm BioComposite™ interference tenodesis screw  was completed without complication. The Arthrex distal biceps repair using the BicepsButton™ and tension-slide technique surgical technique guide was followed, except that a 7.5 mm reamer was used in place of the 8.0 mm described in the technique guide . The posAt 3.5 months postop, the patient reported numbness to the dorsum of his index and long fingers. Examination revealed an intact distal biceps tendon, a normal biceps hook maneuver, full range of motion, decreased sensation over the superficial radial nerve distribution, with normal strength of muscles innervated by the radial, median, and ulnar nerve. X-ray evaluation at 3.5 months postop follow-up demonstrated proximal migration of the tenodesis screw but intact suture button on the posterior cortex of the radius Figure . Final evaluation at 15 months postop revealed an intact distal bicep tendon, normal biceps hook maneuver, normal sensation, full strength, radiographic confirmation of tenodesis screw resorption, and continued full-duty work as a sheriff Figure .Case 2A 52-year-old man presented with left elbow pain and deformity after lifting a toilet into a dumpster. He felt a tear and noted difficulty lifting.Physical examination revealed proximal migration of the left biceps muscle mass approximately 6-8 cms, ecchymosis, abnormal biceps hook maneuver, and inability to palpate the distal biceps tendon. He had increased discomfort with resisted forearm supination with the elbow at 90 degrees and 0 degrees. X-ray evaluation demonstrated mild degenerative arthritis and calcification at the tip of the olecranon.The patient elected for surgery, and an anterior single incision distal biceps tendon repair utilizing a BicepsButton™ and 7 mm x 10 mm BioComposite™ interference tenodesis screw was completed without complication. The identical surgical technique described in Case 1 was followed for Case 2. Ten days post-operatively, he was placed in a removable splint and instructed on a physician-guided passive range of motion home therapy program.At nine weeks postop, the patient reported fullness and numbness around his incision. Examination revealed an intact distal biceps tendon, a normal biceps hook maneuver, normal sensation, and normal motor strength. X-ray evaluation demonstrated the proximal migration of the tenodesis screw but an intact suture button abutting the posterior cortex of the radius Figure .Clinical evaluation at eight months postop revealed an intact distal biceps tendon, normal biceps hook maneuver, normal sensation, full strength, radiographic confirmation of the tenodesis screw resorption, and return to his occupation in construction Figure .Failure of surgical fixation is rare in distal biceps tendon repair, with a recent meta-analysis reporting a rate of 0.6-2% for the varied fixation techniques -7. HowevWe report two cases with failure of the interference tenodesis screw but with preservation of the suture button construct still allowing for successful distal biceps tendon repair. In our cases, the ruptured biceps tendon was repaired using a SpeedWhip™ technique  with a number 2 FiberLoop® , BicepsButton™, and BioComposite™ interference screw . IntraopThese cases raise the question of whether the interference tenodesis screw is necessary for distal biceps repair with a cortical button. Biomechanical studies demonstrate that the cortical button provides the most load to failure, followed by suture anchor repair, bone tunnel, and interference screw . MazzoccPost-operative distal biceps tendon re-rupture is low, with re-rupture rates after primary repair most prevalent within three weeks of the original repair ,16. Re-rDistal biceps tendon rupture is an uncommon form of biceps rupture, typically seen in middle-aged men. This case report highlights the addition of a FiberWire® construct to secure the interference screw from backing out and emphasizes the BicepsButton™ as the primary biomechanical anchor in maintaining a successful distal biceps tendon repair. Further investigation should pursue the necessity of both the interference screw and suture button in the fixation of the distal biceps tendon. However, we currently recommend securing the interference tenodesis screw with an additional FiberWire® to provide a more secure fixation of the screw than traditional approaches.


The 2014–2015 “Monster”/“Super” El Niño failed to be predicted one year earlier due to the growing importance of a new type of El Niño, El Niño Modoki, which reportedly has much lower forecast skill with the classical models. In this study, we show that, so far as of today, this new El Niño actually can be mostly predicted at a lead time of more than 10 years. This is achieved through tracing the predictability source with an information flow-based causality analysis, which has been rigorously established from first principles during the past 16 years . We show that the information flowing from the solar activity 45 years ago to the sea surface temperature results in a causal structure resembling the El Niño Modoki mode. Based on this, a multidimensional system is constructed out of the sunspot number series with time delays of 22–50 years. The first 25 principal components are then taken as the predictors to fulfill the prediction, which through causal AI based on the Liang–Kleeman information flow reproduces rather accurately the events thus far 12 years in advance. Now it has been gradually clear that there are different types of El Niño; particularly, there exists a new type that warms the Pacific mainly in the center, and tends to be more unpredictable than the traditional El Niño with the present coupled models2. This phenomenon, which has caught much attention recently7 (c.f.8 for an earlier account), has been termed El Niño Modoki6, Central-Pacific (CP) type El Niño5, Date Line El Niño4, Warm Pool El Niño7, etc.; see9 for a review. El Niño Modoki has left climate imprints which are distinctly different from that caused by the canonical El Niño. For example, during El Niño Modoki episodes, the western coast region of the United States suffers from severe drought, whereas during canonical El Niño periods it is usually wet10; in the western Pacific, opposite impacts have also been realized for the tropical cyclone activities during the two types of El Niño periods. El Niño Modoki can reduce more effectively the Indian monsoon rainfall, exerting influences on the rainfall in Australia and southern China in a way different from that canonical El Niño does; also notably, during the 2009 El Niño Modoki, a stationary anticyclone is induced outside Antarctica, causing the melting the ice11.El Niño prediction has become a routine practice in operational centers all over the world because it helps make decisions in many sectors of our society such as agriculture, hydrology, health, energy, to name a few. Recently, however, a number of projections fell off the mark. For example, in 2014, the initially projected “Monster El Niño” did not show up as expected; in the meantime, almost no model successfully predicted the 2015 super El Niño at a 1-year lead time12). Though recently it is reported to correspond to one of the two most unstable modes13 for the Zebiak–Cane model14, the excitation of the mode, if true, remains elusive. It has been argued that the central Pacific warming is due to ocean advection7, wintertime midlatitude atmospheric variations15, wind-induced thermocline variations6, westerly wind bursts16, to name a few. But these proposed mechanisms are yet to be verified. One approach to verification is to assess the importance of each factor through sensitivity experiments with numerical models. The difficulty here is, a numerical climate system may involve many components with parameters yet to be determined empirically, let alone the highly nonlinear components, say, the fluid earth subsystem, may be intrinsically uncertain. Besides, for a phenomenon with physics largely unknown, whether the model setup is dynamically consistent is always a concern. For El Niño Modoki, it has been reported that the present coupled models tend to have lower forecast skill for El Niño Modoki than that for canonical El Niño2, probably due to the fact that, during El Niño Modoki, the atmosphere and ocean fail to connect. For all the above, without a correct attribution, it is not surprising to see that the 2014–2015 forecasts fell off the mark—essentially no model predicted the 2015 El Niño at a 1-year lead time (cf.17).El Niño Modoki prediction is difficult because its generating mechanisms are still largely unknown. Without a correct and complete attribution, the dynamical models may not have all the adequate dynamics embedded  actually appears in a similar fashion in many other disciplines, and now has evolved into a new science, namely, data science. Data science is growing rapidly during the past few years, one important topic being predictability. Recently it has been found that predictability can be transferred between dynamical events, and the transfer of predictability can be rigorously derived from first principles in physics21. The finding is expected to help unravel the origin(s) of predictability for El Niño Modoki, and hence guide its prediction. In this study, we introduce this systematically developed theory, which was in fact born from atmosphere-ocean science, and, after numerous experiments, show that El Niño Modoki actually can be mostly predicted at a lead time of 13 years or over, in contrast to the canonical El Niño forecasts. We emphasize that it is NOT our intention to do dynamical attributions here. We just present a fact on accomplished predictions. There is still a long way to go in pursuit