The eukaryotic kinase domain has multiple intrinsically disordered regions whose conformation dictates kinase activity. Small molecule kinase inhibitors (SMKIs) rely on disrupting the active conformations of these disordered regions to inactivate the kinase. While SMKIs are selected for their ability to cause this disruption, the allosteric effects of conformational changes in disordered regions is limited by a lack of dynamic information provided by traditional structural techniques. In this study, we integrated multiscale molecular dynamics simulations with FRET sensors to characterize a novel allosteric mechanism that is selectively triggered by SMKI binding to the protein kinase Cα domain. The indole maleimide inhibitors BimI and sotrastaurin were found to displace the Gly-rich loop (G-loop) that normally shields the ATP-binding site. Displacement of the G-loop interferes with a newly identified, structurally conserved binding pocket for the C1a domain on the N lobe of the kinase domain. This binding pocket, in conjunction with the N-terminal regulatory sequence, masks a diacylglycerol (DAG) binding site on the C1a domain. SMKI-mediated displacement of the G-loop released C1a and exposed the DAG binding site, enhancing protein kinase Cα translocation both to synthetic lipid bilayers and to live cell membranes in the presence of DAG. Inhibitor chemotype determined the extent of the observed allosteric effects on the kinase domain and correlated with the extent of membrane recruitment. Our findings demonstrate the allosteric effects of SMKIs beyond the confines of kinase catalytic conformation and provide an integrated computational-experimental paradigm to investigate parallel mechanisms in other kinases. Protein kinases catalyze the transfer of a phosphate group from ATP to a protein substrate . Kinase PKCα is a member of the AGC kinase superfamily  and is i2+, diacylglycerol (DAG), and phorbol ester  results in membrane translocation and kinase activation. Activated PKC is known to self-associate through intramolecular and intermolecular interactions between the regulatory and catalytic domains . Hence, structural characterization of PKC oligomers has been challenging. Nonetheless, multiple reports have documented their formation in live cells  that normally shields the ATP-binding site. Displacement of the G-loop interferes with a structurally conserved binding pocket at the N-terminus of the kinase domain. This binding pocket in PKCα is occupied by the C1a regulatory domain, where it masks a DAG binding site. BimI/sotrastaurin binding displaces the G-loop, releasing C1a and exposing the DAG binding site. Engaging this allosteric mechanism leads to enhanced PKCα translocation both to synthetic lipid bilayers and to live cell membranes in the presence of DAG. Inhibitor chemotype determines the extent of allosteric effects on the kinase domain, in turn correlating with the pattern of membrane recruitment. Our findings demonstrate the allosteric effects of SMKIs, beyond the confines of kinase catalytic conformation and provide an integrated computational-experimental paradigm to investigate parallel mechanisms in other kinases.A) to examine the influence of SMKIs on interactions between the kinase and regulatory domains of PKCα. The sensors contain a single α-helical ER/K linker flanked by a FRET donor/acceptor pair that sets the effective concentration of the intramolecular interaction  correlates linearly with the fraction of molecules in the bound state . In contrast, the indole maleimide inhibitors, BimI and sotrastaurin, substantially inhibited this interaction. Interestingly, the effects of this panel of inhibitors on the kinase-regulatory domain interaction recapitulate the results from our previous report on the kinase-substrate peptide interaction .We have previously shown that ATP-competitive SMKIs can allosterically influence the kinase-substrate interaction in PKCα . Here, wFig. 1eraction . FRET rand state . We founeraction . Owing tE), and the two domains (PS and C1a) together showed similar changes in FRET ratio as the complete regulatory domain . While we have previously established that the allosteric effects of BimI on substrate binding is mediated by changes in conformation of the kinase domain activation loop . GNEIMO-MD simulations were used to predict possible binding sites for the C1a domain on the kinase domain under the constraints from two flexible linkers. The snapshots of MD simulation trajectories representing the potential interacting sites of C1a were grouped into conformational clusters, and the top four conformational clusters were rank ordered by Rosetta energy units . The most energetically favored cluster was further analyzed to identify the top five scoring structures based on energy of the C1a-kinase domain complex . Model 1 and 5 were selected for experimental testing based on interface interaction energy  and Rosetta mutagenesis . Three single point mutations that showed gain in interface energy upon mutation and three single point mutations that led to weakening of the interface energy all calculated using Rosetta energy function upon mutation in model 1 and model 5 were independently identified . For model 1, C53E/G61W/C78D were identified as stabilizing (9 REU lower than WT) whereas F60D/R77D/T83K were identified as destabilizing (22 REU higher than WT). For model 5, T54F/D55N/H75W were identified as stabilizing (10 REU lower than WT), and G64F/G59R/F56K were identified as destabilizing (10 REU higher than WT). Stabilizing and destabilizing mutations for model 1 and 5 were assessed in an in vitro kinase activity assay . Destabilizing mutations in model 5 resulted in a significant increase in in vitro kinase activity, consistent with the release of basal autoinhibition in PKCα, suggesting model 5 as the putative interaction site. The Rosetta-based interface energy calculation (REU) is a crude measure that does not take into account the explicit desolvation energies. Therefore, the predictions of the effect of both destabilizing and stabilizing mutations affected the kinase activity but did not correlate with the activity as predicted. However, the average C1a–CD interface energy calculated for the mutants using the snapshots from all-atom MD simulations performed in explicit solvent agreed well with the FRET measurements as shown in Figure 2C.The single, partial structure of a classical PKC (PKCβII) does not resolve the potential binding interface for C1a on the kinase domain . Hence, e domain A. GNEIMOits REU; B. The moC, left axis). To refine the structural models of C1a kinase domain interactions extracted from GNEIMO torsion MD simulations, we performed all-atom MD simulations on model 5 and the mutants shown in Figure 2C. Using the snapshots from the all-atom MD simulations for the mutants and the WT, we calculated the average difference in the C1a-kinase domain interaction energies between the WT and the mutant as shown in Figure 2C (right axis). These more accurate interface interaction energies calculated using all-atom force fields in explicit solvent correlate well with the changes in FRET intensities, as measured using C1a-kinase domain FRET sensors .To test the effect of these mutations on the strength of the C1a interaction with the kinase domain (and not kinase activity), we used FRET sensor measurements . Sequence conservation analysis of the interface residues suggests that they are highly conserved across all PKCs with a C1a domain, further validating them their role in C1a engagement . All classical and novel PKC isoforms contain a C1a domain . In contrast, with exception to the eukaryotic kinase-conserved GxGxxG motif, the kinase-C1a interface residues are not conserved across AGC kinases, of which PKCs are a subfamily . These data suggest that the C1a binding pocket can be used to selectively target PKC function. Independently, the FindBindSite (FBS) technique , suggesting that it is a promising location to allosterically modulate PKCα kinase function.Residues on the kinase domain that interface with C1a form a binding pocket encompassing the G-loop  identifique see . The G-lique see ; Fig. 3CA). In contrast, neither the staurosporine analogs (Staur and Tetra) nor the ATP analogs (Sang and Toyo) have significant effects on G-loop conformation relative to the nucleotide-free (Apo) state (A). Interestingly, the distinct conformational states of the G-loop observed in our MD simulations of the PKCα kinase domain in the presence of BimI and sangivamycin are also apparent in published crystal structures of PDK1 complexed with BimI (1UU8) and GRK6 complexed with Sang (3NYN) (B). These comparisons suggest that the inhibitor-triggered G-loop conformational states are prevalent across AGC kinases. To quantify the effects of inhibitors on C1a binding, change in interface binding energies relative to the nucleotide-free (Apo) state were computed (C). Changes in interface binding energy were consistent with changes in the strength of interaction measured as reported by FRET ratio for all six inhibitors tested in this study (C).The GxGxxG motif within the G-loop is a highly conserved sequence motif in eukaryotic kinases. In our MD simulations, the G-loop was found to shield ATP from solvent suggesting an allosteric link between the C1a and ATP-binding sites. To address this possibility, the experimentally validated model of the C1a-kinase domain interaction was used in MD simulations that examine the impact of the six different ATP-site kinase inhibitors. Simulations revealed that the BimI analogs (Sotra and BimI) displace the G-loop away from the nucleotide binding pocket, which in turn interferes with the kinase-C1a binding interface A. In cono) state A. Intereg (3NYN) B. These computed C. Changeis study C.Figure A) and further shielded from solvent by the PKCα N-terminus (B and C). These simulations further suggest that BimI binding to the kinase domain displaces C1a, which in turn alters the conformation of the V1 variable linker and the PKCα N-terminus . The combined effect of these conformational changes is a model that hints at solvent exposure of the C1a DAG binding site . The exposure of this DAG binding site would suggest that inhibitor treatment would enhance membrane-kinase interactions, which are a hallmark of PKC activation.A key step in PKC activation is its recruitment to cell membranes through