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High-Order Curvilinear Finite Element Methods for Lagrangian Hydrodynamics [High Order Curvilinear Finite Elements for Lagrangian Hydrodynamics]

The numerical approximation of the Euler equations of gas dynamics in a movingLagrangian frame is at the heart of many multiphysics simulation algorithms. Here, we present a general framework for high-order Lagrangian discretization of these compressible shock hydrodynamics equations using curvilinear finite elements. This method is an extension of the approach outlined in [Dobrev et al., Internat. J. Numer. Methods Fluids, 65 (2010), pp. 1295--1310] and can be formulated for any finite dimensional approximation of the kinematic and thermodynamic fields, including generic finite elements on two- and three-dimensional meshes with triangular, quadrilateral, tetrahedral, or hexahedral zones. We discretize the kinematic variables of position and velocity using a continuous high-order basis function expansion of arbitrary polynomial degree which is obtained via a corresponding high-order parametric mapping from a standard reference element. This enables the use of curvilinear zone geometry, higher-order approximations for fields within a zone, and a pointwise definition of mass conservation which we refer to as strong mass conservation. Moreover, we discretize the internal energy using a piecewise discontinuous high-order basis function expansion which is also of arbitrary polynomial degree. This facilitates multimaterial hydrodynamics by treating material properties, such as equations of state and constitutive models, as piecewise discontinuous functions which vary within a zone. To satisfy the Rankine--Hugoniot jump conditions at a shock boundary and generate the appropriate entropy, we introduce a general tensor artificial viscosity which takes advantage of the high-order kinematic and thermodynamic information available in each zone. Finally, we apply a generic high-order time discretization process to the semidiscrete equations to develop the fully discrete numerical algorithm. Our method can be viewed as the high-order generalization of the so-called staggered-grid hydrodynamics (SGH) approach and we show that under specific low-order assumptions, we exactly recover the classical SGH method. We also present numerical results from an extensive series of verification tests that demonstrate several important practical advantages of using high-order finite elements in this context.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

When Do Band Gap Calculations Agree with Experiments in Monolayer-Protected Cu 14 and Au 20 Atomically Precise Nanoclusters? A (TD)-DFT Comparison of HOMO–LUMO, Fundamental, Optical, and Electrochemical Energy Gaps

In view of the tremendous progress in atomically precise metal nanoclusters where electrochemical and optical energetics are routinely supported by computations to establish structure−function correlations, we explore the relationship between different protocols for measuring and computing band gaps of two distinct organic ligand-protected nanoclusters: [Cu 14 H 10 (MBN) 3 (PPh 3 ) 8 ] + and Au 20 (TBBT) 16 . Through UV/visible spectroscopy and differential pulse voltammetry, we measure optical and electrochemical band gaps in those systems. We then compare these experimentally determined gaps to HOMO−LUMO gaps, fundamental gaps, vertical excitation energies, and E o ox − E o red potentials computed using different density functional theory (DFT) or time-dependent DFT (TDDFT) methods. Specifically, in both copper and gold nanoclusters, we test the effect of truncating inert ligands from the model and compare density functionals with varying degrees of Hartree−Fock (HF) exchange from 0 to 50%, range-separated hybrids with a varying long-range tuning parameter, different correlation functionals, basis sets, and (equilibrium and nonequilibrium) continuum solvation models. Despite having different frontier orbital characters (the copper nanocluster has a metal-to-ligand charge transfer character while the gold nanocluster has metal-centered frontier orbitals), both nanoclusters display a similar sensitivity of the HOMO−LUMO gap to the HF exchange that is partially mitigated when computing the fundamental, optical, and electrochemical gaps. Other factors, such as the nature of the correlation functional, basis set, and geometry relaxation, have a considerably smaller effect on computed band gaps in these systems. Overall, this work provides guidelines for factors of varied importance for correlating computed and experimental band gap values.

