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Stellarator optimization for good magnetic surfaces at the same time as quasisymmetry
A method is demonstrated to optimize a stellarator's geometry to eliminate magnetic islands and achieve other desired physics properties at the same time. For many physics quantities that have been used in stellarator optimization, including quasisymmetry, neoclassical transport, and magnetohydrodynamic stability, it is convenient to use a magnetic equilibrium representation that assures the existence of magnetic surfaces. However, this representation hides the possible presence of magnetic islands, which are typically undesirable. To include both surface-based objectives and island widths in a single optimization, two fixed-boundary equilibrium calculations are run at each iteration of the optimization: one that enforces the existence of magnetic surfaces (the Variational Moments Equilibrium Code) [S. P. Hirshman and J. C. Whitson, Phys. Fluids 26, 3553 (1983)] and one that does not (the Stepped Pressure Equilibrium Code) [Hudson et al., Phys. Plasmas 19, 112502 (2012)]. By penalizing the island residues in the objective function, the two magnetic field representations are brought into agreement during the optimization. Here, an example is presented in which, particularly on the surface where quasisymmetry was targeted, quasisymmetry is achieved more accurately than in previously published examples.
Hybrid Improved Empirical Mode Decomposition and Artificial Neural Network Model for the Prediction of Critical Heat Flux (CHF)
Three Hybrid artificial neural network (ANN) models namely radial basis function (RBF), generalized regression neural networks (GRNN), and multi-layer perceptron (MLP) combined with empirical mode decomposition (EMD) are developed for CHF predictive modelling using CHF experimental databases.First, the original experimental inputs data series are decomposed into several intrinsic mode functions (IMFs) and one residual by EMD, whose components are divided into high, medium and low components. The performance parameters of the hybrid models indicates that the root mean square error (RMSE) are 0.8831, 0.6522, and 0.4149; the mean absolute error (MAE) are 0.6697, 0.4636, and 0.1935. The values of the R-square of the developed prediction approach utilizing EMD-RBF, EMD-GRNN, and EMD-MLP models are 0.8553, 0.9302, and 0.9818, and the index of agreement are 0.9464, 0.9700, and 0.9894., The value of the R-square and the index of agreement of the proposed models are much higher than those of the simple models .The Pearson's test results show that the association strength between the measured and the predicted values of the proposed model EMD-MLP is the strongest. These results show the following: (a) compared with other related, recent studies, the prediction accuracy of the hybrid model EMD- MLP proposed in this research is the best hybrid model; (b) the proposed hybrid model (EMD-MLP) attains superior performance compared with simple models.
Sensor Domain of Histidine Kinase VxrA of Vibrio cholerae : Hairpin-Swapped Dimer and Its Conformational Change
VxrA and VxrB are cognate histidine kinase (HK)-response regulator (RR) pairs of a two-component signaling system (TCS) found in Vibrio cholerae, a bacterial pathogen that causes cholera. The VxrAB TCS positively regulates virulence, the type VI secretion system, biofilm formation, and cell wall homeostasis in V. cholerae, providing protection from environmental stresses and contributing to the transmission and virulence of the pathogen. The VxrA HK has a unique periplasmic sensor domain (SD) and, remarkably, lacks a cytoplasmic linker domain between the second transmembrane helix and the dimerization and histidine phosphotransfer (DHp) domain, indicating that this system may utilize a potentially unique signal sensing and transmission TCS mechanism. Here, we have determined several crystal structures of VxrA-SD and its mutants. These structures reveal a novel structural fold forming an unusual β hairpin-swapped dimer. A conformational change caused by relative rotation of the two monomers in a VxrA-SD dimer could potentially change the association of transmembrane helices and, subsequently, the pairing of cytoplasmic DHp domains. Based on the structural observation, we propose a putative scissor-like closing regulation mechanism for the VxrA HK. IMPORTANCE V. cholerae has a dynamic life cycle, which requires rapid adaptation to changing external conditions. Two-component signal transduction (TCS) systems allow V. cholerae to sense and respond to these environmental changes. The VxrAB TCS positively regulates a number of important V. cholerae phenotypes, including virulence, the type six secretion system, biofilm formation, and cell wall homeostasis. Here, we provide the crystal structures of the VxrA sensor histidine kinase sensing domain and propose a mechanism for signal transduction. The cognate signal for VxrAB remains unknown; however, in this work we couple our structural analysis with functional assessments of key residues to further our understanding of this important TCS.