C1a/b interactions with DAG . The C1aFig. S3in vitro and in live cell membranes (A). Under activating conditions (3.2 μM PMA and 1.5 mM CaCl2), both BimI-like inhibitors (BimI and sotrastaurin) and staurosporine-like inhibitors (staurosporine and tetrahydrostaurosporine) showed substantial increases in homo-oligomerization of recombinant PKCα relative to the Apo state (B). In contrast, ATP-analog inhibitors (sangivamycin and toyocamycin) caused a modest decrease in homo-oligomerization (B).We have previously shown that PKCα activation results in its homo-oligomerization with nanomolar affinity, both embranes , 15. Ourembranes A. Under po state B. In conrization B.sn-glycerol (DiC8), a DAG analog (A). Following stimulation, PKCα translocated from the cytoplasm to the cell membrane, as seen by an increase in the membrane intensity (B). The six different inhibitors showed marked differences in the shapes of their normalized membrane intensity profiles (C). While addition of BimI and sotrastaurin resulted in a rapid initial translocation followed by a plateau, staurosporine and tetrahydrostaurosporine resulted in a slower rate of translocation. These differences were quantified using the maximum membrane intensity (Imax) and the initial slope of the intensity curve (Islope) (D and E). Imax is defined as the highest point on the membrane intensity curve and is a measure of the total amount of PKCα recruited to the membrane. For traces that did not plateau within the 15-min imaging period, this is equal to the intensity of the final frame. Correspondingly, Islope is the initial rate of translocation, determined from a linear fit to the intensity for 100 s following stimulation and normalized to the maximum intensity to account for differences in Imax. A larger Islope indicates faster translocation. Because two of the inhibitors, sangivamycin and toyocamycin, and the dimethyl sulfoxide (DMSO) control resulted in very weak translocation, Islope values for these conditions are unreliable and are therefore not shown. The remaining four inhibitors significantly enhanced maximal membrane recruitment (Imax) with the aggregate rates of BimI-like inhibitors (BimI and sotrastaurin) greater than staurosporine-like inhibitors (staurosporine and tetrahydrostaurosporine). Taken together, these data demonstrate the differential effects of SMKIs on membrane localization of activation PKCα.To address the impact of inhibitors on membrane recruitment, mCitrine-PKCα was transiently expressed in COS7 mammalian cells, and its membrane translocation was measured in response to stimulation with 1,2-dioctanoyl-G analog A. Followntensity B. The siprofiles C. While (Islope) , D and EF). Additionally, these lipid bilayers contain rhodamine-PE to aid in the evaluation of membrane integrity (see G). Lipid recruitment was quantified from fluorescence intensity normalized to the ATP condition. Recruitment with 2 mM CaCl2, a known driver of PKCα lipid binding, was used as a positive control. Consistent with live cell observations, the nucleotide analogs toyocamycin and sangivamycin were indistinguishable from the ATP control. In contrast, BimI-like and staurosporine-like inhibitors significantly enhanced surface recruitment, with staurosporine-like inhibitors performing the best overall. These in vitro studies support the intrinsic effects of SMKIs on membrane recruitment of PKCα.Given that membrane recruitment of PKCs in cells could be influenced by a number of factors, including membrane-localized proteins, we examined the intrinsic effects of SMKIs using synthetic lipid bilayers. Supported lipid bilayers mimicking the composition of cellular membranes were prepared on coverslips F. Additirity see . mCer-PKrity see G. Lipid The eukaryotic kinase domain contains a constellation of nonconsecutive amino acid residues, termed spines, whose relative spatial arrangement is critical for the catalytic transfer of phosphate from ATP to a protein substrate. Several of these residues reside in two unstructured segments, the G-loop and the activation segment. To achieve the structural alignment of spines necessary for catalysis, the G-loop and the activation segment adopt similar “active” conformations in catalytically active kinases. The mechanism of inhibition by SMKIs often relies on disrupting this structural alignment of spines to trap the kinase in an inactive conformation. While SMKIs are often selected for their ability to cause this disruption, interpreting inhibitor-specific conformations is limited by the lack of dynamic information provided by traditional structural techniques. Here, we leverage multiscale MD and FRET sensors to highlight the allosteric effects of SMKIs driven by conformational effects on unstructured loop segments. Specifically, the G-loop was found to hover over the nucleotide binding site, shielding ATP from solvent. Our MD simulations in PKCα reveal that SMKIs such as BimI hit the “roof” of the ATP binding site and therefore displace the G-loop. In contrast, we found that ATP analog inhibitors and staurosporine-like inhibitors draw the G-loop into the catalytic site akin to ATP. The behavior of the G-loop observed in the PKCα MD simulations is consistent with two previously reported X-ray crystal structures of AGC kinases , 23. Thede novo identify potential C1a-kinase domain interfaces. Subsequently, mutagenesis of FRET sensors that probe the C1a-kinase domain interaction strength was used to experimentally validate the interaction site. Taken together, our study illustrates an integrated approach involving MD simulations and FRET sensors to map binding interfaces in multidomain kinases.Multidomain kinases such as PKCα often contain a series of regulatory domains that are tethered to a conserved kinase domain by unstructured linkers. The dynamic, multiplexed nature of kinase-regulatory interactions has limited high-resolution structural information on kinase-regulatory domain interfaces. There are as yet no full-length structures of any PKC isoform. In the absence of such structural information, this study engaged multiscale MD simulations validated by FRET sensor measurements to identify the structural interface of a key regulatory-kinase domain interaction in PKCα. The multiscale MD simulations leveraged structural information on an anomalous high affinity kinase-substrate peptide interaction in PKCiota to reconstruct the regulatory interaction between PKCα and its PS peptide. In full-length PKCα, the PS peptide is followed by an unstructured linker and subsequently the C1a domain. Hence, the PS-peptide-kinase domain interaction was used as a spatial constraint that in conjunction with torsional MD simulations was used to 2+ and DAG stimulation facilitate interactions between the regulatory domains and lipid membranes . We have recently shown that the extent and rate of translocation can be tuned by varying the strength of the autoinhibitory interaction between the regulatory and kinase domains (D) and maximal membrane recruitment in cells and synthetic lipid bilayers (E and G). In contrast, pretreatment with the ATP analog inhibitors sangivamycin and toyocamycin had no effect on either the rate of membrane translocation or maximal membrane recruitment compared with a DMSO control (E and G). Given that membrane translocation of PKCs is a hallmark of their activation, the paradoxical enhancement of membrane recruitment by select SMKIs is an important feature that is currently overlooked in the selection of PKC-specific inhibitors. PKCs phosphorylate a range of kinase substrates, many of which are localized to cell membranes . es (EGFR . While tB). However, we have previously shown that the size and distribution of PKCα oligomers is heterogeneous, complicating quantitative characterization of the relative influence of SMKIs . However, outside of the GxGxFG motif in the G-loop, there is no sequential conservation across the broader AGC family, of which PKCs are a prominent member. This suggests that the conserved binding interface between the C1 and catalytic domains that we report here is unique to PKCs. Interestingly, closer examination of the interface on the kinase domain revealed a hydrophobic binding pocket containing the G-loop that is capable of accommodating a drug-like small molecule. Given that the G-loop forms the floor of this binding pocket, we termed this the G-loop pocket. Given that the G-loop is essential for positioning Mg2+-ATP for phosphoryl-transfer, small-molecule ligands that occupy the G-loop pocket are likely to influence G-loop conformation and consequently kinase activity. Analysis of the entire kinase domain in PKCα using fragment-based screening showed the G-loop pocket to be among the five most accessible pockets on the kinase domain for small-molecule ligands, including the nucleotide binding site. The lack of sequence conservation supports a potential role for the G-loop pocket as a kinase-selective target site for small-molecule allosteric modulators that merits further investigation in future studies.The amino acid residues on the PKCα kinase domain that form the binding interface with the C1a regulatory domain are conserved across the PKC superfamily B. Howevein vitro assays were cloned into pBiex1 (Novagen) plasmid vector for expression in Sf9 insect cells (ThermoFisher). Constructs expressed in mammalian cells were cloned into pcDNA/FRT (ThermoFisher) plasmid vector as previously described , 0.5% IGEPAL (% v/v), 2 mM DTT, 100 μg/ml of PMSF, 10 μg/ml of aprotinin, and 10 μg/ml of leupeptin. Lysate was incubated with anti-FLAG M2 affinity resin (MilliporeSigma) for at least 2 h. Resin was washed four times with 20 mM Hepes (pH 7.5), 150 mM NaCl, 10 mM MgCl2, 2 mM DTT, 100 μg/ml of PMSF, 10 μg/ml of aprotinin, and 10 μg/ml of leupeptin. Protein was eluted with FLAG peptide (MilliporeSigma). Protein concentrations were determined using mCitrine absorbance on a NanoDrop One (ThermoFisher) or mCitrine  or mCerulean  fluorescence on a on a FluoroMax-4 fluorometer (Horiba Scientific). For all experiments using purified PKCα, protein was centrifuged at >200,000g for 10 min to remove aggregates.PKCα constructs in pBiex1 vectors were transiently transfected in Sf9 insect cells as described earlier . Culture2, 0.5 mM EGTA, and 2 mM DTT). Intramolecular FRET assays used 25 nM protein, and intermolecular FRET assays used 40 nM mCerulean-tagged PKC