Chemical calculations↗

Molecular basis of functional exchangeability between ezrin and other actin-membrane associated proteins during cytokinesis

Highlights: • Anillin or supervillin depletion affects localization of different domains of ezrin. • Actin binding domains are compatible between ezrin and anillin for furrow ingression. • All ezrin and anillin domains are incompatible for polar cortical control. The mechanism that mediates the interaction between the contractile ring and the plasma membrane during cytokinesis remains elusive. We previously found that ERM (Ezrin/Radixin/Moesin) proteins, which usually mediate cellular pole contraction, become over-accumulated at the cell equator and support furrow ingression upon the loss of other actin-membrane associated proteins, anillin and supervillin. In this study, we addressed the molecular basis of the exchangeability between ezrin and other actin-membrane associated proteins in mediating cortical contraction during cytokinesis. We found that depletion of anillin and supervillin caused over-accumulation of the membrane-associated FERM domain and actin-binding C-terminal domain (C-term) of ezrin at the cleavage furrow, respectively. This finding suggests that ezrin differentially shares its binding sites with these proteins on the actin cytoskeleton or inner membrane surface. Using chimeric mutants, we found that ezrin C-term, but not the FERM domain, can substitute for the corresponding anillin domains in cytokinesis and cell proliferation. On the other hand, either the membrane-associated or the actin/myosin-binding domains of anillin could not substitute for the corresponding ezrin domains in controlling cortical blebbing at the cell poles. Our results highlight specific designs of actin- or membrane-associated moieties of different actin-membrane associated proteins with limited exchangeability, which enables them to support diverse cortical activities on the shared actin-membrane interface during cytokinesis.

60 APPLIED LIFE SCIENCES↗

What do physics-informed DeepONets learn? Understanding and improving training for scientific computing applications

Physics-informed deep operator networks (DeepONets) have emerged as a promising approach toward numerically approximating the solution of partial differential equations (PDEs). In this work, we aim to develop further understanding of what is being learned by physics-informed DeepONets by assessing the universality of the extracted basis functions and demonstrating their potential toward model reduction with spectral methods. Results provide clarity about measuring the performance of a physics-informed DeepONet through the decays of singular values and expansion coefficients. In addition, we propose a transfer learning approach for improving training for physics-informed DeepONets between parameters of the same PDE as well as across different, but related, PDEs where these models struggle to train well. This approach results in significant error reduction and learned basis functions that are more effective in representing the solution of a PDE.

Deep operator networks↗

Towards oscillation-free implementation of the immersed boundary method with spectral-like methods

Highlights: {yields} A radial basis function based smoothing technique is introduced. {yields} It is more general and easier to implement compared to other techniques. {yields} With this technique, a combined immersed boundary and spectral method is developed. {yields} It is shown that the proposed method works better in terms of reducing the non-physical Gibbs oscillation. - Abstract: It is known that, when the immersed boundary method (IBM) is implemented within spectral-like methods, the Gibbs oscillation seriously deteriorates the calculation of derivatives near the body surface. In this paper, a radial basis function (RBF) based smoothing technique is proposed with the intention of eliminating or efficiently reducing the Gibbs oscillation without affecting the flow field outside the body. Based on this technique, a combined IBM/spectral scheme is developed to solve the incompressible Navier-Stokes equations. Numerical simulations of flow through a periodic lattice of cylinders of various cross sections are performed. The results demonstrate that the proposed methodology is able to give accurate and nearly oscillation-free numerical solutions of incompressible viscous flows.

97 MATHEMATICS AND COMPUTING↗

Effective dynamics of two-dimensional Bloch electrons in external fields derived from symmetry

