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Stress concentration around curvilinear holes in plates and shell, conformal mapping and other procedures for mathematical problems, and dynamic problems in bodies weakened by holes
Multidrug efflux pumps are dynamic molecular machines that drive antibiotic resistance by harnessing ion gradients to export chemically diverse substrates. Despite their clinical importance, the molecular principles underlying multidrug promiscuity and energy efficiency remain poorly understood. Using multiparametric deep mutational scanning across eight substrates and two energy conditions, we deconvolute the contributions of substrate recognition, energetic coupling, and protein stability, providing an integrated, high-resolution view of multidrug transport. We find that substrate specificity arises from a distributed network of residues extending beyond the binding site, with mutations that reshape binding, coupling, conformational flexibility, and membrane interactions. Further, we apply a pH-based selection scheme to measure the effect of mutation on pH-dependent transport efficiency. By integrating these data, we reveal a fundamental relationship between efficiency and promiscuity: Highly efficient variants exhibit broad substrate profiles, while inefficient variants are narrower. In conclusion, these findings establish a direct link between energy coupling and polyspecificity, uncovering the biochemical logic underlying multidrug transport.
Abstract We design the conforming virtual element method for the numerical approximation of the two‐dimensional elastodynamics problem. We prove stability and convergence of the semidiscrete approximation and derive optimal error estimates under h ‐ and p ‐refinement in both the energy and the L 2 norms. The performance of the proposed virtual element method is assessed on a set of different computational meshes, including nonconvex cells up to order four in the h ‐refinement setting. Exponential convergence is also experimentally observed under p ‐refinement. Finally, we present a dispersion‐dissipation analysis for both the semidiscrete and fully discrete schemes, showing that polygonal meshes behave as classical simplicial/quadrilateral grids in terms of dispersion‐dissipation properties.
We design the conforming virtual element method for the numerical approximation of the two dimensional elastodynamics problem. We prove stability and convergence of the semi-discrete approximation and derive optimal error estimates under $\textit{h}$-refinement in both the energy and the $L^2$ norms, and optimal error estimates under $\textit{p}$-refinement in the energy norm. The performance of the proposed virtual element method is assessed on a set of different computational meshes, including non-convex cells up to order four in the h-refinement setting. Exponential convergence is also experimentally observed under p-refinement. Finally, we present a dispersion-dissipation analysis for both the semi-discrete and fully-discrete schemes, showing that polygonal meshes behave as classical simplicial/quadrilateral grids in terms of dispersion-dissipation properties.
We consider a class of models in which the neutrinos acquire Majorana masses through mixing with singlet neutrinos that emerge as composite states of a strongly coupled hidden sector. In this framework, the light neutrinos are partially composite particles that obtain their masses through the inverse seesaw mechanism. We focus on the scenario in which the strong dynamics is approximately conformal in the ultraviolet, and the compositeness scale lies at or below the weak scale. The small parameters in the Lagrangian necessary to realize the observed neutrino masses can naturally arise as a consequence of the scaling dimensions of operators in the conformal field theory. We show that this class of models has interesting implications for a wide variety of experiments, including colliders and beam dumps, searches for lepton flavor violation and neutrinoless double beta decay, and cosmological observations. At colliders and beam dumps, this scenario can give rise to striking signals involving multiple displaced vertices. The exchange of hidden sector states can lead to observable rates for flavor violating processes such as μ → eγ and μ → e conversion. If the compositeness scale lies at or below a hundred MeV, the rate for neutrinoless double beta decay is suppressed by form factors and may be reduced by an order of magnitude or more. The late decays of relic singlet neutrinos can give rise to spectral distortions in the cosmic microwave background that are large enough to be observed in future experiments.
Several reduced order models have been successfully developed for nonlinear dynamical systems. To achieve a considerable speed-up, a hyper-reduction step is needed to reduce the computational complexity due to nonlinear terms. Many hyper-reduction techniques require the construction of nonlinear term basis, which introduces a computationally expensive offline phase. A novel way of constructing nonlinear term basis within the hyper-reduction process is introduced. In contrast to the traditional hyper-reduction techniques where the collection of nonlinear term snapshots is required, the SNS method avoids collecting the nonlinear term snapshots. Instead, it uses the solution snapshots that are used for building a solution basis, which enables avoiding an extra data compression of nonlinear term snapshots. As a result, the SNS method provides a more efficient offline strategy than the traditional model order reduction techniques, such as the DEIM, GNAT, and ST-GNAT methods. The SNS method is theoretically justified by the conforming subspace condition and the subspace inclusion relation. It is useful for model order reduction of large-scale nonlinear dynamical problems to reduce the offline cost. It is especially useful for ST-GNAT that has shown promising results, such as a good accuracy with a considerable online speed-up for hyperbolic problems in a recent paper by Choi and Carlberg [SIAM J. Sci. Comput., 41 (2019), pp. A26--A58], because ST-GNAT involves an expensive offline cost related to collecting nonlinear term snapshots. Error analysis for the SNS method is presented. Numerical results support that the accuracy of the solution from the SNS method is comparable to the traditional methods and a considerable speed-up (i.e., a factor of two to a hundred) is achieved in the offline phase.