plus 160 nM mCitrine-tagged PKC. Intramolecular measurements were taken both under basal and stimulating (1.5 mM CaCl2 and 3.2 μM PMA) conditions and were incubated at room temperature for 30 min before measurement. FRET spectra were measured by exciting mCerulean at 430 nm with an 8 nm bandpass and monitoring emission from 450 to 650 nm in 1 nm increments with a bandwidth of 4 nm. FRET ratio was calculated as the emission intensity at 525 nm divided by the emission intensity at 475 nm. Proteins were treated with inhibitors at the following concentrations: 1 μM BimI, 1 μM sotrastaurin, 1 μM staurosporine, 10 μM tetrahydrostaurosporine, 100 μM sangivamycin, or 100 μM toyocamycin. Samples were prepared in tubes precoated with 0.1 mg/ml bovine serum albumin to prevent protein from sticking to the sides of the tubes.All FRET measurements were performed in PKC buffer (20 mM Hepes (pH 7.5), 5 mM MgCl2 (% v/v). For live cell imaging, cells were transfected with fluorescent PKCα using X-tremeGENE HP (Roche Applied Science) and plated on 35 mm glass-bottom dishes (MatTek Corp). Immediately before imaging, cells were washed twice with Hepes imaging buffer  and exchanged into 0.5 ml of imaging buffer with the selected inhibitor or DMSO. Inhibitors were used at the following concentrations: 10 μM BimI, 10 μM sotrastaurin, 10 μM staurosporine, 10 μM tetrahydrostaurosporine, 100 μM sangivamycin, or 100 μM toyocamycin. Imaging was performed on a Nikon Eclipse Ti epifluorescence microscope with a 40x or 60x oil objective and a perfect focus system. Samples were illuminated through a dichroic containing a 500/40 nm excitation filter, a 520 long-pass dichroic, and a 535/30 nm emission filter to select for mCitrine fluorescence. Video was captured on a Photometrics Evolve camera at 0.5 frames per second with 400 ms exposure time for 15 min. After 20 frames (40 s), cells were stimulated with 0.5 ml of imaging buffer containing inhibitor and 0.2 mg/ml 1,2-dioctanoyl-sn-glycerol , for a final concentration of 0.1 mg/ml DiC8.Mammalian COS-7 cells (ATCC) were cultured in DMEM  supplemented with 10% fetal bovine serum , 1% GlutaMAX , and 20 mM Hepes (pH 7.5) at 37 °C with controlled humidity in 5% COA. Briefly, this was done by measuring the average intensity of a cytoplasmic region around the nucleus (C) and of the membrane at the cell periphery (M) over time (t) for each cell. Normalized membrane intensity was calculated as (Mt/Ct) (Ct = 0/Mt = 0) to correct for photobleaching and cell to cell differences in total intensity. For each condition, ≥2 separate experiments were performed with ≥2 dishes and ≥2 cells per experiment. The three highest and three lowest normalized membrane intensity trajectories (or two highest and two lowest if N < 10 cells) for each condition were discarded as outliers. Following outlier removal there were N ≥ 6 cells for all conditions. Imax and Islope were calculated for individual traces. For Imax calculations, traces were median filtered over five frames to eliminate any intensity spikes. Islope was calculated using a linear fit to the first 100 s following stimulation. Data were fit using Origin (OriginLab Corporation).Images were analyzed with ImageJ (NIH)  as indicFigure 42, or 1 mM ATP and measuring mCerulean intensity at the membrane surface. Inhibitors were used at the following concentrations: 10 μM sotrastaurin, 10 μM tetrahydrostaurosporine, or 100 μM sangivamycin. Imaging was performed on a Nikon Eclipse Ti epifluorescence microscope with a 100x oil objective and a perfect focus system. Samples were illuminated through a dichroic containing a 436/40 nm excitation filter, a 455 long-pass dichroic, and a 480/30 nm emission filter to select for mCerulean (PKCα) fluorescence or containing a 545/30 nm excitation filter, a 570 long-pass dichroic, and a 610/75 emission filter to select for rhodamine (bilayer) fluorescence. Movies were captured on a Photometrics Evolve camera at 10 frames per second for 15 min with gain and multiplier held constant for all PKCα movies on a given day. Bilayer fluorescence recovery after photobleaching was measured both before and after addition of PKCα. PKCα intensity was measured in eight regions for each flow cell. Background intensities were measured by imaging a bilayer with the mCerulean filters before adding PKCα. Intensities for each flow cell were averaged and background subtracted and normalized to the ATP, no inhibitor condition for each day to correct for day-to-day lipid and intensity variability. Data were analyzed using ImageJ (NIH)  in between a cleaned glass coverslip and a glass slide. Coverslips were cleaned by soaking in acetone overnight. Excess acetone was removed by evaporation with dry nitrogen gas. Coverslips were then soaked in 7× Cleaning Solution (MP Biosciences), diluted 1:3 in deionized water for 1 h, and bath sonicated for 20 min. Coverslips were then washed in a stream of DI water for 5 min to remove excess detergent. The coverslips were then soaked in 100% ethanol for 1 h, followed by bath sonication for 20 min. Excess ethanol was removed by evaporation with dry nitrogen gas. Cleaned coverslips prepared using this protocol were used on the same day. Lipids in chloroform were combined, and the chloroform was evaporated using dry nitrogen gas. Residual chloroform was removed by incubating under vacuum for ≥30 min. To solubilize, lipids were resuspended to 4 mM in PKC buffer without DTT and incubated at 37 °C for ≥2 h. Small unilamellar vesicles were formed by tip sonication on ice (10–15 s bursts for 5–10 min) followed by bath sonication for 15 min. Lipids were used the same day. Bilayers were formed by flowing lipids into the flow cell and incubating for ≥30 min. Membrane fluidity was verified for every flow cell using fluorescence recovery after photobleaching. PKCα binding was measured by flowing in 100 nM mCerulean-tagged PKC in PKC buffer with inhibitor, 2 mM CaCleJ (NIH) . For eacA). However, there is currently no crystal structure of the full-length PKCα. In our previous work, we started from the crystal structure of the kinase domain of PKCα (PDB ID: 3IW4) and derived a model of the kinase domain interacting with PS using GNEIMO running replica exchange MD (REMD) simulations . GNEIMO is the internal coordinate MD package that has been combined with Rosetta software  at constant temperature . These conformations were clustered by RMSD in coordinates of the Cα atoms of the whole complex with a cutoff of 0.9 Å and identified 137 conformation clusters. We saved the representative frame of each conformational cluster and deleted the V1’ and C1b domain for further refinement of the models. All selected kinase domain-C1a bound models were energy minimized. We then calculated the energy of the C1a-kinase domain complex for all these representative conformations. The top five best scoring structures sorted by energy of the CD-C1a complex were chosen for analysis of interface interaction energy as described below.GNEIMO-REMD conformations that showed C1a interacting directly with the kinase domain were selected for further analysis C. These D). During the interface interaction energy calculation, every residue in the C1a domain (residues 38–96) was considered interface 1, and every residue in the kinase domain (residues 333–666) was considered as interface 2. A short energy minimization was performed using the minimize.static.linuxgccrelease protocol, with minimization method set to lbfgs_armijo_nonmonotone, and tolerance set to 0.001. The interface energy was calculated using the interface_energy.static.linuxgccrelease protocol. This analysis identifies models 1 and 5 as candidate strong interactions.All selected kinase domain-C1a–bound models were energy minimized and the binding interface interaction energies were evaluated by Rosetta  Fig. S1Fig. S1D.E). Models with more favorable interface interaction energy are likely to show greater changes upon mutagenesis, reinforcing their selection for experimental validation. We calculated the interaction energies of the C1a domain (residue number range 38–96) with the catalytic domain (residue range 333–666) using Rosetta mutation protocol . To minimize experimental iteration and enhance mutant effects, triple mutant combinations were chosen for experimental testing based on the difference of interface interaction energy on kinase domain-C1a interaction.From all of the single mutations, we chose the top three single mutations that caused the greatest change in the interface interaction energy upon mutation  in explicit solvent on the model 5 starting from the GNEIMO-REMD Rosetta energy minimized structure, for the WT and the four mutants proposed in previous step, using GROMACS MD package . For the3 cubic TIP3 water box, then the system was neutralized with 0.15 M NaCl. The LINCS algorithm was applied on all bonds and angles of water molecules with a 2 fs time step used for integration. We used a cut-off of 12 Å for nonbond interactions and a particle mesh Ewald method for long range van der Waals interaction. Each system was slowly heated from 0 K to 310 K in NVT ensemble during a 1 ns heating process. The temperature was maintained using a Nosé-Hoover thermostat A are representative structures of the most occupied conformation cluster extracted for each inhibitor from these simulations. The conformation clustering was done using the 1 μs long aggregated trajectories for each inhibitor. A RMSD cutoff of 1.5 Å for the Cα atoms was used in GROMACS to do this clustering. The representative structures were aligned by the Cα atoms of the whole C1a–CD complex and shown in Figure 4A.The kinase domain-C1a interaction energies in the presence of different inhibitors were calculated using the last 500 ns of each production run. The kinase domain-C1a interaction energy was calculated by mmpbsa method . The strFigure 4Some of the SMKIs showed displacement of the C1a from the kinase domain as the result of inhibitors binding. To simulate the early events of this dissociation or weakening of kinase domain-C1a interactions, we performed torsion angle GNEIMO-REMD simulations on the apo and BimI bound C1a-kinase domain-PS models derived in the previous section. We performed 200,000 cycles of GNEIMO-REMD annealing simulations totaling to 6 μs each for BimI and apo conditions. The trajectories of the GNEIMO simulations showed a 5 Å displacement of the center of mass of C1a from the G-loop when BimI was bound in the ATP binding site compared with the apo protein with nothing bound. The resulting GNEIMO trajectory was subjected to conformational clustering analysis. The representative structure from the most populated conformational cluster of the BimI bound C1-kinase domain-PS system was compared with that of the apo system.We performed amino acid sequence alignment of the N-lobe of the kinase domain of PKCα to check if the residues on the kinase domain lining the C1a binding pocket are conserved across AGC kinases. The sequence alignment was performed using Clustal Omega .et al. . All remaining data are contained within the manuscript.The starting structures and all-atom MD trajectories are available upon request (The authors declare no conflicts of interest in regard to this manuscript.