We develop a comprehensive theory for the effective dynamics of Bloch electrons based on symmetry. We begin with a scheme to systematically derive the irreducible representations (IRs) characterizing the Bloch eigenstates in a crystal. Starting from a tight-binding (TB) approach, we decompose the TB basis functions into localized symmetry-adapted atomic orbitals and crystal-periodic symmetry-adapted plane waves. Each of these two subproblems is independent of the details of a particular crystal structure and it is largely independent of the relevant aspects of the other subproblem, hence permitting for each subproblem an independent universal solution. Taking monolayer MoS 2 and few-layer graphene as examples, we tabulate the symmetrized p and d orbitals as well as the symmetrized plane-wave spinors relevant for these crystal structures. The symmetry-adapted basis functions block-diagonalize the TB Hamiltonian such that each block yields eigenstates transforming according to one of the IRs of the group of the wave vector G k . For many crystal structures, it is possible to define multiple distinct coordinate systems such that for wave vectors k at the border of the Brillouin zone the IRs characterizing the Bloch states depend on the coordinate system, i.e., these IRs of G k are not uniquely determined by the symmetry of a crystal structure. The different coordinate systems are related by a coordinate shift that results in a rearrangement of the IRs of G k characterizing the Bloch states. We illustrate this rearrangement with three coordinate systems for MoS 2 and trilayer graphene. The freedom to choose different distinct coordinate systems can simplify the symmetry analysis of the Bloch states. Given the IRs of the Bloch states in one coordinate system, a rearrangement lemma yields immediately the IRs of the Bloch states in the other coordinate systems. The rearrangement of the IRs in different coordinate systems does not affect observable physics such as selection rules or the effective Hamiltonians for the dynamics of Bloch states in external fields. Using monolayer MoS 2 as an example, we combine the symmetry analysis of its bulk Bloch states with the theory of invariants to construct a generic multiband Hamiltonian for electrons near the K point of the Brillouin zone. Here, the Hamiltonian includes the effect of spin-orbit coupling, strain, and external electric and magnetic fields. Invariance of the Hamiltonian under time reversal yields additional constraints for the allowed terms in the Hamiltonian and it determines the phase (real or imaginary) of the prefactors.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

A POD reduced order model for resolving angular direction in neutron/photon transport problems

This article presents the first Reduced Order Model (ROM) that efficiently resolves the angular dimension of the time independent, mono-energetic Boltzmann Transport Equation (BTE). It is based on Proper Orthogonal Decomposition (POD) and uses the method of snapshots to form optimal basis functions for resolving the direction of particle travel in neutron/photon transport problems. A unique element of this work is that the snapshots are formed from the vector of angular coefficients relating to a high resolution expansion of the BTE's angular dimension. In addition, the individual snapshots are not recorded through time, as in standard POD, but instead they are recorded through space. In essence this work swaps the roles of the dimensions space and time in standard POD methods, with angle and space respectively. It is shown here how the POD model can be formed from the POD basis functions in a highly efficient manner. The model is then applied to two radiation problems; one involving the transport of radiation through a shield and the other through an infinite array of pins. Both problems are selected for their complex angular flux solutions in order to provide an appropriate demonstration of the model's capabilities. It is shown that the POD model can resolve these fluxes efficiently and accurately. In comparison to high resolution models this POD model can reduce the size of a problem by up to two orders of magnitude without compromising accuracy. Solving times are also reduced by similar factors.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Effects of cluster expansion on the locations of phase transition boundary as a first step to quantify uncertainty in first principles statistical mechanics framework

Predicting phase diagrams from first principle calculations eliminates the need of tedious experimental trials and errors. Fully automating first principle phase diagram calculations without any sort of human intervention has been a long daunting task and troubling scientific communities for decades. This grand problem remains not fully resolved, largely due to the vastly high-dimensional parameter space associated with density functional theory, cluster expansion, lattice Monte Carlo, and the substantial uncertainty propagating through a set of complex simulations. As a first step to tackle this grand problem, we reported a first demonstration of how sensitive phase boundary locations can be to various cluster expansion fittings and input DFT training data. To the best knowledge of the authors, this study reported the first ever attempt to quantify uncertainty in first principles statistical mechanics framework. In addition, a semi-automated phase transition detection algorithm has been devised in this paper to deal with the associated statistical errors and uncertainties from Monte Carlo method and its predecessor DFT calculations and cluster expansions. This algorithm has been applied in a classical cluster expansion Mg-Cd binary alloy system to detect phase transitions at various locations of phase diagram using different cluster expansions to demonstrate its predictive power and quantify uncertainties. The results suggested that using Chebyshev basis function shifted the transition locations toward the dilute solid solution phase and expanded the phase stability of concentrated ordered phases to wider composition range. The addition of perturbed defect configurations into training data set lowered the order-disorder transition temperature to be away from true transition temperature, suggesting the transition nature is indeed configurational disorder dominated rather than defect assisted. Finally, we found that the weighting has negligible effect on the transition locations, except for the case of using Chebyshev basis function to fit all non-weighted configurations that can be susceptible to Monte Carlo sampling hysteresis.