Higher order divergence- and curl-conforming bases have been shown to provide significant benefits, in both convergence rate and accuracy, in the 2D hybrid finite element/boundary element formulation (P. Fink and D. Wilton, National Radio Science Meeting, Boulder, CO, Jan. 2000). A critical issue in achieving the potential for accuracy of the approach is the accurate evaluation of all matrix elements. These involve products of high order polynomials and, in some instances, singular Green's functions. In the 2D formulation, the use of a generalized Gaussian quadrature method was found to greatly facilitate the computation and to improve the accuracy of the boundary integral equation self-terms. In this paper, a 3D, hybrid electric field formulation employing higher order bases and higher order elements is presented. The improvements in convergence rate and accuracy, compared to those resulting from lower order modeling, are established. Techniques developed to facilitate the computation of the boundary integral self-terms are also shown to improve the accuracy of these terms. Finally, simple preconditioning techniques are used in conjunction with iterative solution procedures to solve the resulting linear system efficiently. In order to handle the boundary integral singularities in the 3D formulation, the parent element- either a triangle or rectangle-is subdivided into a set of sub-triangles with a common vertex at the singularity. The contribution to the integral from each of the sub-triangles is computed using the Duffy transformation to remove the singularity. This method is shown to greatly facilitate t'pe self-term computation when the bases are of higher order. In addition, the sub-triangles can be further divided to achieve near arbitrary accuracy in the self-term computation. An efficient method for subdividing the parent element is presented. The accuracy obtained using higher order bases is compared to that obtained using lower order bases when the number of unknowns is approximately equal. Also, convergence rates obtained using higher order bases are compared to those obtained with lower order bases for selected sample
Machine-readable chemical structure representations are foundational in all attempts to harness machine learning for the prediction of reactivities, selectivities, and chemical properties directly from molecular structure. The featurization of discrete chemical structures into a continuous vector space is a critical phase undertaken before model selection, and the development of new ways to quantitatively encode molecules is an active area of research. Here, we highlight the application and suitability of different representations, from expert-guided “engineered” descriptors to automatically “learned” features, in different prediction tasks relevant to organic and organometallic chemistry, where differing amounts of training data are available. These tasks include statistical models of stereo- and enantioselectivity, thermochemistry, and kinetics developed using experimental and quantum chemical data. The use of expert-guided molecular descriptors provides an opportunity to incorporate chemical knowledge, domain expertise, and physical constraints into statistical modeling. In applications to stereoselective organic and organometallic catalysis, where data sets may be relatively small and 3D-geometries and conformations play an important role, mechanistically informed features can be used successfully to obtain predictive statistical models that are also chemically interpretable. We provide an overview of several recent applications of this approach to obtain quantitative models for reactivity and selectivity, where topological descriptors, quantum mechanical calculations of electronic and steric properties, along with conformational ensembles, all feature as essential ingredients of the molecular representations used. Alternatively, more flexible, general-purpose molecular representations such as attributed molecular graphs can be used with machine learning approaches to learn the complex relationship between a structure and prediction target. This approach has the potential to out-perform more traditional representation methods such as “hand-crafted” molecular descriptors, particularly as data set sizes grow. One area where this is particularly relevant is in the use of large sets of quantum mechanical data to train quantitative structure–property relationships. A general approach toward curating useful data sets and training highly accurate graph neural network models is discussed in the context of organic bond dissociation enthalpies, where this strategy outperforms regression using precomputed descriptors. Finally, we describe how graph neural network predictions can be incorporated into mechanistically informed statistical models of chemical reactivity and selectivity. Once trained, this approach avoids the expensive computational overhead associated with quantum mechanical calculations, while maintaining chemical interpretability. We illustrate examples for which fast predictions of bond dissociation enthalpy and of the identities of radicals formed through cleavage of a molecule’s weakest bond are used in simple physical models of site-selectivity and reactivity.