of the dynamical processes underlying the new type of El Niño.Rather than based on dynamical models, an alternative approach relies heavily on observations and gradually becomes popular as data accumulate. This practice, commonly known as statistical forecast in climate science 20, initially motivated by the predictability study in atmosphere-ocean science19. Since its birth it has been validated with many benchmark dynamical systems (cf.20), and has been successfully applied to different disciplines such as earth system science, neuroscience, quantitative finance, etc. (cf.24). Refer to the “The major research methodology is based on a recently rigorously developed theory of information flow25 and other mechanical system modeling26, as well as in climate science. We particularly need to use the formula  for the prediction. Covariate selection, also known as sparsity identification, is performed before parameter estimation. It arises in all kinds of engineering applications such as helicopter control formula  as shown27.) We then check whether the resulting causal structure resembles the El Niño Modoki pattern, say, the pattern in the Fig. 2b of6. We have tried many indices , and have found that the series of sunspot numbers (SSN) is the very one. In the following we present the algorithm and results.At the first step we sort of use brute force: compute the information flows from the index series of some prospect driver to the sea surface temperature (SST) at each grid point of the tropical Pacific. Because of its quantitative nature, the resulting distribution of information flow will form a structure which we will refer to “causal structure” henceforth. While it may be within expectation that information flow may exist (different from zero) for the SST at some grid points, it is not coincidental if the flows at all grid points organize into a certain pattern/structure.  Here, based on the above rough estimates, we choose to form a dynamical system with components corresponding to the SST series and the time-delayed series SSN7)) to do29 for empirical methods for time delay choosing. Fortunately, this does not make a problem for our causal inference, thanks to a property of the information flow ab initio, which asserts thatThe information flow between two coordinates of a system stays invariant upon arbitrary nonlinear transformation of the remaining coordinates.More details are referred to the “29. Here we choose by adding new coordinates and examining the information flow; if it does not change much, the process stops and the dimension is hence determined. For this problem, as shown above, the SSN series at delays of 22–50 years every 5 years are chosen. This results in six auxiliary coordinates, which together with the SST and SSN That is to say, the information flow from SSN to the Pacific SST does form a spatially coherent structure resembling to El Niño Modoki.Remarkably, the causal structure in Fig. To see whether the computed causal structure or causal pattern is statistically significant, significance test is performed using the techniques as described in the “6 . This indicates that the bivariate information flow analysis provides a good initial guess, but the result is yet to be rectified due to the potentially incorrect dimensionality.Comparing to the rough estimate in the bivariate case  that measures the strength of the event, over the forecast period be unavailable. We have computed the information flow with different years of availability. Shown in Supplementary Fig. As information flow tells the transfer of predictability, SSN forms a natural predictor for El Niño Modoki. This will be further confirmed in the next section.The remarkable causal pattern in Fig. 30. Since it is required that the series length be a power of 2, we choose a time range for the monthly SSN series from May 1847 to December 2017, depending on the availability of the data when this research was initialized. This totals 170 years and 8 months (170.67 years), or Let us start with a simple linear regression model for the prediction of El Niño Modoki Index (EMI) from SSN. Build the model using the EMI data from 1975–2005  analysis for the 336 time-delayed SSN series, which forms a column vector with 336 entries at each time step: , as the validation period, and use the rest data to train the model. Then, swap the interval until all the 5-year intervals throughout have been utilized. The “forecasts” for all the validation periods are then pieced together to form a plot , although the prediction made early in 2018  agrees with the observation so far as of today. Here the best 1000 out of the 10,000 forecasts are plotted in Supplementary Fig. 38). Something similar happens with El Niño cycle’s causality, as discovered in39. In order to see how causality evolves, we need to choose a time window of some length, compute the information flow on that window, slide it forward and repeat the computation. The resulting information flow on a window can be taken as that at the center of that window. For this purpose, the window size should be as small as possible, so as to arrive at a causality local enough. But it must also be long enough to have “sufficient” data. Here for a rough estimate, we choose it to be one solar cycle. Considering its short length, we can only try the bivariate formula  for a dynamical phenomenon, and this forms the basis of causal AI. In this study, it is found that the delayed causal pattern from SSN to the Pacific SST resembles very much the El Niño Modoki mode; the former hence can be used to predict the latter. Indeed, as detailed above, with all the observations we have had so far, the El Niño Modoki events so far as of today can be essentially predicted based solely on SSN at a lead time of 12 years or over. Particularly, the strong event in 2009/2010 and the elusive event during 2014–2016 have been well predicted , there does exist evidence on the lagged response as identified here; the North Atlantic climate response is such an example42.We, however, do NOT claim that El Niño Modoki is ultimately driven by solar activities. Indeed, as is found above, the causality is actually changing. It is NOT our intention in this study to investigate on the dynamical aspects of this climate mode. We just present an observational fact on fulfilled predictions. There is still a very long way to go in unraveling the dynamical origin(s) of El Niño Modoki. The success of atmosphere-ocean coupled models during the past decades confirms that the canonical El Niño is an intrinsic mode in the climate system; El Niño Modoki may be so also. Nonetheless, despite the long-standing controversy on the role of solar activity in climate change As a final remark, it is interesting to see that the maximum information flow from the SSN lagged by 45 years to the Pacific SST agrees very well with frequent occurrences of El Niño Modoki during the period of 2000–2010: three of the four El Niño events are of this type . If we go back to 45 years ago, the sun is most active during the period of 1955–1965 , and has been applied with success to different problems in earth system science, neuroscience and quantitative finance, e.g.,24, to name a few. Hereafter we just give a very brief introduction.Causal inference is of central importance in scientific researchm matrix, and m-vector of white noise. Here we follow the convention in physics and do not distinguish the notation of a random variable from that of a deterministic variable. Liang20 established that the rate of uncertainty (in terms of Shannon entropy) transferred from E stands for mathematical expectation, , and Consider a dynamical system21it is invariant upon arbitrary nonlinear transformation ofprinciple of nil causality, which asserts that, if the evolution of Generally 20:causation implies correlation, while correlation does not imply causation, fixing the long-standing philosophical debate over causation versus correlation ever since Berkeley45.In the case of linear systems where  formula  becomes 40, and can be found in46. The following is just a brief summary of some relevant pieces as detailed in46.To arrive at a practically applicable formula, we need to estimate , given \N data points 40, when N (overdetermined) algebraic equations40, the least square solution of T is understood as the MLE of T. We slightly abuse notation for the sake of simplicity.) For two-dimensional (2D) systems, 40 and frequently used in applications .Suppose we have 40. By the MLE property  that The significance of 48. Autoregressive (AR) surrogates provide typical realizations; particularly, red noise can be perfectly described by the AR model of the first order, written AR(1), while a large portion of climate data has a red noise background. See the comprehensive review48 and the references therein. We hence adopt for our purpose the following modela, b are parameters. By the algorithm in Lancaster et al.48, with the AR(1) noise assumption, surrogates for a given series are generated via two steps: (1) fit the series to the model to obtain the parameters as mentioned above; (2) produce a set of surrogate series by solving  noise model, which implies that, for two series, there is no causality between the respective surrogates of them. To reject the null hypothesis, the information flows computed with the observational series should lie beyond the preset percentile of the information flows based on the surrogates. Usually one may choose a 90th percentile, a 95th percentile, or a 99th percentile.M, makes an issue in this study, as there are more than 10,000 time series within the study domain. According to48, K is some integer and The number of surrogates, written Supplementary Information.