We reveal relations between the duality of capacities and the duality between Sobolev extendability of Jordan domains in the plane, and explain how to read the curve conditions involved in the Sobolev extendability of Jordan domains via the duality of capacities. Finally as an application, we give an alternative proof of the necessary condition for a Jordan planar domain to be  The (semi)-norm in Let roven in .Letbe a Jordan domain. Then it is aextension domain if and only ifis aextension domain forandp-capacity betweenEandFinE, and F. Observe that by definition the p-capacity is increasing with respect to This duality of extendability is indeed hinted by the following duality of capacities in the plane, which originally comes from  and can Letbe a Jordan domain enclosed by four arcsandcounterclockwise. Then we haveforand, 19) Let Let19]) p-capacity functions in p-capacity functions in a planar Jordan domain implies the extendability of To see how the duality in Theorem roven in  via an iroven in  for furtp-capacity function in a Jordan domain To be more specific, for 1<p<2 in  we firstThe curve condition  has beensee e.g. , 16. Alsinstance , 12, 20.p-subhyperbolic length ofp-subhyperbolic distance betweenp-subhyperbolic length among all the curves joining In this paper, we show the relation between  and the refer to .p-capacity betweenandinFor p-capacity metric and the The theorems below indicate the relation between the Letandbe a Jordan domain andandThen for the hyperbolic geodesicjoiningwe havewhere the constants depend only onp.n-capacity metric and quasihyperbolic metric was studied via quasiconformal mappings in We note that, in  the relasides of  in termsLetbe a Jordanextension domain in the plane withThen for any two pointsthere exists a curvejoiningandsuch thatwhere the constant depend only on the norm of the extension operator andq.All the results above can be extended to the case where We usually write the constants as positive real numbers A and B by A by I in path and its image a curve; the image of an injective map we call an arc. We denote by x and y in For Euclidean spaces Jordan curve and, by the Jordan curve theorem, the set Jordan domains. By the Riemann mapping theorem, for each Jordan domain Recall that the image see e.g. .Recall that for points conformal annulusLet For the conformal annuli, we have the following comparison lemma; the proof of the analog of it in , p. 645 Letbe a Jordan domain,andletbe the hyperbolic geodesic injoiningandFor eachletThenFurthermore, ifis a curve injoining components ofthenThe constants of comparability in  base pointWe can apply Lemma With the assumptions and notation in Lemma  for every conformal annuluswithone hasfor eachwhere the constant depends only onp.q-capacity of (a part of) the outer boundary and (a part of) the inner boundary of the conformal annulus A of Fix the domain A. Inside the topological rectangle A, via an argument similar to [A into three topological rectangles Let us fix one of the component p-capacity of a spherical annulus in the plane; see e.g. [A fundamental estimate is the LetThen, for anyandwe haveLet Case 1Case 1.1p. The other direction follows from a proof similar to the one of [If the curve Case 1.2p. Since p-metric and p-capacity metric, respectively, we conclude the theorem in the special case.Suppose the curve Case 2p-capacity we conclude thatp. By Lemma p.We first show thatp.For the other direction, let on. Thus  follows The rest part of the theorem follows analogously according to the calculation above: For example, by choosing ent}γ in  one concLet us first consider the case p-capacity,Since Now for a pair of points p-capacity for (When isk; see –9, 11. Htion and  via Theocity for  and 2-ca


The residual deformation of a goaf is studied to improve the foundation stability assessment for metro lines passing through the subsidence area of steeply inclined extra-thick coal seams. The variable mining influence propagation angle is introduced to describe the special form of the rock movement. Based on the modified parameters in the traditional probability integral model, a subsidence prediction model is established. Then, based on the idea of an equivalent mining thickness, Kelvin model is introduced to analyze the creep characteristics of the old goaf, and the dynamic prediction function of the residual subsidence is constructed to realize the dynamic analysis of the residual deformation. Moreover, a case study is used to evaluate the predictive effectiveness of the prediction model, and the results are compared with the monitoring data and numerical simulation results. The results show that the values with a relative error between the predicted value and measured value are in the range of ±7%, indicating that the prediction model based on the mining influence propagation angle is feasible. Thus, the residual deformation prediction model based on the mining influence propagation angle is considered to be suitable for predicting the subsidence of engineering projects crossing a goaf. With the rapid development of urban rail systems and the continuous construction of mining areas in China, some new metro lines will inevitably pass through an old goaf. Although the old goaf has experienced long-term natural compaction, it is still possible that the broken rock mass gap is not compacted. The relative stress balance in the broken rock mass is likely to be broken under the influence of the external environment, such as construction. The secondary deformation in the collapsed area can occur, and then the metro structure will be destroyed by the larger residual deformation above the goaf. Therefore, the prediction of residual movement and deformation is very important for the construction of metro structures above old goafs.When constructing a metro above an old goaf, the evaluation of the foundation stability is a key issue that must be studied, and residual deformation is the main factor affecting foundation stability. Many scholars have constructed the corresponding prediction model for the residual deformation of a goaf. Zhu et al. analyzed the evolution of the overburden structure in a goaf, and defined two deformational phases of the surface residual movement. The detrimental impact on the buildings above a goaf is the residual deformation of the second stage . Guo et However, the existing research was on the study of the residual deformation of thin horizontal coal seams or gently inclined coal seams in long-wall mining or on the study of the surface deformation caused by the mining of steeply inclined extra–thick seams . There iThe surface deformation caused by mining can be divided into two stages. The first stage is the deformation of the overburden rock during the mining process and the surface deformation within 3~5 years after mining, which is called the large deformation stage. The mining regulation notes that the surface is stable after the large deformation stage . The seci) Large deformation stage The destruction process of the top coal and surrounding rock due to mining can be generalized into three regions, as shown in (ii) Small deformation stage The continuous surface deformation time is 3~5 years, that is, it starts from a surface subsidence of 10 mm and continues until it sinks no more than 30 mm in 6 consecutive months  for steeply inclined extra-thick coal with a soft floor.For steep seam  is the subsidence value of point  caused by unit mining; rz is the main influence radius of the subsidence basin where the depth of the overlying rock from the working face is z.The expression of the unit mining subsidence basin is as follows.Wu(s) of surface point A with horizontal coordinate s, is the sum of the subsidence values caused by each unit mining in the range of 0 to l.For the whole unit thickness seam mining, the subsidence value m, the subsidence value W(s) of surface point A can be written as follows.q is the subsidence coefficient of slicing mining in the large deformation stage; α' is the dip angle of the slicing working face, where α' = 0 when the horizontal slicing method is adopted.If the slicing thickness is S0 = 0. When calculated by the probability integral method [l−S0 = l. In addition, the residual deformation is calculated using the equivalent mining thickness m'.The residual deformation of the goaf in the steeply inclined extra-thick coal seam resulted from the compaction of the collapsed area during the small deformation stage. The goaf does not form a boundary zone and an intermediate zone but forms a whole collapsed area, that is, the inflection point offset is l method , the calm, and the ultimate subsidence coefficient will be 1.0 [m' of residual deformation is as follows.When the collapsed area of the goaf is activated, assuming that all the voids of the fractured rock mass are fully compacted, the maximum deformation value of the surface caused by single-layer mining will not exceed the thickness l be 1.0 . The equBased on Eq  and Eq , the resic(s), residual curvature deformation kc(s), residual horizontal displacement Uc(s), and residual horizontal deformation ε(s) can be obtained.b is the coefficient of horizontal movement, which is the ratio of the maximum horizontal movement value Umax to the measured maximum surface subsidence value Wmax.Then, residual inclination deformation The predicted residual deformation value of the above models is the potential maximum residual value. The mining voids are fully compacted after the collapsed area is activated. Therefore, the potential maximum residual subsidence value can be obtained by the surface residual subsidence curve function of Eq . The voiKelvin model is a kind of viscoelastic body, and the mechanical model is as follows:(1) Constitutive equationThe relation between stress and strain.Then, the constitutive equation of Kelvin model can be obtained by Eq .