36 MATERIALS SCIENCE↗

Machine-learning based model reduction for partial differential equations

We develop a novel synergistic approach between model reduction and machine learning. The specific goal of this project is to aid in the construction of reduced order models for basis functions that are custom-made to represent the solution of partial differential equations. Partial differential equations (PDEs) are one of the main mathematical tools for describing physical phenomena. However, due to either efficiency or necessity, for many real-world problems, we are interested in constructing reduced order models (ROMs) which focus only on the explicit computation of subsets of the active spatio-temporal scales in the problem, while treating the interaction with the rest of the scales approximately. The task of accurate representation of such interactions (usually called memory terms) constitutes a vast area of research known as model reduction. PI Stinis has significant expertise in the construction of ROMs for complex systems. In addition, in recent work with the project key participant Qadeer, they have utilized machine learning to acquire custom-made basis functions (CBFs) to expand the solutions of PDEs. In the proposed work, we will merge the two concepts by constructing ROMs for subsets of the CBFs needed to represent the solution of a PDE. Specifically, we will use the Mori-Zwanzig model reduction formalism to construct ROMs for subsets of CBFs for nonlinear PDEs of various complexity, as well as investigate the usage of CBFs in the spectral vanishing viscosity method for problems that can form shocks in finite time. The outcome of the research is aimed to be proof-of-concept about a novel synergistic approach between model reduction and machine learning, thus advancing the field of scientific machine learning. Such a capability will benefit the efficient modeling of physical systems appearing in various areas of interest to the DOE.

97 MATHEMATICS AND COMPUTING↗

Extended virtual element method for the Laplace problem with singularities and discontinuities

In this paper, we propose the extended virtual element method (X-VEM) to treat singularities and crack discontinuities that arise in the Laplace problem. The virtual element method (VEM) is a stabilized Galerkin formulation on arbitrary polytopal meshes, wherein the basis functions are implicit (virtual)—they are not known explicitly nor do they need to be computed within the problem domain. In this work, suitable projection operators are used to decompose the bilinear form on each element into two parts: a consistent term that reproduces the first-order polynomial space and a correction term that ensures stability. A similar approach is pursued in the X-VEM with a few notable extensions. To capture singularities and discontinuities in the discrete space, we augment the standard virtual element space with an additional contribution that consists of the product of virtual nodal basis (partition-of-unity) functions with enrichment functions. For discontinuities, basis functions are discontinuous across the crack and for singularities a weakly singular enrichment function that satisfies the Laplace equation is chosen. For the Laplace problem with a singularity, we devise an extended projector that maps functions that lie in the extended virtual element space onto linear polynomials and the enrichment function, whereas for the discontinuous problem, the consistent element stiffness matrix has a block-structure that is readily computed. An adaptive homogeneous numerical integration method is used to accurately and efficiently (no element-partitioning is required) compute integrals with integrands that are weakly singular. Once the element projection matrix is computed, the same steps as in the standard VEM are followed to compute the element stabilization matrix. Numerical experiments are performed on quadrilateral and polygonal (convex and nonconvex elements) meshes for the problem of an $\textit{L}$-shaped domain with a corner singularity and the problem of a cracked membrane under mode III loading, and results are presented that affirm the sound accuracy and demonstrate the optimal rates of convergence in the $\textit{L}^2$ norm and energy of the proposed method.

42 ENGINEERING↗

Coupling a nano-particle with isothermal fluctuating hydrodynamics: Coarse-graining from microscopic to mesoscopic dynamics

We derive a coarse-grained description of the dynamics of a nanoparticle immersed in an isothermal simple fluid by performing a systematic coarse graining of the underlying microscopic dynamics. As coarse-grained or relevant variables, we select the position of the nanoparticle and the total mass and momentum density field of the fluid, which are locally conserved slow variables because they are defined to include the contribution of the nanoparticle. The theory of coarse graining based on the Zwanzing projection operator leads us to a system of stochastic ordinary differential equations that are closed in the relevant variables. We demonstrate that our discrete coarse-grained equations are consistent with a Petrov-Galerkin finite-element discretization of a system of formal stochastic partial differential equations which resemble previously used phenomenological models based on fluctuating hydrodynamics. Key to this connection between our “bottom-up” and previous “top-down” approaches is the use of the same dual orthogonal set of linear basis functions familiar from finite element methods (FEMs), both as a way to coarse-grain the microscopic degrees of freedom and as a way to discretize the equations of fluctuating hydrodynamics. Another key ingredient is the use of a “linear for spiky” weak approximation which replaces microscopic “fields” with a linear FE interpolant inside expectation values. For the irreversible or dissipative dynamics, we approximate the constrained Green-Kubo expressions for the dissipation coefficients with their equilibrium averages. Under suitable approximations, we obtain closed approximations of the coarse-grained dynamics in a manner which gives them a clear physical interpretation and provides explicit microscopic expressions for all of the coefficients appearing in the closure. Our work leads to a model for dilute nanocolloidal suspensions that can be simulated effectively using feasibly short molecular dynamics simulations as input to a FEM fluctuating hydrodynamic solver.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Sparse Cholesky factorization for solving nonlinear PDEs via Gaussian processes