The wave of differentiation in the Drosophila brain, the ‘proneural wave’, is an excellent model for studying Notch signaling in vivo. Here, we show that strong nonlinearity in cis-inhibition reproduces the second peak of Notch activity behind the proneural wave in silico. Based on this, we demonstrate that Delta expression induces a quick degradation of Notch in late endosomes and the formation of the twin peaks of Notch activity in vivo. Indeed, the amount of Notch is upregulated and the twin peaks are fused forming a single peak when the function of Delta or late endosomes is compromised. Additionally, we show that the second Notch peak behind the wavefront controls neurogenesis. Thus, intracellular trafficking of Notch orchestrates the temporal dynamics of Notch activity and the temporal patterning of neurogenesis.While Delta non-autonomously activates Notch in neighboring cells, it autonomously inactivates Notch through  Drosophila development, two peaks of Notch activity propagate across the neuroepithelium to generate neuroblasts. Here, the authors show Notch cis-inhibition under the control of intracellular Notch trafficking establishes these two peaks, which temporally control neurogenesis in the brain.During  N-mediated lateral inhibition is reiteratively used to select a small number of differentiated cells from a large number of undifferentiated cells in a spatially and temporally regulated manner2. We previously demonstrated that N-mediated lateral inhibition regulates the speed of proneural wave progression when combined with epidermal growth factor (EGF)-mediated reaction diffusion4.Notch (N) signaling plays diverse roles in many biological processes5. It non-autonomously activates N in adjacent cells through a process “trans-activation.” Upon binding with Dl, the intracellular domain of N is cleaved to produce the N intracellular domain (NICD), which forms a complex with a DNA-binding transcription regulator, Suppressor of Hairless (Su(H)), and regulates target gene transcription8. On the other hand, N is autonomously inactivated by Dl expressed in the same cell through a process “cis-inhibition,” whose molecular mechanism and biological significance remain largely elusive12.A membrane-bound ligand, Delta (Dl), plays major roles in N-mediated lateral inhibitioncis-inhibition by inhibiting N prior to or following its transport to the plasma membrane13. There are two possible mechanisms of cis-inhibition. First, the cis-interaction of the ligand and receptor may shut off the transport of N from the endoplasmic reticulum (ER) to the plasma membrane14. Second, the cis-interaction may trigger the catalytic process that results in N degradation. For example, the Dl–N complex may be internalized from the plasma membrane to cause N degradation. Protein degradation in late endosomes has been shown to play important roles in activating and inactivating N signaling during trans-activation24. However, the potential roles of intracellular trafficking of Dl and N in cis-inhibition remain largely unknown.The direct interaction between Dl and N seems to trigger N), Dl expression (D), EGF signal activity (E), and the state of NB differentiation (A). A is related to the expression levels of Achaete-Scute Complex proteins (AS-C). The model successfully reproduces the complex behaviors of the proneural wave in various genetic backgrounds26. N is activated along the wavefront, forming an activity peak that negatively regulates the wave propagation28. However, N is activated again behind the proneural wave, showing twin peaks of N activity in vivo29 , which sequentially differentiate into neuroblasts (NBs), the neural stem-like cells. In the previous study, we formulated a mathematical model of the proneural wave, which includes N activity , Klumpfuss (Klu), Eyeless (Ey), Sloppy paired (Slp), Dichaete (D), and Tailless (Tll) are known to act as the temporal transcription factors in the developing medulla Fig. 30,31. Whcis-inhibition robustly reproduces the twin peaks. As a potential candidate mechanism of the nonlinear behavior of cis-inhibition, we assume that Dl may transport N to late endosomes, in which Rab7 and the ESCRT  complex quickly degrade N, which results in the inactivation of N between the twin peaks. Indeed, partial knockdown of Dl or inactivation of ESCRT complex causes upregulation of N activity and fusion of the twin peaks, forming a single peak of N activity. These results support the idea that intracellular trafficking of N triggers cis-inhibition, which changes the dynamics of N activity. We further explore the biological significance of the twin peaks of N activity. Interestingly, the second N activity peak coincides with Klu expression in the medulla NBs. We demonstrate that Klu expression depends on Dl expression along the proneural wavefront, and the formation of the single N peak by inhibiting ESCRT function results in the abnormal temporal patterning of NBs and neurons. Thus, we demonstrate the molecular mechanism of cis-inhibition that orchestrates the temporal dynamics of N activity and the temporal patterning of neurogenesis.In this study, we reproduce the twin peaks of N activity by modifying the previous mathematical model and demonstrate that a strong nonlinearity in cis-inhibition term was proportional to Dl expression3. When the magnitude of trans-activation and cis-inhibition is roughly equivalent, N is activated only once around the wavefront. However, N is activated again behind the wavefront, showing the twin activity peaks mγ-GFP (mγGFP) shows nuclear signals that are more prominent in the first peak than in the second peak , but quickly inactivates N when Dl expression exceeds the threshold  and activation coefficient  strains. When expressed in the retina under the control of GMR-Gal4, the mild Dl RNAi reduced the eye width from 0.37 to 0.35 mm, while it was further reduced to 0.31 mm by the strong Dl RNAi  and NBs (second peak). N activity is downregulated at the wavefront between the twin peaks of N activity Fig. . HoweverDl mutant clones were generated at the wavefront . In contrast, N messenger RNA (mRNA) level was not affected in Dl mutant clones , the other transmembrane ligand of N35. The formation of the Dl–N complex in cis may be the cause of the rapid N degradation. It has been reported that protein degradation in late endosomes regulates N signaling24. However, these studies did not focus on the process of cis-inhibition. In order to examine if the degradation machinery in late endosomes is responsible for cis-inhibition at the proneural wavefront, we asked whether N and Dl are transported through the intracellular trafficking pathways.It has been reported that Dl and N expressed in the same cell form a complex36. Since N is downregulated at the wavefront, we initially compared Dl expression with Rab-EYFP distribution. We found that Rab4 and Rab7 are colocalized with Dl at the wavefront outside the nucleus and inside the membranous Ecad signals  also suggested that Rab7 forms a complex with Dl in vivo , Rab7 and the ESCRT complex (ESCRT-I–III) regulate protein degradation through the fusion of late endosomes with lysosomes24. On the other hand, it is also known that late endosome function is required for N activation. Indeed, N activity is downregulated when the function of the ESCRT protein is compromised in some experimental conditions20. Thus, late endosomes appear to be involved in multiple aspects of N signaling.Many studies have reported the multiple roles of late endosomes in N signaling. When the function of late endosomes is compromised, the expression of Dl and N is upregulated. As a result, N signaling is ectopically activatedrab7 by expressing the dominant-negative form of rab7 or rab7 RNAi, N protein level was slightly upregulated, showing punctate signals as visualized by N antibody , N activity was specifically upregulated in cells situated between the twin peaks nearby the wavefront indicated by Lsc expression. The level of full-length N protein was slightly upregulated forming a dotted pattern. At the same time, the twin peaks were fused to form a single peak . Low-level N activity was observed in a wide area encompassing the wavefront . These results cannot be explained by the previously proposed roles of late endosomes that nonspecifically and uniformly degrade N and Dl. Thus, late endosomes play specific