(2) Creep equationσ0 is applied at t = 0, the constitutive equation can be expressed as follows.If an invariant stress Then, the following result can be obtained.(3) Residual subsidence dynamic prediction modelε = σ0/k tends to be constant when t→∞. In fact, in the process of rock creep, the voids of the fractured rock mass in the collapsed area of the goaf are compacted, and the residual subsidence value tends to the maximum potential subsidence Wc(s). The parameter k/η in the creep equation can be integrated into the parameter μ, which is affected by time. The dynamic prediction model of surface residual subsidence can be written as follows.From the creep equation, Urumqi Metro Line–1 starts from Santunbei Station in the south and ends at Diwopu Airport Station in the north. The metro line goes through the Liudaowan coal mine, and the diagram of the mining horizon is shown in When the metro is built above the collapsed area, the collapsed area will generate residual deformation under the disturbance of external forces and cause uneven ground settlement, which in turn affects the normal use of the metro structure and ground buildings. Therefore, it is necessary to carry out research on the residual deformation of collapsed areas to analyze the problem of foundation stability.q = 0.98 based on the monitoring data. The basic parameters of the surface deformation of the Liudaowan coal mine in Urumqi are listed in To verify the accuracy of the residual deformation prediction model based on the mining influence propagation angle, the monitoring data of the Beidacao and the Nandacao of the Liudaowan coal mine in Urumqi are chosen as samples . For theFor Beidacao, the highest value of relative error is only 6%, that is, the difference between the measured values and the predicted values is small. For Nandacao, the values of relative error are in the range of ±7%, and the maximum predicted values are close to the maximum measured values. It can be said that the prediction model can accurately predict the residual deformation of the goaf.μ and maximum measured value of residual subsidence Wc(s) can be obtained, whose values are 0.0784 and 614 mm, respectively. The monitoring value and dynamic prediction value of the residual subsidence in the Beidacao goaf are shown in To guide the subsequent metro construction, the crossing section of the designed metro line is selected as an example to analyze the dynamic residual subsidence. The residual deformation data for the Beidacao goaf of the Liudaowan coal mine in 2008–2016 are applied to the residual subsidence dynamic prediction model (Eq ) for curAs shown in According to the general situation for the Nandacao and Beidacao goafs of the Liudaowan coal mine in Urumqi and the investigation report of Urumqi Metro Line 1 , the numAfter the excavation is completed, collapse occurs in the Nandacao and Beidacao goafs, and two collapse pits are formed on the surface, resulting in subsidence of the surface. Then, the goaf is filled with broken rock masses, which are loose and not dense. When the old goaf is activated, the gaps of these broken rocks are continuously compacted, resulting in residual deformation on the surface. Because Urumqi Metro Line 1 passes through the Nandacao and Beidacao goafs, it is of great importance to analyze the residual deformation of the goaf before metro excavation.The numerical simulation result of the residual subsidence before the metro excavation can be seen in As shown in In this paper, the mining influence propagation law in the steeply inclined extra-thick coal seam is analyzed, and the variable mining influence propagation angle is used to describe the special form of the rock movement. A subsidence prediction model based on the variable mining influence propagation angle is constructed according to the modified parameters in the traditional probability integral model. Considering that the residual deformation is due to the compaction of the broken rock mass space in the caving zone, Kelvin model is introduced to study the creep characteristics of the old goaf, and the dynamic prediction function of residual subsidence is constructed.Finally, the prediction models are applied for residual subsidence prediction. The results of the case study show that the predicted maximum value of the surface residual deformation is relatively close to the measured maximum value. Therefore, the residual deformation prediction model based on the mining influence propagation angle is a promising method for the evaluation of the foundation stability of engineering projects crossing a goaf.


UBE3A gene. The abundance and subcellular distribution of UBE3A has been the topic of many previous studies as its dosage and localization has been linked to neurodevelopmental disorders including Autism, Dup15q syndrome, and Angelman syndrome. While commercially available antibodies have been widely employed to determine UBE3A localization, an extensive analysis and comparison of the performance of different UBE3A antibodies has not been conducted. Here we evaluated the specificities of seven commercial UBE3A antibodies in two of the major experimental models used in UBE3A research, mouse and human pluripotent stem cell-derived neural cells and tissues. We tested these antibodies in their two most common assays, immunofluorescence and western blot. In addition, we also assessed the ability of these antibodies to capture dynamic spatiotemporal changes of UBE3A by utilizing human cerebral organoid models. Our results reveal that among the seven antibodies tested, three antibodies demonstrated substantial nonspecific immunoreactivity. While four antibodies show specific localization patterns in both mouse brain sections and human cerebral organoids, these antibodies varied significantly in background signals and staining patterns in undifferentiated human pluripotent stem cells.UBE3A is an E3 ubiquitin ligase encoded by the neurally imprinted  In addition to this role, UBE3A also has a putative role in transcriptional regulation where it co-activates steroid hormone receptors such as progesterone and estrogen2. Although biallelic in most tissues, UBE3A is expressed exclusively from the maternal allele in neurons due to tissue specific paternal imprinting3. Mutations or deletions of maternal UBE3A, leads to loss of UBE3A in neurons and Angelman syndrome (AS), a severe neurodevelopmental disorder characterized by delayed development, speech impairment, ataxia, and intellectual disability4. On the other hand, increased levels of UBE3A activity due to gene duplication or mutation has been associated with Dup15q syndrome and Autism Spectrum Disorder (ASD)7.UBE3A is a HECT domain E3 ubiquitin ligase that targets substrate proteins, including itself, for proteasomal degradation9. Although it has a cytoplasmic component, UBE3A is predominantly nuclear in human and mouse neurons13; however, its roles in these subcellular compartments in different cell types and developmental stages have not been fully uncovered. Previous reports show that while mice lacking the nuclear UBE3A isoform (mIso3) exhibit electrophysiological and behavioral deficits similar to other AS model mice13, the cytoplasmic UBE3A isoform (mIso2) is important for polarized dendrite morphogenesis14. Taken together, these findings indicate that both cytoplasmic and nuclear components of UBE3A may be critical for proper brain development and underscore the importance of studying its subcellular distribution and abundance.In addition to its imprinted expression, one of the key molecular features of UBE3A is its distinct subcellular localization patterns, potentially regulated by its three isoforms12 and human stem cell derived neurons9, others are less well documented. Furthermore, except for the mouse monoclonal antibody from Sigma-Aldrich (SAB1404508)9 and rabbit polyclonal antibody from Bethyl Laboratories (A300-351A)15, the specificities of most antibodies in human samples remain unknown, and even when validated, were tested only in limited cell types. With the growing use of human pluripotent stem cell-derived neuronal cultures and three-dimensional cerebral organoids as models to study human UBE3A biology, it will be important to assess the specificities of UBE3A antibodies in human stem cell-derived systems as well as mouse models. Human stem cells and cerebral organoids are therefore the major focus of this work, with the use of mouse tissues to provide comparisons to prior work and to identify potential species-specific differences.The primary methods to determine UBE3A localization have been the use of commercially available antibodies in immunoassays such as western blot, subcellular fractionation followed by immunoblotting, or immunostaining of fixed cell culture or tissue samples. Although a few commercial UBE3A antibodies have been rigorously validated in the published literature for mouse brain tissueUBE3A m−/p− hESC line as negative controls. In addition to specificity, we also evaluated the ability of these antibodies to capture important disease relevant features of UBE3A through the use of whole brain human cerebral organoid (hCO) models generated from a large panel of human pluripotent stem cell (hPSC) lines including isogenic wild-type (H9WT), AS (H9UBE3A m−/p+), and double knockout models (H9UBE3A m−/p−), two additional WT hPSC lines , and two patient-derived AS hiPSC lines .In this work we evaluated seven commercial UBE3A antibodies including those most commonly used in the field. We tested antibody specificities in immunofluorescence (IF) and western blotting (WB) assays using AS model mice and the H913 and the E6 oncoprotein binding domain  and AS (Ube3am−/p+) mouse brain sections. Mouse models are widely used in the field and they have been shown to successfully model some of the core molecular features of UBE3A including imprinting of the paternal allele and nuclear localization of Ube3a in neurons16. They have also been extensively studied using IF, especially with the Sigma-Aldrich antibody (SAB1404508), and would therefore serve as a point