In recent years, there has been widespread adoption of machine learning-based approaches to automate the solving of partial differential equations (PDEs). Among these approaches, Gaussian processes (GPs) and kernel methods have garnered considerable interest due to their flexibility, robust theoretical guarantees, and close ties to traditional methods. They can transform the solving of general nonlinear PDEs into solving quadratic optimization problems with nonlinear, PDE-induced constraints. However, the complexity bottleneck lies in computing with dense kernel matrices obtained from pointwise evaluations of the covariance kernel, and its partial derivatives, a result of the PDE constraint and for which fast algorithms are scarce. The primary goal of this paper is to provide a near-linear complexity algorithm for working with such kernel matrices. We present a sparse Cholesky factorization algorithm for these matrices based on the near-sparsity of the Cholesky factor under a novel ordering of pointwise and derivative measurements. The near-sparsity is rigorously justified by directly connecting the factor to GP regression and exponential decay of basis functions in numerical homogenization. We then employ the Vecchia approximation of GPs, which is optimal in the Kullback-Leibler divergence, to compute the approximate factor. This enables us to compute ϵ-approximate inverse Cholesky factors of the kernel matrices with complexity O(N log d (N/ϵ)) in space and O(N log 2d (N/ϵ)) in time. We integrate sparse Cholesky factorizations into optimization algorithms to obtain fast solvers of the nonlinear PDE. We numerically illustrate our algorithm’s near-linear space/time complexity for a broad class of nonlinear PDEs such as the nonlinear elliptic, Burgers, and Monge-Ampère equations. In summary, we provide a fast, scalable, and accurate method for solving general PDEs with GPs and kernel methods.

97 MATHEMATICS AND COMPUTING↗

Quantifying the agreement between observed and simulated extratropical modes of interannual variability

Using historical simulations of the Coupled Model Intercomparison Project-5 (CMIP5) and multiple observationally-based datasets, we employ skill metrics to analyze the fidelity of the simulated Northern Annular Mode, the North Atlantic Oscillation, the Pacific North America pattern, the Southern Annular Mode, the Pacific Decadal Oscillation, the North Pacific Oscillation, and the North Pacific Gyre Oscillation. We assess the benefits of a unified approach to evaluate these modes of variability, which we call the common basis function (CBF) approach, based on projecting model anomalies onto observed empirical orthogonal functions (EOFs). The CBF approach circumvents issues with conventional EOF analysis, eliminating, for example, corrections of arbitrarily assigned, but inconsistent, signs of the EOF’s/PC’s being compared. It also avoids the problem that sometimes the first observed EOF is more similar to a higher order model EOF, particularly if the simulated EOFs are not well separated. Compared to conventional EOF analysis of models, the CBF approach indicates that models compare significantly better with observations in terms of pattern correlation and root-mean-squared-error (RMSE) than heretofore suggested. In many cases, models are doing a credible job at capturing the observationally-based estimates of patterns; however, errors in simulated amplitudes can be large and more egregious than pattern errors. In the context of the broad distribution of errors in the CMIP5 ensemble, sensitivity tests demonstrate that our results are relatively insensitive to methodological considerations (CBF vs. conventional approach), observational uncertainties in pattern (as determined by using multiple datasets), and internal variability (when multiple realizations from the same model are compared). The skill metrics proposed in this study can provide a useful summary of the ability of models to reproduce the observed EOF patterns and amplitudes. Additionally, the skill metrics can be used as a tool to objectively highlight where potential model improvements might be made. Finally, we advocate more systematic and objective testing of simulated extratropical variability, especially during the non-dominant seasons of each mode, when many models are performing relatively poorly.