roles in N degradation that are essential for cis-inhibition at the proneural wavefront in addition to the roles in uniform nonspecific N degradation.We repeated the same experiments for the other ESCRT complex genes and found essentially the same results Fig. . Importas22 Fig. . Note thWe hypothesize that the Dl–N complex is transported to late endosomes, where only N is degraded Fig. . We alsorab4 with RNAi, Dl expression was accumulated at the wavefront in a milder condition at 25 °C  is a family of proteins that regulate endocytic trafficking by regulating the assembly and activity of vacuolar-ATPase (V-ATPase), which is responsible for the acidification of intracellular compartments44. Thus, we focused on the roles of Rbcn and vha68-2, a member of V-ATPase genes, in this process. In vha68-2 mutant clones, Dl was aggregated and colocalized with Rab7 . The residual Klu expression along the clone boundary may be due to the non-autonomous effect of N trans-activation. In contrast, the expression Hth, Ey, and Slp was not significantly affected in Dl mutant clones -positive neurons, forming a concentric zone just outside the Bsh-positive neurons31. Consistent with the precocious Klu expression in NBs, we occasionally observed Run-positive neurons in an area inside the Bsh-positive neurons in Dl and vps2 RNAi conditions -positive neurons that form the innermost concentric zone in the larval medulla Fig. 47,48. Inons Fig. . These dain Fig. . The Kluain Fig. . Note th48. Similarly, the results of clonal analysis using run-Gal4 demonstrate that Run-positive neurons differentiate into Mi4 and TmY16 neurons . The neuronal-type TmY16 has not been documented based on its projection pattern in the medulla, lobula, and lobula plate . Thus, the temporal regulation of the N dynamics at the proneural wavefront controls the temporal pattern of neuronal-type specification through the expression of the temporal transcription factor Klu.We have demonstrated that Bsh-positive neurons give rise to Mi1 medulla neuronscis-inhibition to the mathematical model of the proneural wave and reproduced the twin activation peaks of N signaling at the wavefront as observed in vivo. The fast nonlinear dynamics of cis-inhibition compared with those of the gradual kinetics of trans-activation is consistent with the results of the in vitro cell culture system11. The differential kinetics of trans-activation and cis-inhibition provide the rich dynamics of N activity that enable the formation of the twin activation peaks and the regulation of the temporal patterning of neurogenesis.In this study, we incorporated nonlinearity in 35, which leads to an acute suppression of N signal activity via cis-inhibition  and active form of N (S). In a wide range of parameter settings, this model reproduces the formation of the twin peaks of N activity, fast degradation, and gradual recovery of the expression level of full-length N  by focusing on the transition of the temporal transcription factor Klu, whose expression is upregulated in the medulla NBs49. In this process, the basic helix–loop–helix transcription factors show oscillatory expression in NPCs and N signaling appears to perform lateral inhibitory feedback during NPC differentiation. The roles of cis-inhibition in this process remain largely elusive. It will be interesting to see how the molecular mechanisms revealed in the current study are conserved in a wide variety of developmental processes.In the NPCs of the developing cerebral cortex, the temporal dynamics of N activity also play important roles in the temporal patterning of neurogenesis and gliogenesis3. The mesh size of the square grid model is equal to the cell size , and the time step size is 0.01.The differential equations were calculated using the explicit finite difference method with the zero flux boundary condition as described previouslyFour-variable model: The model contains four equations and four variables. E is a composite variable for EGF ligand concentration and EGF signaling. N represents N signal activity. D and A represent expression levels of Dl and AS-C, respectively. de is the diffusion coefficient of EGF. dt and dc represent magnitudes of the trans-activation and cis-inhibition, respectively. i, l and j, m are integers indicating the location of a cell along the x and y axes, respectively. l and m indicate the location of four cells adjacent to a cell indicated by i and j. The initial conditions for A, E, and D in the anterior-most cells  are A = 0.90, 0.31, and 0.02; E = 0.054, 0.021, and 0.0016; and D = 0.062, 0.021, and 0.0013, respectively, to stabilize the proneural wave progression. The initial condition of N is 0 in all cells.E was calculated as follows: deΔEi,j = de /dx2. ke, kn, and kd are passive degradation rates of EGF, N, and Dl, respectively. ae and ad indicate EGF and Dl regulation by AS-C, respectively. When A = 1, the cells are fully differentiated as NBs. ea reflects the speed of differentiation under the control of EGF and N, and is set to 100. The other parameters are set to 1 unless otherwise noted.The diffusion of Linear cis-inhibition: In the previous model, the trans-activation and cis-inhibition are linear , but quickly induces N inactivation when it exceeds the threshold. kn = 1, dt = 0.25, dc = 0.1, and ec = 0.07  and threshold (ec) of cis-inhibition are changed in the range 0.07–0.15 and 0.04–0.08, respectively  and activation coefficient (kt and kc) specify the kinetics of the reaction. kn = 1, dt = 0.25, dc = 0.1, nt = 1, kt = 1, nc = 5, and kc = 0.09  and activation coefficient (kc) of cis-inhibition are changed in the range 2–7 and 0.07–0.11, respectively  and activation coefficient (K1 and K2) specify the kinetics of the reaction. kt represents the degradation rate of full-length N upon trans-activation. kf represents passive degradation rate of active form of N. n = 1, Fmax = 1, kf = 0.1, dc = 5, nt = 1, K1 = 0.3, kt = 0.1, dt = 0.25, and ks = 2. Hill’s coefficient (nc) and activation coefficient (K2) for Hill function in cis-inhibition are changed in the range 1–7 and 0.05–0.3, respectively . The source codes for the numerical simulations will be deposited to a public repository service.Two- and one-dimensional plots in Figs. Drosophila medium at 25 °C. rab4 RNAi was performed at 25 and 30 °C. The following mutant and transgenic flies were used: DlRevF10FRT82B, UAS-Dl3-1, UAS-Dl RNAi , Dl-GFP (BDSC59819), rab7-EYFP (BDSC62545L), rab4-EYFP (BDSC62542), UAS-rab7DN (BDSC9778), UAS-rab7 RNAi , UAS-rab4DN , vps2pp6FRT82B, vps22NN31FRT82B, UAS-vps2 RNAi (BDSC38995), UAS-vps 22RNAi (BDSC38289), UAS-vps23 RNAi (BDSC38306), UAS-vps25 RNAi (BDSC26286), UAS-vps24 RNAi (BDSC38281), UAS-vps32 RNAi (BDSC38305), UAS-vps20 RNAi (BDSC40894), UAS-vps36 RNAi (BDSC38286), UAS-vps37B RNAi (BDSC44010), UAS-vha68-2 RNAi (BDSC34582), vha68-2R6FRT40A (BDSC39621), UAS-rbcn3A RNAi (BDSC34612), optix-Gal4 (NP2631), Ay-Gal450, UAS-CD8GFP, UAS-GFP, hs-flp, ubi-GFP FRT82B, and ubi-RFP FRT82B. N activity was visualized by E(spl)-mγGFP (mγGFP) and NRE-dVenus33.Fly strains were maintained on standard Dl overexpression clones were generated by crossing hs-flp; Ay-Gal4 UAS-GFP strain with UAS-Dl3-1 and applying 15 min heat shock at 34 °C. Dl mutant clones were generated by crossing hs-flp; ubi-GFP FRT82B strain with DlRevF10FRT82B and applying 50 min heat shock at 37 °C. vps mutant clones were generated by crossing hs-flp; mγGFP; ubi-RFP FRT82B or hs-flp; NRE-dVenus; ubi-RFP FRT82B with vps FRT82B and applying 50 min heat shock at 37 °C. run-Gal4 MARCM clones were generated by crossing run-Gal4 UAS-CD8GFP FRT19F; FRT40A strain with hs-flp; tubP-Gal80 FRT40A and applying 15 min heat shock at 34 °C.run was replaced by the fragment containing attP site and GMR-white via the homologous recombination with the homology arms for run (runLp and runRp)51 in the presence of FRT19F (Kyoto125719). The Gal4 containing fragment was integrated into the attP site in the run locus by co-injecting PhiC31 plasmid and run-Gal4/pGEattB, which contains attB site, the fragment containing the translational start site of run (run5pri) and GMR-white. The expression pattern of run-Gal4 was verified by expressing UAS-GFP and co-staining with anti-Run antibody. runLp (2.0 kb), runRp  were amplified using the following PCR primers: runLp5_NotI (catgcggccgcccaagtatgacacttccgcatc), runLp3_KpnI (catggtaccctttatcgggggtcacttggaa), runRp5_AscI (catggcgcgcccgggagccaagaagtaagcaaa), runRp3_XhoI (catctcgagggccaactgtgataggaagttc), runGal5-Not (catgcggccgcttccaagtgacccccgataaag), and runGal3-Bam (catggatcctgtgttgttggccaccatcgtt). Underlined sequences are homologous to the genomic sequences.The second exon containing the translational start site of 48. Details are available upon request. Brains were dissected in phosphate-buffered saline (PBS), transferred to ice-cold 0.8% formaldehyde/PBS solution, and fixed in 4% formaldehyde/PBS at room temperature for 30–60 min. The brains were washed in PBT (0.3% Triton X in PBS) and blocked in 5–10% normal serum/PBT solution at room temperature for 30–60 min. Primary antibody reaction was performed in a solution containing primary antibodies and 1% normal serum in PBT at 4 °C overnight. The brains were washed in PBT. Secondary antibody reaction was performed in a solution containing secondary antibodies and 1% normal serum in PBT at 4 °C overnight. After washing in PBT and PBS, the brains were mounted in VECTASHIELD (Vector Laboratories).Immunohistochemistry was performed as described belowThe following primary antibodies were used: guinea pig anti-Lsc (1:1200), mouse anti-Dl , mouse anti-N , rat anti-Ecad , rabbit anti-Klu , guinea pig anti-Run , and rabbit anti-Rab7 . The following secondary antibodies were used: anti-mouse Cy3 , anti-mouse Cy5 , anti-guinea pig Alexa647 , and anti-rabbit Alexa546 . Confocal images were obtained by Zeiss LSM880 and processed using ZEN, Fiji, and Adobe Photoshop. Signal intensity was quantified within the indicated rectangle areas by ImageJ.N gene labeled with Quasar 570), the brains were incubated at 37 °C for 8 h in the dark. Incubation at 37 °C for 30 min after replacing the solution with Wash Buffer A. Replacing the solution with TO-PRO3/PBS, the brains were incubated at 37 °C for 30 min. After washing in PBS, the brains were mounted in 80% glycerol in PBS.In situ hybridization was performed as briefly described below. Details are available upon request. Larval brains were dissected in ice-cold PBS, transferred to 4% formaldehyde/PBS solution, and fixed at 4 °C overnight. The formaldehyde solution was removed, and the brains were washed with PBS and 70% ethanol. Incubation at room temperature for 2–5 min after replacing the solution with Wash Buffer A . Replacing the solution with Hybridization Buffer (90 μl Hybridization Buffer mix with 2 μl Stellaris RNA FISH probe designed for exon 6 of PLA was performed using Duolink (Sigma-Aldrich). The dissected fly brains were fixed in 4% formaldehyde in PBT (0.3% Triton X in PBS). After finishing the Lsc immunostaining, the brains were incubated with Duolink blocking solution for 60 min at 37 °C and in the Duolink antibody diluent containing mouse anti-Dl and rabbit anti-Rab7 antibodies for overnight at 4 °C. The brains were washed in Duolink Wash Buffer A three times at room temperature, incubated in a solution containing PLA PLUS anti-mouse and PLA MINUS anti-rabbit probes for 120 min at 37 °C, washed in Duolink Wash Buffer A, and incubated with Duolink ligation stock for 60 min at 37 °C. Then, the brains were washed in Wash Buffer A and incubated with Duolink polymerase in Duolink amplification stock for 100 min at 37 °C. Finally, the brains were washed in Wash Buffer B and mounted in Duolink in situ mounting medium with DAPI .Fly brains were dissected in cold S2 medium and incubated in PBS containing LysoTrancker Red DND99  for 30 min at room temperature. The brains were washed in PBS and fixed in 4% formaldehyde in PBS. After washing in PBS, the brains were mounted in VECTASHIELD (Vector Laboratories).t test was used for the statistical test. Image intensities were not artificially processed, except as otherwise noted. When statistics were not applicable, experiments were independently repeated at least three times with similar results.For quantification and statistical analysis, distinct brain areas or samples were measured and analyzed as indicated below. Two-sided R value to quantify the colocalization between two different signals (Figs. Signal intensity was quantified within the indicated rectangle areas using Fiji Figs. . Coloc 2ls Figs. .xy coordinates of cells were obtained by manually selecting individual cells expressing Run or Bsh (Fig. x coordinate of the origin was calculated as the average of cell locations along the x-axis. The y coordinate of the origin was determined so that the standard deviation of R, the distance from the origin to cells, is minimized. Δθ, the angle of mutant area from the origin, was determined based on the mutant area of Bsh-positive cells. The same Δθ was used to determine the control area to be analyzed at the dorsal–ventral boundary where optix-Gal4 is not expressed. Sizes of the intersection between Run- and Bsh-positive areas in the control and mutant areas were calculated using “convhull,” “polyshape,” and “intersects” functions of MATLAB (Fig. The Bsh Fig. . The x cLAB Fig. .We have complied with all relevant ethical regulations for animal testing and research. This study did not require an ethical approval.Further information on research design is available in the Supplementary InformationPeer Review FileReporting Summary


A preoperative cone-beam computed tomography scan and an intraoral scan were performed and uploaded to implant-planning software to plan the virtual osteotomy site preparations for apical location. Subsequently, the osteotomy site preparations were performed in the experimental models with both osteotomy site preparation techniques and a postoperative CBCT scan was performed and uploaded into the implant-planning software and matched with the virtually planned osteotomy site preparations to measure the deviation angle and horizontal deviation as captured at the coronal entry point and apical end-point between osteotomy site preparations using Student’s t-test statistical analysis. (2) Results: The paired t-test found statistically significant differences at the coronal entry-point deviations (p = 0.0104) and apical end-point deviations (p = 0.0104) between the TB and PUI study groups; however, no statistically significant differences were found in the angular deviations (p = 0.309) between the trephine bur and piezoelectric ultrasonic insert study groups. (3) Conclusions: The results showed that the TB is more accurate than the PUI for apical location.To compare and contrast the accuracy of piezoelectric ultrasonic insert (PUI) and trephine bur (TB) osteotomy site preparation techniques for apical location. (1) Material and methods: A total of 138 osteotomy site preparations were randomly distributed into one of two study groups. Group A: TB technique ( Periapical tissue damage as a result of the pulp necrosis process is considered the most common pathology found in the alveolar bone. The exposure of dental pulp to bacteria and their products (antigens) can lead to nonspecific inflammatory and specific immune responses in the surrounding root tissues, which can lead to periapical tissues damage ,2,3,4. S0) states that there is no difference in apical location between PUI and TB osteotomy site preparation techniques.The present study aims to analyze, compare and contrast the accuracy of PUI and TB osteotomy site preparation techniques for apical location. The null hypothesis  guidelines [Two hundred and twenty-four upper teeth from all dental sectors, which were extracted due to periodontal and orthodontic concerns, were selected for study at the Dental Centre of Innovation and Advanced Specialties at Alfonso X El Sabio University , between February and April 2021. The sample size was selected according to a previous study  with a pidelines ,19. In a®, Buehler, IL, USA) with 14 teeth each. One hundred and thirty-eight osteotomy site preparations were randomly distributed  into one of two study groups: group A. Trephine bur  (TB) (n = 69) and B. Piezoelectric ultrasonic insert  (PUI) (n = 69). The teeth assigned to the experimental models presented the same anatomy and were positioned in the experimental model using a silicone splint to prevent different apical position between the different teeth of the experimental models. The silicone splint was created by conventional impression using a dental training model made of acrylic resin , which the teeth were subsequently placed on. The epoxy resin  was