Abstract Introduction Adverse reactions are relatively common during peanut oral immunotherapy. To reduce the risk to the patient, some researchers have proposed modifying the allergen to reduce IgE reactivity, creating a putative hypoallergen. Analysis of recently cloned human IgG from patients treated with peanut immunotherapy suggested that there are three common conformational epitopes for the major peanut allergen Ara h 2. We sought to test if structural information on these epitopes could indicate mutagenesis targets for designing a hypoallergen and evaluated the reduction in IgE binding via immunochemistry and a mouse model of passive cutaneous anaphylaxis (PCA). Methods X‐ray crystallography characterized the conformational epitopes in detail, followed by mutational analysis of key residues to modify monoclonal antibody (mAb) and serum IgE binding, assessed by ELISA and biolayer interferometry. A designed Ara h 2 hypoallergen was tested for reduced vascularization in mouse PCA experiments using pooled peanut allergic patient serum. Results A ternary crystal structure of Ara h 2 in complex with patient antibodies 13T1 and 13T5 was determined. Site‐specific mutants were designed that reduced 13T1, 13T5, and 22S1 mAbs binding by orders of magnitude. By combining designed mutations from the three major conformational bins, a hexamutant (Ara h 2 E46R, E89R, E97R, E114R, Q146A, R147E) was created that reduced IgE binding in serum from allergic patients. Further, in the PCA model where mice were primed with peanut allergic patient serum, reactivity upon allergen challenge was significantly decreased using the hexamutant. Conclusion These studies demonstrate that prior knowledge of common conformational epitopes can be used to engineer reduced IgE reactivity, an important first step in hypoallergen design.
A theoretical search for the most stable conformations (i.e., stacked or hydrogen bonded) of the base pairs A-U and G-C in water, CCl4, and CHCl3 solutions is presented. The calculations of free energies indicate a significant role of the solvent in determining the conformations of the base-pair complexes. The application of the continuum method yields preferred conformations in good agreement with experiment. Results of the calculations with this method emphasize the importance of both the electrostatic interactions between the two bases in a complex, and the dipolar interaction of the complex with the entire medium. In calculations with the solvation shell method, the last term, i.e., dipolar interaction of the complex with the entire medium, was added. With this modification the prediction of the solvation shell model agrees both with the continuum model and with experiment, i.e., in water the stacked conformation of the bases is preferred.
We compute observables of the critical 3d Ising model to high precision by applying the numerical conformal bootstrap to mixed correlators of the leading scalar operators σ and ϵ, and the stress tensor T μν . We obtain new precise determinations of scaling dimensions (∆ σ , ∆ ϵ ) = (0.518148806(24), 1.41262528(29)) as well as OPE coefficients involving σ, ϵ, and T μν . We also describe several improvements made along the way to algorithms and software tools for the numerical bootstrap.
We study propagation of a probe particle through a series of closely situated gravitational shocks. We argue that in any UV-complete theory of gravity the result does not depend on the shock ordering — in other words, coincident gravitational shocks commute. Shock commutativity leads to nontrivial constraints on low-energy effective theories. In particular, it excludes non-minimal gravitational couplings unless extra degrees of freedom are judiciously added. In flat space, these constraints are encoded in the vanishing of a certain “superconvergence sum rule.” In AdS, shock commutativity becomes the statement that average null energy (ANEC) operators commute in the dual CFT. We prove commutativity of ANEC operators in any unitary CFT and establish sufficient conditions for commutativity of more general light-ray operators. Superconvergence sum rules on CFT data can be obtained by inserting complete sets of states between light-ray operators.
NADPH-dependent assimilatory sulfite reductase (SiR) from Escherichia coli performs a six-electron reduction of sulfite to the bioavailable sulfide. SiR is composed of a flavoprotein (SiRFP) reductase subunit and a hemoprotein (SiRHP) oxidase subunit. There is no known high-resolution structure of SiR or SiRFP, thus we do not yet fully understand how the subunits interact to perform their chemistry. Here, we used small-angle neutron scattering to understand the impact of conformationally restricting the highly mobile SiRFP octamer into an electron accepting (closed) or electron donating (open) conformation, showing that SiR remains active, flexible, and asymmetric even with these conformational restrictions. From these scattering data, we then model the first solution structure of SiRFP. Further, computational modeling of the N-terminal 52 amino acids that are responsible for SiRFP oligomerization suggests an eight-helical bundle tethers together the SiRFP subunits to form the SiR core. Finally, mass spectrometry analysis of the closed SiRFP variant show that SiRFP is capable of inter-molecular domain crossover, in which the electron donating domain from one polypeptide is able to interact directly with the electron accepting domain of another polypeptide. This structural characterization suggests that SiR performs its high-volume electron transfer through both inter- and intramolecular pathways between SiRFP domains and, thus, cis or trans transfer from reductase to oxidase subunits. Such highly redundant potential for electron transfer makes this system a potential target for designing synthetic enzymes.