of comparison for our IF methodology which closely mirrors prior work12. We focused specifically on cortical regions with a high density of neurons, as indicated by MAP2 staining, that previous work showed exhibits strong nuclear Ube3a signal in WT mice and no Ube3a signal in AS mice12  WT  due to paternal imprinting. Among them, the Sigma-Aldrich antibody (SAB1404508) demonstrated the lowest background signal followed by Bethyl Laboratories A300-352A and Bethyl Laboratories A300-351A  and exhibited the expected prominent nuclear localization pattern in WT neurons 13, the specificity of this commonly used antibody has not been evaluated in human knockout models until recently9. Here we expanded upon this analysis and evaluated the specificities of the 7 antibodies in IF using H9WT and H9UBE3A m−/p− hESC lines   of H9Os Figs.  and S3. UBE3A m−/p+ and hiPSCASdel) indicating imprinting and silencing of the paternal allele, as was previously observed15   of both AS model hCOs  Figure B. CollecASmut hCOs which was an anticipated result  on the N-terminal region of the N lobe of HECT domain, and previous reports indicate that this variant does not exhibit protein folding issues20. Furthermore, immunogens of the antibodies tested in this study do not directly align with the mutated region, with one exception being mouse monoclonal Sigma-Aldrich antibody (E8655) that was raised against full length human recombinant UBE3A (isoform1).Furthermore, all four antibodies also showed a striking nuclear localization pattern in the neurons of hiPSClt Figs. B and S3BUBE3A m−/p− and AS models. Interestingly, while the staining patterns of the Bio-Rad and Novus Biologicals antibodies appeared to be diffuse and nonspecific, the Proteintech antibody exhibited strong nuclear labeling in neuronal regions of all hCO models  and another Sigma-Aldrich (E8655) antibody showed similar specific staining patterns in mouse brain tissue. However, while Bio-Rad and Novus Biologicals antibodies were raised against the same epitope sequence as the established Sigma-Aldrich antibody (SAB1404508), these antibodies revealed different patterns of reactivity with significant nonspecific signal in AS mice, potentially due to the differences in selected antibody clones . While consistent with each other, Bio-Rad and Novus Biologicals antibodies also produced a distinct nonspecific band pattern in WB analysis with human hPSC lysates. These results indicate that these antibodies recognize unknown proteins of diverse molecular sizes other than UBE3A and highlight the importance of clone selection and validation in monoclonal antibody production.Our analysis in mouse brain sections with the commonly used Sigma-Aldrich antibody (SAB1404508) showed that the IF protocol used in this study produced comparable results to previously published work9. This may imply a reduced affinity for the majority of the UBE3A protein expressed in a cell. Moreover, the polyclonal nature of this antibody may also contribute to its cross-reactivity with other targets. Due to its misleading IF staining pattern in WT models that looks like a specific signal, future studies that plan to utilize this antibody to determine UBE3A expression and localization should make sure the proper negative controls are employed.Among the tested antibodies, the Proteintech antibody yielded the most unusual results. When tested in IF with adult WT mouse brain and WT hCO samples, it demonstrated the expected nuclear staining pattern in neuronal regions. However, it also showed the identical staining pattern and comparable signal strength in AS mouse sections and double knockout hCO sections. Consistent with this result, even though the WB analysis for the 100 kDa UBE3A target appeared as expected in WT lysate while being absent in the double UBE3A knockout samples, the Proteintech antibody also showed another band with similar signal strength to the UBE3A bands which appeared in both WT and double knockout cell lysates. These results indicate that the immunoreactivity observed with the Proteintech antibody is not solely related to the presence or absence of the UBE3A and that this antibody reacts with another distinct unknown protein. Although basic local alignment search tool (BLAST) analysis did not yield another potential target, the comparison of the epitope sequence used to raise this antibody with the protein coding UBE3A isoform sequences showed that it does not have 100% sequence homology with the most common UBE3A variant (hUBE3A iso1 and mUbe3a iso3) Figs. A8,9. Thi9. This discrepancy between the two studies could be due to differences in culture conditions , where the morphology and gene expression state of pluripotent cells can vary substantially. This possible explanation is also supported by the results from hCOs where both Bethyl Laboratories and both Sigma-Aldrich antibodies demonstrated the expected nuclear staining pattern in the neurons of WT hCOs, captured indications of paternal imprinting in AS hCOs, and showed significantly reduced signal in hCOs generated from the double knockout hESC line.Our IF analysis specifically in human hPSCs in their undifferentiated states revealed distinct staining patterns between the antibodies. These differences were stark, particularly between the polyclonal Bethyl Laboratories antibodies (diffuse cytoplasmic and nuclear staining) and the monoclonal Sigma-Aldrich antibodies (strongly cytoplasmic staining). In contrast, all four antibodies performed similarly in mouse brain sections and differentiated hCOs. Our analysis with the Sigma-Aldrich (SAB1404508) antibody also showed differences in staining pattern and background signal compared to a recently published study using the same double knockout hPSC line25; however, IF analysis with these antibodies was limited to a few studies in mouse models26. The present work indicates that the Bethyl A300-351A is a viable antibody option with performance at least on par with the Sigma-Aldrich antibodies and could be used for future IF and WB assays in both mouse and human model systems. Finally, it is not advised to use the Bio-Rad, Novus Biologicals, and Proteintech antibodies as they exhibit considerable non-specific staining in both IF and WB applications.This study highlights the importance of testing multiple UBE3A antibodies in different detection methods. The two Sigma-Aldrich antibodies have been the primary choice in the majority of the literature. Based on our results they are suitable for both IF and WB assays, albeit with a still unknown nonspecific signal in undifferentiated double UBE3A knockout hESCs. Both Bethyl Laboratories antibodies have previously been used in WB of mouse, hPSCs, and hPSC-derived neuronal lysatesdel) were developed by the laboratories of Stormy J. Chamberlain and Marc Lalande at the University of Connecticut27 and obtained from Kerafast. H9UBE3A m−/p− and H9UBE3A m−/p+ cells with a 66 kb deletion (chr15: 25338949–25405676) and AS point mutation hiPSC line (F583S) (ASmut) were provided by Dr. Stormy Chamberlain (UCONN). The H9UBE3Am−/p− hESC cell line was generated and validated by Sirois and colleagues9. Our group also confirmed the deletion in these cells in an earlier study15. All cell lines were maintained in 6-well tissue culture dishes (Fisher Scientific) coated with 0.5 mg/cm2 Vitronectin (VTN-N) (Thermo Fisher) in E8 medium (Thermo Fisher) and passaged using standard protocols. Whole brain human cerebral organoids (hCOs) were generated and maintained using the same protocols as described28. Cells and hCOs were maintained in a humid incubator at 37 °C with 5% CO2.Feeder-independent H9 and H1 hESCs (WA09 and WA01) were obtained from WiCell. Neurotypical hiPSCs were purchased from Systems Biosciences (Cat# SC102-A1). Angelman Syndrome (AS) hiPSCs with a class II deletion (ASUbe3am+/p+) and Angelman Syndrome (AS) (Ube3am−/p+) mouse brain sections were residual samples from unrelated experiments and were provided by Dr. Ben Philpot (UNC). Mice carrying the Ube3a knock-out allele were originally generated by the laboratory of Dr. Arthur Beaudet29 and back-crossed  to a congenic C57BL/6J background. AS model mice were generated by mating WT male mice to female mice with paternal inheritance of the Ube3a knock-out allele (Ube3am+/p−), which themselves are phenotypically normal29. Genotyping regarding the AS model mice has previously been described12. The sections used in this study are from a single perfused animal for each genotype (Ube3am+/p+ and Ube3am−/p+).All methods to generate the original animal sections were carried out in accordance with the relevant guidelines and regulations of the University of North Carolina Institutional Animal Care and Use Committee. All experimental protocols using vertebrate animals to generate the original animal sections were approved by the University of North Carolina Institutional Animal Care and Use Committee. This study was carried out in compliance with the Animal Research: Reporting of in vivo Experiments (ARRIVE) guidelines. Wild-type (WT) . Slides were mounted using ProLong Antifade Diamond (Thermo Fisher Scientific). Secondary antibodies used were donkey Alexa Fluor 488, 546 and 647 conjugates . Details on primary antibodies can be found below. Images were taken using a Nikon A1R confocal microscope (Nikon Instruments). High magnification images were captured using thin (1.5 μm) optical sections. All samples immunostained with the same antibody were processed at the same time, imaged using the same microscope settings, and adjusted identically. UBE3A antibody information including citations and antibody specifications provided by the vendors have been downloaded and stored on the Keung Lab GitHub page to provide access in the future if any of the antibodies used in this study are discontinued. The link to the publicly available GitHub repository is http://github.com/keung-lab/UBE3A_Antibodies.Tissues and cells were fixed and immunostained as previously describedAdditional primary antibodies used in immunofluorescence assays:WT, H9UBE3A m−/p−, and mouse cerebellum (mCER) derived from C57BL/6 mice were prepared as previously described30. Proteins separated in PAGE gel were transferred to PVDF membranes and treated with UBE3A antibodies (Figs. Whole cell lysates from H9es Figs. A and S1APrimary and secondary antibodies used in immunoblotting assays:Supplementary Information.