then mixed following the manufacture’s recommendations and poured into the silicone splint with the teeth. After the epoxy resin set, the silicone splint was removed from the epoxy resin model. In addition, the apical locations where osteotomy site preparations were performed were also randomly selected .The teeth were embedded in 16 experimental models of epoxy resin  were preoperatively scanned using cone-beam computed tomography (CBCT)  under the following exposure parameters: 105.0 kV peak, 8.0 mA, 7.20 s, and a 15 × 13-mm2 field of view. Next, a 3D surface scan was performed via 3D intraoral scan  using 3D in-motion video imaging technology. Datasets obtained from the digital workflow were then uploaded to 3D implant planning software  prior to designing the virtual osteotomy site preparations for apical location. The virtual osteotomy site preparations randomly assigned to TB study group were designed with 3.5-mm diameter and 13.0-mm length by matching the data from the 3D surface scan and CBCT, aligning the key points identified on the crowns of the teeth. Virtual osteotomy site preparations were designed until the apex of each tooth and at an insertion angle of 90° in relation to the teeth’s longitudinal axes. Virtual osteotomy site preparations randomly assigned to PUI study group were designed with 3.3-mm diameter and 13.0-mm length by matching the data from the 3D surface scan and CBCT, aligning the key points identified on the crowns of the teeth. Virtual osteotomy site preparations were designed until the apex of each tooth and at an insertion angle of 90° in relation to the teeth’s longitudinal axes . These data were then matched in order to record deviation angle (taken in the center of the cylinder) and horizontal deviation . The measurements were taken by an independent observer ; p < 0.05 was defined as statistically significant.All variables of interest were input into SPSS 22.00 for Windows for statistical analysis with SPSS. Descriptive statistical analysis of quantitative variables was expressed as the mean and standard deviation (SD) of said variables. Comparative analysis was carried out by assessing difference in mean deviation between planned and performed osteotomy site preparations for the apical location between TB and PUI study groups using Student’s t-test found statistically significant differences in the coronal entry point deviations of the planned and performed osteotomy site preparations for the apical location between TB and PUI study groups (p = 0.0104) (The paired  0.0104) .t-test also found statistically significant differences in the apical end-point deviations of the planned and performed osteotomy site preparations for the apical location between TB and PUI study groups (p = 0.004)  .t-test found no statistically significant differences in the angular deviations of planned and performed osteotomy site preparations for the apical location between TB and PUI study groups (p = 0.309)  .0) that states that there is no difference in apical location between TB and PUI osteotomy site preparation techniques.The results of the present study reject the null hypothesis , apical (p < 0.0001), and angular (p < 0.0001) levels [Many authors have evaluated the accuracy of various therapeutic procedures with this methodological procedure, such as the accuracy of dental implant placement using computer-aided static navigation techniques, which showed a 0.99-mm horizontal deviation (ranging between 0.0–6.5 mm) at the dental implant platform, 1.24-mm horizontal deviation (ranging between 0.0–6.9 mm) at the dental implant apex, and an average angle deviation of 3.81° (ranging between 0.0–24.0°) relative to the longitudinal axis of dental implants ,21. The ) levels . Both roRoot apex location presents a major challenge for clinicians performing endodontic microsurgical procedures . Magnifip ˂ 0.05) at the coronal entry point (0.71 ± 0.40 mm), apical end point (1.00 ± 0.49 mm) and angular deviation (2.26 ± 1.62°) when compared with traditional freehand dental implant placement techniques [p = 0.185) [p < 0.0001) [However, no technology has been found capable of guaranteeing 100% success in locating the root apex, and thus new technologies have been tested for the accurate location of the root apex. Gambarini et al. reported a clinical case in which computer-assisted dynamic navigation techniques were used for apical location in endodontic microsurgery. These techniques employ an optical triangulation tracking system with stereoscopic motion-tracking cameras that guide the drilling process in real time, ensuring that the planned angle, trajectory and depth of the osteotomy are achieved . These tiation 2. ± 1.62° chniques . Additiochniques ,28,29. H= 0.185) . Moreove 0.0001) . Nonethe 0.0001) ,14,15,16This in vitro study is potentially limited due to its experimental nature; for example, similarities in tooth anatomy and the dental position of teeth may differ from a real clinical situation. However, the teeth were selected based on anatomy and were also randomized. Furthermore, the silicone splint enabled a repeatable dental position across all experimental models. In addition, the methodological procedure used in this study is easily applicable to clinical studies.Bearing in mind the limitations of this in vitro study, the results of the present study found that the trephine bur is more accurate than piezoelectric ultrasonic insert for apical location.


We show, using a combination of X-ray and neutron diffraction, that the structure of these frameworks depends on the A-site cation, and that these frameworks possess complex vacancy-ordering patterns and cooperative octahedral tilts distinctly different from atomic perovskites. Density functional theory calculations uncover the energetic origin of these complex orders and allow us to propose a simple rule to predict favoured A-site cation orderings for a given tilt sequence. We use these insights, in combination with symmetry mode analyses, to show that these complex orders suggest a new route to non-centrosymmetric perovskites, and mean this family of materials could contain excellent candidates for piezo- and ferroelectric applications.We report four new A-site vacancy ordered thiocyanate double double perovskites,  Metal thiocyanate hybrid perovskites can have multiple simultaneous complex orderings and combining these orderings appropriately can produce non-centrosymmetric structures. One area of particular interest is using the molecular components to create electrical polarisation, without the need for the second-order Jahn–Teller distortions or stereoactive lone pairs that drive piezo- and ferroelectricity in atomic perovskites, e.g. BaTiO3 or PbO3.2 Molecular perovskites now possess polarisations and transition temperatures which approach those of inorganic perovskites.3 However, their polarity is typically produced by the orientational order of polar A-site cations.4 The functionality often bestowed by the MX3 framework, e.g. ferromagnetism or ferroelasticity, therefore usually couples weakly to the polarisation, limiting the scope for multiferroicity.Molecular perovskites, perovskites of composition AMXvia collective distortions of MX3 framework is difficult as the conventional cooperative tilts of the MX6 octahedra are intrinsically non-polar. However, by combining octahedral tilts with other symmetry-breaking orders, such as A-site or M-site occupational order, we can generate polar structures: the so-called hybrid improper ferroelectrics.5 Furthermore, recent work has shown that the unusual framework distortions possible in molecular perovskites, such as unconventional tilts and columnar shifts, while non-polar, offer new routes to polarity.1 Creating materials capable of sustaining new ordering types and sustaining multiple simultaneous orders is therefore a powerful method for generating novel function.6Generating polarisation  where rA is the radius of the A cation, rM is the radius of the M cation and rX is the radius of the X anion, which quantifies our intuition that the A-site cation has to fit well into the MX3 cage. It indicates whether AMX3 is likely to be a perovskite, rather than (τ > 1) 1D or 2D structure types  or (τ < 0.8) other, dense non-perovskite structure types (e.g. ilmenite). Although originally developed for atomic perovskites, the tolerance factor approach can