How to effectively remove toxic dyes from the industrial wastewater using a green low-cost lignocellulose-based adsorbent, such as lignin, has become a topic of great interest but remains quite challenging. In this study, cosolvent-enhanced lignocellulosic fractionation (CELF) pretreatment and Mannich reaction were combined to generate an aminated CELF lignin which is subsequently applied for removal of methylene blue and direct blue (DB) 1 dye from aqueous solution. 31P NMR was used to track the degree of amination, and an orthogonal design was applied to determine the relationship between the extent of amination and reaction parameters. The physicochemical, morphological, and thermal properties of the aminated CELF lignin were characterized to confirm the successful grafting of diethylenetriamine onto the lignin. The aminated CELF lignin proved to be an effective azo dye-adsorbent, demonstrating considerably enhanced dye decolorization, especially toward DB 1 dye (>90%). It had a maximum adsorption capacity of DB 1 dye of 502.7 mg/g, and the kinetic study suggested the adsorption process conformed to a pseudo-second-order kinetic model. The isotherm results also showed that the modified lignin-based adsorbent exhibited monolayer adsorption. The adsorbent properties were mainly attributed to the incorporated amine functionalities as well as the increased specific surface area of the aminated CELF lignin.
Polystyrene (PS) is a widely used thermoplastic polymer, but its very low recycling rate has motivated consideration of chemical conversion strategies to convert waste PS into value-added products. Oxidation methods have been widely studied, but they typically generate benzoic acid, a product with a relatively low market demand. Phenol is a higher volume chemical that would be an appealing target, but no methods currently exist for the conversion of PS into phenol. The repeat unit in PS closely resembles cumene, the primary feedstock used to produce phenol through the Hock process. Here, we investigate prospects for adapting the Hock process to PS, generating hydroperoxides through the autoxidation of benzylic C–H bonds followed by the acid-promoted rearrangement of the hydroperoxides to afford phenol and a partially oxygenated polymer. Experimental and computational studies of dimeric and trimeric PS model compounds show that neighboring phenyl rings impose conformational constraints that raise the barrier to hydrogen-atom transfer from the tertiary benzylic C–H bond. These effects are also evident with PS and contribute to lower yields of phenol when PS is subjected to Hock process conditions. Furthermore, these results provide valuable insights that have important implications for other efforts that seek to adapt small-molecule reactivity to polymeric feedstocks.
Abstract RexA and RexB function as an exclusion system that prevents bacteriophage T4rII mutants from growing on Escherichia coli λ phage lysogens. Recent data established that RexA is a non-specific DNA binding protein that can act independently of RexB to bias the λ bistable switch toward the lytic state, preventing conversion back to lysogeny. The molecular interactions underlying these activities are unknown, owing in part to a dearth of structural information. Here, we present the 2.05-Å crystal structure of the λ RexA dimer, which reveals a two-domain architecture with unexpected structural homology to the recombination-associated protein RdgC. Modelling suggests that our structure adopts a closed conformation and would require significant domain rearrangements to facilitate DNA binding. Mutagenesis coupled with electromobility shift assays, limited proteolysis, and double electron–electron spin resonance spectroscopy support a DNA-dependent conformational change. In vivo phenotypes of RexA mutants suggest that DNA binding is not a strict requirement for phage exclusion but may directly contribute to modulation of the bistable switch. We further demonstrate that RexA homologs from other temperate phages also dimerize and bind DNA in vitro. Collectively, these findings advance our mechanistic understanding of Rex functions and provide new evolutionary insights into different aspects of phage biology.
In this work, we propose a new formula that extracts the quantum Hall conductance from a single (2+1) D gapped wave function. The formula applies to general many-body systems that conserve particle number, and is based on the concept of modular flow, i.e., unitary dynamics generated from the entanglement structure of the wave function. The formula is shown to satisfy all formal properties of the Hall conductance: it is odd under time reversal and reflection, even under charge conjugation, universal and topologically rigid in the thermodynamic limit. Further evidence for relating the formula to the Hall conductance is obtained from conformal field theory arguments. Finally, we numerically check the formula by applying it to a noninteracting Chern band where excellent agreement is obtained.
Archaea share genomic similarities with Eukarya and cellular architectural similarities with Bacteria, though archaeal and bacterial surface layers (S-layers) differ. Using cellular cryo–electron tomography, we visualized the S-layer lattice surroundingMethanospirillum hungatei, a methanogenic archaeon. Though more compact than known structures,M. hungatei’s S-layer is a flexible hexagonal lattice of dome-shaped tiles, uniformly spaced from both the overlying cell sheath and the underlying cell membrane. Subtomogram averaging resolved the S-layer hexamer tile at 6.4-angstrom resolution. By fitting an AlphaFold model into hexamer tiles in flat and curved conformations, we uncover intra- and intertile interactions that contribute to the S-layer’s cylindrical and flexible architecture, along with a spacer extension for cell membrane attachment.M. hungateicell’s end plug structure, likely composed of S-layer isoforms, further highlights the uniqueness of this archaeal cell. These structural features offer advantages for methane release and reflect divergent evolutionary adaptations to environmental pressures during early microbial emergence.