Structural Diversity in Eukaryotic Photosynthetic Light Harvesting
Photosynthesis has been using energy from sunlight to assimilate atmospheric CO 2 for at least 3.5 billion years. Through evolution and natural selection, photosynthetic organisms have flourished in almost all aquatic and terrestrial environments. This is partly due to the diversity of light-harvesting complex (LHC) proteins, which facilitate photosystem assembly, efficient excitation energy transfer, and photoprotection. Structural advances have provided angstrom-level structures of many of these proteins and have expanded our understanding of the pigments, lipids, and residues that drive LHC function. In this review, we compare and contrast recently observed cryo-electron microscopy structures across photosynthetic eukaryotes to identify structural motifs that underlie various light-harvesting strategies. We discuss subtle monomer changes that result in macroscale reorganization of LHC oligomers. Additionally, we find recurring patterns across diverse LHCs that may serve as evolutionary stepping stones for functional diversification. Advancing our understanding of LHC protein–environment interactions will improve our capacity to engineer more productive crops.
The carboxylation status of osteocalcin has important consequences for its structure and dynamics
The carboxylation status of Osteocalcin (Ocn) not only influences formation and structure in bones but also has important endocrine functions affecting energy metabolism and expenditure. In this study, the role of γ-carboxylation of the glutamate residues in the structure-dynamics-function relationship in Ocn is investigated. Three forms of Ocn, differentially carboxylated at the Glu-17, 21 and 24 residues, along with a mutated form of Ocn carrying Glu/Ala mutations, are modeled and simulated using molecular dynamics (MD) simulation in the presence of calcium ions. Characterization of the global conformational dynamics of Ocn, described in terms of the orientational variations within its 3-helical domain, highlights large structural variations in the non-carboxylated osteocalcin (nOcn). The bi-carboxylated Ocn (bOcn) and tri-carboxylated (tOcn) species, in contrast, display relatively rigid tertiary structures, with the dynamics of most regions strongly correlated. Radial distribution functions calculated for both bOcn and tOcn show long-range ordering of the calcium ion distribution around the carboxylated glutamate (γGlu) residues, likely playing an important role in promoting stability of these Ocns. Additionally, the same calcium ions are observed to coordinate with neighboring γGlu, better shielding their negative charges and in turn stabilizing these systems more than do the singly coordinating calcium ions observed in the case of nOcn. bOcn is also found to exhibit a more helical C-terminal structure, that has been shown to activate its cellular receptor GPRC6A, highlighting the allosteric role of Ocn carboxylation in modulating the stability and binding potential of the active C-terminal. Furthermore, the carboxylation status of Ocn as well and its calcium coordination appear to have a direct influence on Ocn structure and dynamics, possibly leading to the known differences in Ocn biological function.
Analytic Theory for the Dynamics of Wide Quantum Neural Networks
Here, parametrized quantum circuits can be used as quantum neural networks and have the potential to outperform their classical counterparts when trained for addressing learning problems. To date, much of the results on their performance on practical problems are heuristic in nature. In particular, the convergence rate for the training of quantum neural networks is not fully understood. Here, we analyze the dynamics of gradient descent for the training error of a class of variational quantum machine learning models. We define wide quantum neural networks as parametrized quantum circuits in the limit of a large number of qubits and variational parameters. Then, we find a simple analytic formula that captures the average behavior of their loss function and discuss the consequences of our findings. For example, for random quantum circuits, we predict and characterize an exponential decay of the residual training error as a function of the parameters of the system. Finally, we validate our analytic results with numerical experiments.
New Insights into Nonthermal Plasma-Assisted Poly(vinyl alcohol) Depolymerization Catalyzed by TiO 2
Here, in this study, we investigated the solid residual poly(vinyl alcohol) (PVA) and TiO 2 after nonthermal air, CO 2 , and N 2 plasma depolymerization in the absence and presence of TiO 2 . Scanning electron microscopy studies showed the absence of highly viscous tar and carbonaceous residues on the surfaces of PVA and TiO 2 . In the absence of TiO 2 , PVA particles exhibited micron-sized holes on their surfaces, whereas in the presence of TiO 2 , the surface roughness of PVA particles was observed at the submicron scale. These observations suggest that TiO 2 facilitates the even distribution of nonthermal plasma at a submicron scale, leading to a more uniform depolymerization of PVA surfaces. Raman, Fourier transform infrared spectroscopy, and X-ray absorption spectroscopy showed that (i) the surface of residual PVA contains mainly ketone functional groups and less C-H bonds than the pristine PVA and (ii) further confirmed the absence of highly viscous tar and carbonaceous residues on both used TiO 2 and residual PVA. The nuclear magnetic resonance and mass spectroscopy suggested that the PVA is growing back to poly polyvinyl acetate by the esterification reaction, and the ethers are produced by the acetal reaction between PVA and aldehyde. The transmission electron microscopy and X-ray diffraction analysis indicated no major crystal structural change of the TiO 2 catalyst after the plasma reactions. This study demonstrates that nonthermal plasma-assisted depolymerization is a viable alternative to thermal depolymerization, offering the unique advantage of converting polymer wastes into gaseous small organic molecules without generating recalcitrant viscous tar and carbonaceous residues on the surfaces of the polymer and TiO 2 catalysts.