rationalise the structures of a wide-range of molecular perovskites, including formates and alkylammonium metal halides,8,9 and its fundamental geometric insight has been generalised to other systems.10,11τ is also linked to the size of the octahedral tilts, as smaller τ tends to require large tilts to retain a dense structure. However, creating new function requires controlling the relative sense of the tilts, i.e. whether each layer of octahedral tilts rotates in same sense as the next (a+ in the Glazer notation12), or opposite sense (a−), not just their magnitude. This remains challenging to predict for new perovskites.13Gaining control over these orders, both individually and separately, remains one of the challenges of solid-state chemistry. One key guiding parameter is the tolerance factor τ can be readily tuned by creating solid solutions of cations (or cations and vacancies) on the A or M site, as the entropy of mixing stabilises these phases at the high synthesis temperatures used. Conversely, this means that cation-ordering is uncommon, particularly on the A-site.14 A-site order is most often stabilised by large size differences between A-site cations, especially the extremal size difference between a vacancy and a cation, and therefore typically produces layered order which minimises the local strain, e.g.,15 .22 We focus in this paper on the family of perovskite-like materials derived from thiocyanate, Ax{M[M′(SCN)6]}, of particular interest for their catalytic and optical function.7,23–26 These NCS-perovskites have complete M-site order, due to the difference between N- and S-termini of the ligand, and have large tilts due to the frontier molecular orbitals of the NCS− ligand.7 The robustness of these distortions means NCS-perovskites are an ideal platform for exploring complex orderings.Molecular perovskites are fertile ground for the exploration of multiple simultaneous orders because of their chemical diversity, low temperature syntheses, and the toolbox of crystal engineering 3} (ref. 4)2{Ni[Cd(SCN)6]}.23 Calculation of τ, using empirical cation sizes for molecular ions,8 suggests that organic A-site cations will likely be too large for A{M(NCS)3} perovskites − framework with ReO3 topology, just as in the parent M[Bi(SCN)6], M = Sc, Cr, Fe phases. K+/NH4+ cations are present in half of the pseudocubic Ni4Bi4(NCS)12 cages.We were able to grow large single crystals of phase 1 and 2 by slow evaporation of butanone solutions of the desired stoichiometry. Solution of the structure using single crystal X-ray diffraction (SCXD) showed that the phases are isostructural, as is often found for Kompounds . They co supercell of the hypothetical primitive cubic Pm3̄m aristotype AM(NCS)3, and its structure derives from this Pm3̄m structure (using the setting with the A-site at the origin) through four symmetry-lowering distortions. The M-site cations have rocksalt order and this order transforms as the R2− irreducible representation (irrep).33,34 The A-site cations have columnar order (transforming as the M1+ irrep), and there is no evidence of site-mixing from single-crystal diffraction. The presence of simultaneous A- and M-site occupational order means that 1 and 2 are double double vacancy-ordered perovskites, □A{Ni[Bi(SCN)6]}. 1 and 2 possess the common a−a−c+ (Glazer) or GdFeO3 octahedral tilt sequence (which transforms as a combination of the R5− ⊕ M2+ irreps),12 which is the same as the parent M[Bi(SCN)6] phases and the related M-site defect-ordered NCS-frameworks .7,25 The combination of octahedral tilting and rocksalt M-site order leaves all pseudocubic Ni4Bi4(SCN)12 cages still equivalent by symmetry, meaning that the A-site cation ordering may not be viewed being drive by these three distortions alone. The A-site cation ordering therefore lowers the space-group symmetry further, from P21/n to P1̄, and in addition produces a large shear strain compared to the M[Bi(SCN)6] structures (α ≈ 97° vs. α = 90°).This structure is a 4+ cation in 1 is ordered. Single crystal neutron diffraction (SCND) measurements on a large single crystal (16 mm3) at 20 K, carried out using instrument D19 at the ILL, allowed accurate determination of the H atom positions and its anisotropic atomic displacement parameters, which were consistent with those observed via SCXD. Variable temperature unit cell measurements between 20 K and 260 K and an additional full collection at 260 K found no evidence of any structural phase transitions in this range. Refinement of the 260 K dataset confirmed the presence of NH4+ orientational order throughout this temperature range. The ordering of the NH4+ cation does not lower the symmetry of 1 beyond the symmetry of compound 2.SCXD refinement allowed us to tentatively locate the positions of the H atoms and demonstrate that the orientation of the NH6]}. We carried out geometry optimisations of supercells containing the seven simplest A-site cation orders: rocksalt, layered  and columnar , generated from supercells of the Fe[Bi(SCN)6] structure [ESI Section 4We further investigated the energetic driving force for the observed A-site order using DFT calculations of K{Ni[Bi(SCN)2.23{Ni[Bi(SCN)6]}, 3, using a route analogous to that used for 1 and 2. SCXD studies of MeNH3{Ni[Bi(SCN)6]} revealed that it also crystallises as a double double vacancy-ordered perovskite which, like 1 and 2, has a structure derived from an ReO3-type parent by introducing cations into half of the pseudocubic cages  and [110] lattice directions, which made structure solution and refinement challenging. Using SCXD data collected on a small crystal (65 × 55 × 22 μm) which only had a minor twin component , we were able to produce a stable refinement for the structure.We obtained single crystals of MeNHic cages . However3+ cation and our assignment of the polarity of MeNH3+ cation, i.e. which atom was carbon and which nitrogen, was thus tentative. We therefore carried out a series of SCND studies on large (≈1 mm3) single crystals using instrument D19 at the ILL. These measurements did not allow us to definitively answer these questions because we were unable to obtain an untwinned crystal of sufficient size, but did confirm both the space group symmetry and broad structural features observed via SCXD.We were not able to locate the hydrogen atoms on the MeNHP2/n (2 × 6 × 4) supercell, with no peaks unaccounted for. Rietveld refinement using the model derived from SCXD data gave quantitative agreement − framework and found that the distortion of the structure from the hypothetical parent Pm3̄m structure  could be described well by six symmetry-adapted distortion modes in addition to rocksalt M-site order, one of which describes the global contraction of the structure Γ1+ (Γ1+), and four which describe cooperative rigid octahedral rotations: M2+ (X3+),  and R5− (Γ4+)  in the notation of Peel et al.36 which transforms as a M2+ distortion mode, and each layer alternating in its sense rotation, a−, [CA] and R5−. In 3, the tilts normal to the b and c axes repeat after six and four layers (respectively) and are therefore complex. In total, the tilt sequence for this perovskite is [C][CCCAAA][CCAA] (Peel), or a+b++−++−c+−+− (extended Glazer), where both notations are shown for clarity.The two Tb and c directions are a form of nanoscale ‘tilt-twinning’: sequences of the same tilt sequence interrupted by a tilt of the opposite kind. Symmetry analysis showed that the combined presence of the M2+,  and  tilting modes together with rocksalt M-site order (R2−) was sufficient to produce the observed P2/n (2 × 6 × 4) structure. These modes are therefore likely the primary order parameters, with the R5− (Γ4+) mode being a secondary order parameter. The A-site order can only be described by secondary order parameters arising from all three tilts, with any pairwise combination being insufficient, which suggests that it is the final distribution of anions ordering produced by the complete octahedral tilt pattern which is responsible for the observed ordering.These complex tilts observed along the 2.32+ and Bi(SCN)63− in a 6 : 1 : 1 ratio yielded large single crystals of compound 4. We were again able to determine its structure using SCXD, which revealed that it was also a vacancy ordered double perovskite, in space group Pn3̄, a (2 × 2 × 2) supercell of the Pm3̄m aristotype , corresponding to □9Gua3Ni6[Bi(SCN)6]5. This reduced A-site occupancy and the presence of vacancies also accords with the lower volume of compound 4 compared to 3, despite 4 containing a significantly larger A-site cation },23 and those containing metal coordination-complexes on vacancy sites, Mn2Bi(SCN)7·7H2O and Co9Bi6(SCN)36(H2O)38.25 Perovskites containing organic A-sites cations are of particular interest as these organic cations can possess intrinsic electric dipoles (e.g. MeNH3+) and quadrupoles (e.g. Gua+). The orientational order of organic A-site cations can thus generate electrical polarisation, either directly through ferrodipolar order, as in the formate perovskites,4 or indirectly through coupling of ferroquadrupolar order to other order parameters, for example (Gua){Cu(HCO2)3}.1,38Compounds 3 and 4 are the first NCS-perovskites containing organic A-site cations, adding to the existing NCS-perovskites containing inorganic A-site cations, Cs{Cd(NCS)ECN,av = 16 kJ mol−1 (0.17 eV ≈ 6 kT at room temperature). Careful structural examination revealed that hydrogen bonding is an important factor in the structures of these materials, as in other molecular perovskites,43 and indeed, ΔECN,av is comparable to the H-bonding energies found in formate perovskites.22 This suggests that temperature-induced phase transitions might be uncovered with careful comprehensive variable temperature structural and calorimetric studies, as in (NH4)2{Ni[Cd(SCN)6]}, which undergoes an order–disorder transition associated with the NH4+ cation at around 120 K.23 Optimisation of the orientational order of A-site cations towards ferroic order might be possible through crystal-engineering, by tuning the hydrogen-bonding or introducing halogen-bonding moieties,44 and by deepening our understanding of the role of framework entropy in NCS-perovskites.45We did not find polar orientational order in these new perovskites, and complete orientational order was only present in 1, as 3 shows partial disorder and 4 complete disorder. Our variable temperature diffraction studies found no evidence of any phase transitions below 260 K, implying that the observed A-site disorder is static, which for compound 4 is likely related to the presence of M-site vacancies. Our DFT calculations suggest that orientational order in 3 is moderately favourable as Δ3.2e.g. CaTiO3 adopts the distorted a−a−c+ tilt system at room temperature, whereas SrTiO3 is cubic with no tilts. Although the tolerance factor approach explains which molecular AMX3 frameworks are likely to crystallise with a perovskite structure,8,9 it does not account for either the magnitudes or kinds of framework distortions observed.46,47 For example, in the series of formate perovskites A{Mn(HCO2)3} where A+ = Rb+,48 CH3NH3,49 (CH3)2NH2 (ref. 2)3NH51 (arranged in increasing size of A+/increasing τ), there is no systematic trend in the size or pattern of the octahedral tilting, respectively: a−a−c−, a−a−c+, a−a−c− and a−a−c+.In atomic perovskites, the tolerance factor has been successfully used not only to suggest whether a composition will be a perovskite, but also to provide a first indication of the magnitude of octahedral tilts, NH2 ref.  and  and the BiS6 tilt (∠S–Bi–Ni) change very little for these four compounds from the parent M[Bi(SCN)6] frameworks. This conforms to the general finding that the metal-thiocyanate bond-angles do not vary in NCS-perovskites and that guest–framework interactions exert only second-order effects.7,23,25,26 Compound 4 crystallises with both A- and M-site vacancies, suggesting that there is a maximum average size of A-site cation that can be incorporated within the {Ni[Bi(SCN)6]}− framework and providing further evidence of the ease of formation of [Bi(SCN)6]3− vacancies in these materials. The tolerance factor therefore may provide a useful upper bound on cation size for NCS-perovskites (the lower bound not being meaningful due to the variety of ReO3 structure NCS-frameworks), but we have not found it to be predictive of the tilts or A-site ordering—just as for other molecular perovskites.The scarcity of NCS-perovskites has thus far prevented investigation of the relationship between cation size and tilts. We find, contrary to simple geometric arguments, that the average size of the NiN3.3IIMIII(HCO2)6 compounds adopt niccolite-type structures.52 The Prussian blue analogue cyanides can accommodate the complete range of A-site compositions, which has been exploited for their potential as battery electrode materials,53 but the A-sites are typically disordered. Some degree of rocksalt A-site cation order has been observed in a number of frameworks of approximate composition AMIIMIII(CN)6 3}, H2DABCO2+ = 1,4-diazabicyclo[2.2.2]octane-1,4-diium, where vacancies order into {111}cubic layers presumably, as in A-site vacancy oxides, to minimise strain.47A-site vacancy ordered molecular perovskites are rare, as the additional structural degrees of freedom often mean other structure types are favoured for high vacancy concentrations: for example AMN)6 ref.  but this3+ order into 3 × 2 × 1 blocks and in 4 the cations are present in one quarter of the cages with Cu3Au order. The block-order of cations in MeNH3{Ni[Bi(SCN)6]} is to the best of our knowledge unknown in any other perovskite. It can be related to the nanochequerboard/nanochessboard phases observed in compositionally complex analogues of the rare-earth vacancy perovskites, such as   and M′ = Mn or Fe.59It is therefore noteworthy that A-site vacancy order appears to be the rule in NCS-perovskites, rather than the exception. 1–4 all possess complete A-site order and these orderings are unusual for perovskites molecular or otherwise: in 1 and 2 the cations have columnar order; in 3 the MeNHas  ref.  and .58 −a−c+ tilt, the unique A-site order in 3 is accompanied by the unique complex a+b++−++−c+−+− tilt, and the Cu3Au order occurs with a+a+a+ tilt. One possible reason for this can be seen in the distribution of NCS− anions between pseudocubic cages T2 irrep)  polymorph possessing these distortions using ISODISTORT and then examined the distribution of NCS− anions. The pseudocubic cages contain 0, 2 or 4 NCS− in the ratio 1 : 2 : 6, suggesting that a structure in which  of the cages were occupied by A-site cations would stabilise this distortion 4} 4} . Very en4+ cation determines the coupled A-site occupational order and octahedral tilt distortions of , A = K+, NH4+, MeNH3+ and Gua+, vacancy-ordered perovskites. We have shown that organic cations can be hosted as A-site cations in NCS-perovskites, and that the synthesis of large single crystals of these materials can be achieved via facile solution methods. NCS-perovskites have robust M-site order and nearly fixed magnitude conventional octahedral tilts: in this work we have shown that A-site occupational order can also be readily achieved in NCS-perovskites. We demonstrate that, by controlling these three orders at once, we can produce new and unprecedentedly complex perovskite structures, notably the non-Brillouin zone corner tilts and block A-site order found in (MeNH3){Ni[Bi(SCN)6]}. We have devised a simple counting method for predicting the coupling between octahedral tilts and A-site occupational order, supported by DFT calculations. Finally, we have shown how complex conventional tilts can produce new routes to non-centrosymmetric materials. These results suggest that exploration of NCS-perovskites and complex tilts more generally may uncover further functional behaviour, including ferroelectricity, and anomalous mechanical properties such as negative thermal expansion or negative linear compressibility.In this study we have investigated how the identity of the AJ. L. and M. J. C. synthesised the samples. M. J. C. analysed the X-ray diffraction data. S. J. A. carried out the synchrotron X-ray diffraction experiments. J. L., M. J. C. and L. C. D. carried out the neutron diffraction experiments. J. L. and L. C. D. analysed the neutron diffraction data. S. L. carried out the DFT calculations. M. S. S. carried out the symmetry analysis. M. J. C. wrote the paper, with input from all other authors.There are no conflicts to declare.SC-012-D0SC06619B-s001SC-012-D0SC06619B-s002SC-012-D0SC06619B-s003SC-012-D0SC06619B-s004SC-012-D0SC06619B-s005SC-012-D0SC06619B-s006SC-012-D0SC06619B-s007SC-012-D0SC06619B-s008SC-012-D0SC06619B-s009SC-012-D0SC06619B-s010