Recently, Cu-Ag nanocomposites (NCs) have been extensively used as medical implants and surgical instruments due to their antibacterial properties. Consequently, mechanical behavior analysis of these NCs is of crucial importance with emphasis on their plastic deformation mechanisms. From the materials science perspective, dislocations slip at the room temperature and high strain rates conditions is hindered. However, copper and silver, as two metals with low stacking fault energy are prone to twin formation. Since microstructural changes in these nanostructured composites occur at the atomic scale, molecular dynamics (MD) simulation is undoubtedly a great tool to use. Accordingly, in the present research, first, the deformation mechanism of perfect copper-silver NCs under uniaxial compression is deeply analyzed employing MD. This is followed by inspection of the voids effect on their plastic deformation process. The results show that twinning is the dominant mechanism governing their deformation under uniaxial compressive loading conditions. It is revealed that twins are created by the conversion of internal stacking faults to their external counterparts. Also, investigation of the microstructural evolution demonstrates that the presence of voids within NC samples provides new sites for nucleation of Shockley dislocations in addition to the interface zone. Finally, to address the effect of interfacial coherency on the results, copper-based NCs infused with gold and nickel nanoparticles are also thoroughly examined. Among these, copper-silver NCs can significantly improve the performance of biomedical implants due to their antibacterial effects3. It is worth mentioning that the use of nanocomposites for this goal may face several challenges. For example, an implant as a replacement of the damaged tissue should possess mechanical properties similar to those of the bone structure. Otherwise, under external loading conditions, deformation occurring on the implant is really different from that of the bone leading to the so-called implant loosening6. Accordingly, the analysis of their mechanical behavior and deformation mechanism is a focal point of research. From the materials science perspective, at the atomic scale, plastic deformation of nanocrystalline materials is achieved through twinning and/or slip of dislocations7. Although both of these mechanisms change the mechanical properties of the sample, however, their influence on the microstructural evolution can be completely different. To be more specific, dislocations slip creates local deformations, whereas twinning reorients the crystal structure with the cooperative movement of atoms. However, from the microscale point of view, since deformation by dislocations takes place in the whole material, plastic deformation occurs mainly through this mechanism8. One of the other factors limiting the twinning-based deformation is the fact that slip normally occurs in the discrete multiples of the atomic spacing. Meanwhile, the atom movements are much less than the mentioned parameter during the deformation twinning9.In recent years, metal matrix nanocomposites (MMNCs) have been widely used in health, transportation, electronics, and aerospace industries10. It also depends on the type of crystal structure. In BCC and HCP structures, due to the lack of sufficient active slip systems, deformation occurs by the twinning process. Similar behavior has also been observed in the low stacking fault energy (SFE) metals having the FCC structure such as copper, silver, and aluminum, which is ascribed to the inverse relationship between the SFE and twinning behavior13. Additionally, it has been demonstrated that twinning-based deformation is favored at higher strain rates and lower temperature conditions15.Several factors affect the type of plastic deformation mechanism that occurred within the nanocrystalline metals. For example, in the case of metals with nano-sized grains, twinning is the governing mechanism, whereas with increasing the grain size, dislocation slip is more likely to happen16. Carrying out molecular dynamics (MD) simulations, Weng et al.17 have also shown that the interfacial area is one of the most important sites for the nucleation of dislocations and therefore, can noticeably affect the mechanical behavior of nanocomposites. Regarding this issue, Pogorelko et al.18 demonstrated that copper nanoparticles form a semi-coherent interface with the aluminum matrix and as a result, efficient load transfer cannot be achieved from the matrix to the embedded copper nanofillers. However, the interfacial region can play a different role in the plastic deformation behavior of MMNCs. For example, in the study of Buehler et al.19, it has been observed that the niobium/copper interface would stop the slip of dislocations leading to the enhanced yield strength and morphological stability of the nanocomposite samples at the higher temperature conditions.Concerning the plastic deformation behavior of copper/silver nanocomposites, a key question naturally arises: While a good consistency is predicted for slip planes and slip directions of these two metals owing to their similar structure, why their composites exhibit a different behavior? Finding the possible answer to this question is the main aim of the present work. In this context, most previous studies have been devoted to analyze the plastic deformation behavior of MMNCs in the presence of the second phase. Among these, it has been demonstrated that the formation of stacking fault regions within the bulk matrix has a direct correlation with the geometrical features of the additive phase and its distribution20. However, the formation of these porosities is considered to have negative effects on the mechanical properties. This is attributed to the creation of partial dislocations in the interfacial region as depicted by Zhao et al.21 during the analysis of the defected single crystalline copper sample under tensile loading conditions. This arises because voids can resemble the dislocation generation sources due to the locally induced stress concentrations in their vicinity21. This issue was previously addressed by Zhan et al.22 for copper nanowires analyzed under uniaxial tensile test. It was concluded that porosities can act as new sites for the creation of dislocations, which in turn deteriorates the mechanical characteristics of these nanostructures.An important issue regarding the biomedical applications of these NCs is the adhesion of body cells to the implants, which improves the strength of the implant/tissue interface. It is worth mentioning that this phenomenon could be drastically enhanced through the formation of nanovoids within the bulk matrix25., in the present work, this special shape of Ag NPs has been considered in our models. This paper is organized as follows. The simulation details and sampling techniques are denoted in Section 2 along with introducing the crystal structure analysis tools including Common Neighbor Analysis (CNA), Centrosymmetry Parameter (CSP), and Dislocation Extraction Algorithm (DXA). The most important findings of this work are presented in Section 3 with emphasis on the mechanisms governing the plastic deformation of MMNCs under compression. Section 4 contains the concluding remarks.In recent years, extensive research has been conducted to examine the role of interfacial area, type and location of voids, and geometrical features of the second phase on the mechanical behavior of MMNCs under tension loading conditions. However, the influence of the above-mentioned phenomena on the mechanical response of these nanocomposites to the other loading conditions has rarely been considered using atomic-scale simulation techniques. In particular, to our knowledge, no study has been devoted to examine the mechanical characteristics of defected Cu/Ag nanocomposites under compression. Therefore, in this study, we utilize MD simulation to see the effects of voids content on the compression behavior of copper-based nanocomposites embedded with Ag NPs. Additionally, the underlying plastic deformation mechanisms are introduced and compared to those activated in the tensile loadings. It is worth mentioning that since spherical Ag nanoparticles have more antimicrobial effects compared to the other geometrical features such as nanoplatelets, nanorods, and etcAs mentioned before, this paper is aimed to assess the nanovoids effect on the mechanisms governing the plastic deformation of Cu/Ag nanocomposites subjected to uniaxial compressive loadings. In the following, MD parameters, samples preparation method, and the most common techniques implemented to analyze the crystal structure evolutions within the samples are introduced.https://lammps.sandia.gov)26. In line with the previous studies of various copper-silver systems29, the EAM potential was employed as the interaction model. This many-body potential has been successfully utilized to analyze the dislocations and stacking fault regions in metals, alloys, and MMNCs1. It should be pointed out that in the present work, the EAM potential developed by Williams et al.30 was utilized to mimic the interactions within the Cu-Ag samples. This version of EAM has been successfully employed to reproduce the lattice parameter, cohesive