Conserved conformational dynamics determine enzyme activity
Homologous enzymes often exhibit different catalytic rates despite a fully conserved active site. The canonical view is that an enzyme sequence defines its structure and function and, more recently, that intrinsic protein dynamics at different time scales enable and/or promote catalytic activity. Here, we show that, using the protein tyrosine phosphatase PTP1B, residues surrounding the PTP1B active site promote dynamically coordinated chemistry necessary for PTP1B function. However, residues distant to the active site also undergo distinct intermediate time scale dynamics and these dynamics are correlated with its catalytic activity and thus allow for different catalytic rates in this enzyme family. We identify these previously undetected motions using coevolutionary coupling analysis and nuclear magnetic resonance spectroscopy. Our findings strongly indicate that conserved dynamics drives the enzymatic activity of the PTP family. Characterization of these conserved dynamics allows for the identification of novel regulatory elements (therapeutic binding pockets) that can be leveraged for the control of enzymes.
An efficient method to propagate model uncertainty when inverting seismic data for time domain seismic moment tensors
SUMMARY We present a computationally efficient method to approximately propagate uncertainty when linearly inverting seismic data for point source, time variable moment tensor components. The method is based on the assumption that the data residual, given by the difference between the observed seismic data and the data predicated by a linear inversion, contains the effects of both data and model uncertainty. Our method uses a distribution of data residuals, added directly to the data, in a pseudo-Monte Carlo scheme. Using the assumption that the data residual is a stochastic process, we use the well-known Karhunen–Loève (KL) theorem to construct a distribution of data residuals, where the required basis functions are constructed using Fourier series. The Fourier series are scaled by a product of a random variable and the real-valued spectral amplitudes of the original data residual’s spectrum. Thus, the Fourier series and spectral amplitudes are eigenfunction-eigenvalue pairs used in the KL-based construction of data residual distribution. Using tests with synthetic data, we show that our method compares closely with a Finite Difference Monte Carlo (FDMC) method that we presented previously. More importantly, the method presented here is computationally several orders of magnitude faster than our previous FDMC method, and requires no a priori assumptions of model and/or data uncertainty.
Variational actor-critic algorithms,
We introduce a class of variational actor-critic algorithms based on a variational formulation over both the value function and the policy. The objective function of the variational formulation consists of two parts: one for maximizing the value function and the other for minimizing the Bellman residual. Besides the vanilla gradient descent with both the value function and the policy updates, we propose two variants, the clipping method and the flipping method, in order to speed up the convergence. We also prove that, when the prefactor of the Bellman residual is sufficiently large, the fixed point of the algorithm is close to the optimal policy.
Selective carboxylation of alkenes with CO 2 to form unsaturated carboxylic acid on Sc-exchanged MFI zeolite
Utilization of CO 2 in chemical synthesis as C1 carbon feedstock to introduce a carboxylic group into alkene is valuable for producing unsaturated carboxylic acids. Selective carboxylation of alkenes at targeted positions can be used to regulate the production of such specific unsaturated carboxylic acids or functionalize hydrocarbon plastics that possess residual C=C double bonds. In this study, we investigated the carboxylation of 1-butene and 2-butene (as representative alkene) with CO 2 on Sc-exchanged MFI zeolites using density functional theory calculations. Here, we find that similar to ethylene, the carboxylation of butene is also rate-limited by the β–H transfer. We examined carboxylation at the C1 and C2 positions of 1-butene and cis and trans isomers for 2-butene. Based on activation barriers of the β–H transfer, our results demonstrate that Sc-MFI zeolite preferably carboxylates at the terminal position of butene. In the case of 2-butene, carboxylation of the trans isomer is more favorable than the cis isomer. Furthermore, We show that the energy of degenerate orbitals of C, O and H atoms (involved in the β–H transfer) in the metallalactone ring regulates the activation energy of the β–H transfer.