58 GEOSCIENCES↗

Physics-Informed Machine Learning Models for Predicting the Progress of Reactive-Mixing

This paper presents a physics-informed machine learning (ML) framework to construct reduced-order models (ROMs) for reactive-transport quantities of interest (QoIs) based on high-fidelity numerical simu-lations. QoIs include species decay, product yield, and degree of mixing. The ROMs for QoIs are applied to quantify and understand how the chemical species evolve over time. First, high-resolution datasets for constructing ROMs are generated by solving anisotropic reaction-di?usion equations using a non-negative finite element formulation for di?erent input parameters. The reactive-mixing model input parameters are: time-scale associated with flipping of velocity, spatial-scale controlling small/large vortex structures of velocity, perturbation parameter of the vortex-based velocity, anisotropic dispersion strength/contrast, and molecular diffusion. Second, random forests, F-test, and mutual information criterion are used to evaluate the importance of model inputs/features with respect to QoIs. We observed that anisotropic dispersion strength/contrast is the most important feature and time-scale associated with flipping of velocity is the least important feature. Third, Support Vector Machines (SVM) and Support Vector Regression (SVR) are used to construct ROMs based on the model inputs. The constructed SVR-ROMs are then used to predict scaling of QoIs. We also present estimates and inequalities on the QoIs, which inform that the species decay, mix, and produce in an exponential fashion. These inequalities also inform that a radial basis function is the most suitable kernel for the SVM/SVR models for QoIs. It is observed that R2-score for SVR-ROMs on unseen data is greater than 0.9, implying that the SVR-ROMs are able to predict the reaction-diffusion system state reasonably well. Finally, in terms of the computational cost, the proposed SVM-ROMs are O(107) times faster than running a high-fidelity finite element simulation for evaluating QoIs. This makes the proposed ML-based ROMs attractive for reactive-transport sensing and real-time monitoring applications as they are significantly faster yet reasonably accurate.

Mudunuru, Maruti K.↗

Machine learning-based surrogate modeling for data-driven optimization: a comparison of subset selection for regression techniques

Optimization of simulation-based or data-driven systems is a challenging task, which has attracted significant attention in the recent literature. A very efficient approach for optimizing systems without analytical expressions is through fitting surrogate models. Due to their increased flexibility, nonlinear interpolating functions, such as radial basis functions and Kriging, have been predominantly used as surrogates for data-driven optimization; however, these methods lead to complex nonconvex formulations. Alternatively, commonly used regression-based surrogates lead to simpler formulations, but they are less flexible and inaccurate if the form is not known a priori. In this work, we investigate the efficiency of subset selection regression techniques for developing surrogate functions that balance both accuracy and complexity. Subset selection creates sparse regression models by selecting only a subset of original features, which are linearly combined to generate a diverse set of surrogate models. Five different subset selection techniques are compared with commonly used nonlinear interpolating surrogate functions with respect to optimization solution accuracy, computation time, sampling requirements, and model sparsity. Furthermore, our results indicate that subset selection-based regression functions exhibit promising performance when the dimensionality is low, while interpolation performs better for higher dimensional problems.

42 ENGINEERING↗

Structural Basis of Functional Transitions in Mammalian NMDA Receptors

Excitatory neurotransmission meditated by glutamate receptors including N-methyl-D-aspartate receptors (NMDARs) is pivotal to brain development and function. NMDARs are heterotetramers composed of GluN1 and GluN2 subunits, which bind glycine and glutamate, respectively, to activate their ion channels. Despite importance in brain physiology, the precise mechanisms by which activation and inhibition occur via subunit-specific binding of agonists and antagonists remain largely unknown. Here, we show the detailed patterns of conformational changes and inter-subunit and -domain reorientation leading to agonist-gating and subunit-dependent competitive inhibition by providing multiple structures in distinct ligand states at 4 Å or better. The structures reveal that activation and competitive inhibition by both GluN1 and GluN2 antagonists occur by controlling the tension of the linker between the ligand-binding domain and the transmembrane ion channel of the GluN2 subunit. Our results provide detailed mechanistic insights into NMDAR pharmacology, activation, and inhibition, which are fundamental to the brain physiology.

59 BASIC BIOLOGICAL SCIENCES↗