energy, elastic constants, lattice-defect energies, phonon frequencies, thermal expansion, and stacking faults energy of the Cu–Ag compounds. Additionally, comparing the simulated data with the experimental measurements, it has been shown that the Cu-Ag phase diagram can also be correctly predicted utilizing this potential, which demonstrates the validity of the EAM potential used in the current study. For each simulation, at first, it is required to relax the structure so that the energy of the whole system stabilizes at the lowest possible value. For this purpose, setting the temperature at 300 K, analysis of 200 ps at NVT ensemble was initially performed for all samples. Based on our previous study31, the value of 2 fs was considered as the time-step, which has proven to provide the accurate data at a reasonable computational cost for these systems. For controlling the temperature at the desired value, the Nose-Hoover thermostat was employed. After assigning the initial atomic velocities by the Maxwell-Boltzmann distribution, the well-known velocity Verlet scheme was implemented to advance the system variables32. Following the relaxation, to apply the uniaxial compression load on each sample, the left part was kept fixed  was utilized35.Simulations were carried out using LAMMPS  have been illustrated in Fig. The similar zigzag trend was found in the plastic region of copper-silver nanocomposites under tensile loading conditionszed Fig. –c. As di49. Porter et al.50 showed that for the semi-coherent interface, in the absence of external loading conditions, a cohesive strain is created at the interface with a direction opposite to that of the misfit strain to cancel out its effect. This is not the case happened after yielding in which, the matrix and nanoparticles are deformed resulting in the increase of the discussed atomic misfit. Accordingly, the cohesive strain would not be capable of preserving the continuity of the interface. Thus, this area would be a preferred site for dislocation nucleation. This issue has been experimentally confirmed for Cu-Ag systems in the literature51. For example, Zheng et al.52 introduced the Cu/Ag interfacial zone as the hetero-twin (non-coherent) interface, which is not capable of defects movement across the region  increases to facilitate the process See Fig. . TherefoSee Fig. . As seencompressive loadings. Nucleation of Shockley partial dislocations with concurrent formation of stacking fault regions between them has been enumerated as the main reason for the occurrence of the twinning morphology in the copper-based systems57. Our findings are in line with the experimental observations of Beyerlein et al.58, which confirm that the twinning phenomenon in the copper-silver nanocomposite starts from the interface. It should be pointed out that in addition to the interfacial region, the SFE is also an important parameter affecting the plastic deformation mechanism of these NCs. Accordingly, it can be concluded that if we change the role of the constituents in the discussed composite systems, the plastic deformation will be intensified through the enhanced twinning formation. This is attributed to the lower intrinsic SFE of Ag compared to that of Cu as predicted by Hunter et al.59.Therefore, based on the above discussions, it is clear that the twinning formation is main mechanism dominating the plastic deformation of copper-silver nanocomposite systems subjected to 60. It has been proven that this type of interface is formed for each pair of elements having more than 5% lattice mismatch50. In contrast, for the Cu/Ni sample, a coherent-like interface is formed due to the only 3.1% atomic mismatch between them60. This difference in the interfacial coherency would manifest itself in the emission of partial dislocations nucleated in the interface zone of these composite systems  were also examined under the prescribed compressive loading conditions. It is noted that similar to the Cu/Ag sample, the former resembles a case with the semi-coherent interface owing to 12.5% difference between the atomic radius of Cu and AuSee Fig. . As illu61. To shed more light on this issue, we also approached to explore the role of SFE on the plastic deformation behavior of the introduced samples. Figure 62), the sample embedded with Ni nanoparticle has the lowest number of HCP atoms. In this case, not only a high density of stacking faults cannot be formed within the Ni inclusion, but also, more importantly, their expansion through the interfacial area and finally, the bulk copper is hard to occur. Contrary to the former case, significant regions having HCP atoms were observed for Cu/Ag and Cu/Au nanocomposites, which is attributed to the low values of SFE reported for silver and gold NPs . Accordingly, compared to Ag NPs, the presence of Au inclusion could promote the plastic deformation of the bulk copper through the enhanced twinning formation. However, this mechanism would not be effective in Cu/Ni samples, presumably owing to the lack of sufficient partial dislocations and stacking faults in their interfacial area as the main resources needed for twinning formation.Another important factor leading to the different behavior of these MMNCs is the stacking fault energy. As discussed in the introduction, it has been confirmed that there is a reverse correlation between the SFE and the extent of stacking faults in the metals and metallic systemset al.63. As previously discussed, due to the presence of the hetero-twin interface in these systems, this region would be potentially a preferred site for enhanced deformation twinning. Accordingly, as seen in Fig. 64 demonstrated that this phenomenon could increase the stress required for motions of twins in the nanotwinned metals.As observed in the previous discussion, the type of inclusions is very important in determining the mechanism of MMNCs deformation. But, a vital question that should be answered is as follows: What is the size effect of the interfacial region on the deformation twinning? For this purpose, in addition to the introduced sample infused with the 2 nm diameter Ag NP, we further examined the copper systems embedded with Ag nanoparticles of 1.5 and 2.5 nm diameter having the VF of 1.98 and 3.25%, respectively. Figure mentclasspt{minimatensile loading conditions32.After examining the perfect Cu/Ag NC sample, the subject was thoroughly inspected in the case of defected samples to find out the role of topological voids on the creation of dislocations, stacking fault regions, twins and in general, mechanical features of the NC sample. For this purpose, three samples containing different voids content were subjected to uniaxial compression loading. Geometrical characteristics of the samples have been listed in Table et al.65. For a more detailed investigation of this issue, the cross-section of the nanocomposite sample containing 2.5% porosity was studied using the dislocation extraction algorithm (See Fig. et al.66 showed that the Cu/Ag interface possesses similar misfit dislocations to those of reported by our MD simulations in Figs. et al.49 analyzed the defect-interface interactions in the irradiated Cu/Ag NCs including some voids attached to the interface. TEM image shown in Fig. quantitative tool supporting this idea, the total length of Shockley partial dislocations and the number of stacking fault atoms were obtained for all of the three introduced samples. Figure Considering the proposed mechanism highlighting the role of twinning formation on the plastic deformation of these nanocomposites, it seems that the presence of voids would affect the creation of Shockley partial dislocations and stacking fault regions as the resources of twinning. This was attributed to the stress concentration around the voids as numerically confirmed by Traiviratana See Fig. –d. As seSee Fig. , Zheng eIn summary, several MD simulations were conducted to explore the dominant mechanisms affecting the plastic deformation of perfect and defected copper-silver NCs under compressive loadings. It was deduced that at the room temperature and high strain rate conditions, twinning formation is the governing mechanism. It was found that twins are created from the conversion of intrinsic to extrinsic stacking faults. We further proceeded to examine the proposed mechanism in other copper-based composite systems embedded with Au and Ni nanoparticles. The main aim was to assess the effect of interfacial coherency on the nucleation of partial dislocations and the formation of stacking faults as the main resources of twinning-based plastic deformation in MMNCs. Moreover, the results revealed that the presence of voids within the bulk samples provides more active sites for nucleation of Shockley partial dislocations. This is followed by the conversion of stacking faults to twinning, which leads to a significant drop in the mechanical features of the NC samples. It is worth mentioning that to support the main findings of the present research, several experimental-based observations were also provided throughout the article. Since various factors affecting the plastic deformation of MMNCs under compressive loadings have been thoroughly studied in this work, the introduced mechanisms can be used to tailor the mechanical performance of these NCs as medical implants.