Driving mode analysis—How uncertain functional inputs propagate to an output
Abstract Driving mode analysis elucidates how correlated features of uncertain functional inputs jointly propagate to produce uncertainty in the output of a computation. Uncertain input functions are decomposed into three terms: the mean functions, a zero‐mean driving mode, and zero‐mean residual. The random driving mode varies along a single direction, having fixed functional shape and random scale. It is uncorrelated with the residual, and under linear error propagation, it produces an output variance equal to that of the full input uncertainty. Finally, the driving mode best represents how input uncertainties propagate to the output because it minimizes expected squared Mahalanobis distance amongst competitors. These characteristics recommend interpretation of the driving mode as the single‐degree‐of‐freedom component of input uncertainty that drives output uncertainty. We derive the functional driving mode, show its superiority to other seemingly sensible definitions, and demonstrate the utility of driving mode analysis in an application. The application is the simulation of neutron transport in criticality experiments. The uncertain input functions are nuclear data that describe how Pu reacts to bombardment by neutrons. Visualization of the driving mode helps scientists understand what aspects of correlated functional uncertainty have effects that either reinforce or cancel one another in propagating to the output of the simulation.
Adaptive Data-Driven Deep-Learning Surrogate Model for Frontal Polymerization in Dicyclopentadiene
Frontal polymerization (FP) is a self-sustaining curing process that enables rapid and energy-efficient manufacturing of thermoset polymers and composites. Computational methods conventionally used to simulate the FP process are time-consuming, and repeating simulations are required for sensitivity analysis, uncertainty quantification, or optimization of the manufacturing process. Here, in this work, we develop an adaptive surrogate deep-learning model for FP of dicyclopentadiene (DCPD), which predicts the evolution of temperature and degree of cure orders of magnitude faster than the finite-element method (FEM). The adaptive algorithm provides a strategy to select training samples efficiently and save computational costs by reducing the redundancy of FEM-based training samples. The adaptive algorithm calculates the residual error of the FP governing equations using automatic differentiation of the deep neural network. A probability density function expressed in terms of the residual error is used to select training samples from the Sobol sequence space. The temperature and degree of cure evolution of each training sample are obtained by a 2D FEM simulation. The adaptive method is more efficient and has a better prediction accuracy than the random sampling method. With the well-trained surrogate neural network, the FP characteristics (front speed, shape, and temperature) can be extracted quickly from the predicted temperature and degree-of-cure fields.
SPARC: Structural properties associated with residue constraints
SPARC facilitates the generation of plausible hypotheses regarding underlying biochemical mechanisms by structurally characterizing protein sequence constraints. Such constraints appear as residues co-conserved in functionally related subgroups, as subtle pairwise correlations (i.e., direct couplings), and as correlations among these sequence features or with structural features. SPARC performs three types of analyses. First, based on pairwise sequence correlations, it estimates the biological relevance of alternative conformations and of homomeric contacts, as illustrated here for death domains. Second, it estimates the statistical significance of the correspondence between directly coupled residue pairs and interactions at heterodimeric interfaces. Third, given molecular dynamics simulated structures, it characterizes interactions among constrained residues or between such residues and ligands that: (a) are stably maintained during the simulation; (b) undergo correlated formation and/or disruption of interactions with other constrained residues; or (c) switch between alternative interactions. We illustrate this for two homohexameric complexes: the bacterial enhancer binding protein (bEBP) NtrC1, which activates transcription by remodeling RNA polymerase (RNAP) containing σ 54 , and for DnaB helicase, which opens DNA at the bacterial replication fork. Based on the NtrC1 analysis, we hypothesize possible mechanisms for inhibiting ATP hydrolysis until ADP is released from an adjacent subunit and for coupling ATP hydrolysis to restructuring of σ 54 binding loops. Based on the DnaB analysis, we hypothesize that DnaB ‘grabs’ ssDNA by flipping every fourth base and inserting it into cavities between subunits and that flipping of a DnaB-specific glutamine residue triggers ATP hydrolysis.
Spectroscopy and crystallography define carotenoid oxygenases as a new subclass of mononuclear non-heme Fe II enzymes
Carotenoid cleavage dioxygenases (CCDs) are non-heme Fe II enzymes that catalyze the oxidative cleavage of alkene bonds in carotenoids, stilbenoids, and related compounds. How these enzymes control the reaction of dioxygen (O 2 ) with their alkene substrates is unclear. Here, we apply spectroscopy in conjunction with X-ray crystallography to define the iron coordination geometry of a model CCD, CAO1 (Neurospora crassa carotenoid oxygenase 1), in its resting state and following substrate binding and coordination sphere substitutions. Resting CAO1 exhibits a five-coordinate (5C), square pyramidal Fe II center that undergoes steric distortion toward a trigonal bipyramidal geometry in the presence of piceatannol. Titrations with the O 2 -analog, nitric oxide, show a >100-fold increase in iron–nitric oxide affinity upon substrate binding, defining a crucial role for the substrate in activating the Fe II site for O 2 reactivity. The importance of the 5C Fe II structure for reactivity was probed through mutagenesis of the second-sphere Thr151 residue of CAO1, which occludes ligand binding at the sixth coordination position. A T151G substitution resulted in the conversion of the iron center to a six-coordinate state and a 135-fold reduction in apparent catalytic efficiency toward piceatannol compared with the wildtype enzyme. Substrate complexation resulted in partial six-coordinate to 5C conversion, indicating solvent dissociation from the iron center. Additional substitutions at this site demonstrated a general functional importance of the occluding residue within the CCD superfamily. Taken together, these data suggest an ordered mechanism of CCD catalysis occurring via substrate-promoted solvent replacement by O 2 . CCDs thus represent a new class of mononuclear non-heme Fe II enzymes.
Testing the Cosmological Principle: Astrometric Limits on Systemic Motion of Quasars at Different Cosmological Epochs
A sample of 60,410 bona fide optical quasars with astrometric proper motions in Gaia Early Data Release 3 and spectroscopic redshifts above 0.5 in an oval 8400 square degree area of the sky is constructed. Using orthogonal Zernike functions of polar coordinates, the proper motion fields are fitted in a weighted least-squares adjustment of the entire sample and of six equal bins of sorted redshifts. The overall fit with 37 Zernike functions reveals a statistically significant pattern, which is likely to be of instrumental origin. The main feature of this pattern is a chain of peaks and dips mostly in the R.A. component with an amplitude of 25 μ as yr -1 . This field is subtracted from each of the six analogous fits for quasars grouped by redshifts covering the range 0.5 through 7.03, with median values of 0.72, 1.00, 1.25, 1.52, 1.83, 2.34. The resulting residual patterns are noisier, with formal uncertainties up to 8 μ as yr -1 in the central part of the area. We detect a single high-confidence Zernike term for the R.A. proper motion components of quasars with redshifts around 1.52 representing a general gradient of 30 μ as yr -1 over 150° on the sky. We do not find any small- or medium-scale systemic variations of the residual proper motion field as functions of redshift above the 2.5 σ significance level.
The C‐Terminal Domain of α‐Synuclein Confers Steric Stabilization on Synaptic Vesicle‐Like Surfaces
Abstract While α‐synuclein, an intrinsically disordered protein linked to Parkinson's disease, has been shown to associate with membrane organelles, its overall cellular function remains nebulous. α‐Synuclein binds to membranes through its amino‐terminal domain (first ≈100 residues), but there is no consensus on the biophysical function of the carboxyl‐terminal domain (last ≈40 residues) due, in part, to its lack of strong interaction partners and persisting intrinsic disorder even when membrane bound. Here, by directly applying force on α‐synuclein bound to spherical nanoparticle‐supported lipid bilayers (SSLBs) and tracking higher‐order structural changes through small‐angle X‐ray scattering, strong evidence is presented that α‐synuclein sterically stabilizes membrane surfaces through its carboxyl‐terminal domain. Full‐length α‐synuclein dramatically increases the critical osmotic pressure at which SSLBs cluster ( P C ≈ 1.3 × 10 5 Pa) compared to α‐synuclein without the carboxyl‐terminal domain ( P C ≈ 1.9 × 10 4 Pa) at physiological salt and temperature conditions. This clustering of α‐synuclein‐bound SSLBs is shown to be reversible and sensitive to monovalent/divalent salt, both features of grafted polyelectrolyte‐mediated steric stabilization. In elucidating the biophysical function of α‐synuclein in the framework of polymer science, it is demonstrated that the carboxyl‐terminal domain can potentially utilize its persisting intrinsic disorder to functionalize membrane surfaces.