Isogeometric collocation method for the fractional Laplacian in the 2D bounded domain
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Engineering↗
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Generative AI models for learning flow maps of stochastic dynamical systems in bounded domains
Simulating stochastic differential equations (SDEs) in bounded domains, presents significant computational challenges due to particle exit phenomena, which requires accurate modeling of interior stochastic dynamics and boundary interactions. Despite the success of machine learning-based methods in learning SDEs, existing learning methods are not applicable to SDEs in bounded domains because they cannot accurately capture the particle exit dynamics. We present a unified hybrid data-driven approach that combines a conditional diffusion model with an exit prediction neural network to capture both interior stochastic dynamics and boundary exit phenomena. Our ML model consists of two major components: a neural network that learns exit probabilities using binary cross-entropy loss with rigorous convergence guarantees, and a training-free diffusion model that generates state transitions for non-exiting particles using closed-form score functions. The two components are integrated through a probabilistic sampling algorithm that determines particle exit at each time step and generates appropriate state transitions. Here, the performance of the proposed approach is demonstrated via three test cases: a one-dimensional simplified problem for theoretical verification, a two-dimensional advection-diffusion problem in a bounded domain, and a three-dimensional problem of interest to magnetically confined fusion plasmas.
Bounded domains↗
Inverse point source location with the Helmholtz equation on a bounded domain
The problem of recovering acoustic sources, more specifically monopoles, from point-wise measurements of the corresponding acoustic pressure at a limited number of frequencies is addressed. To this purpose, a family of sparse optimization problems in measure space in combination with the Helmholtz equation on a bounded domain is considered in this study. A weighted norm with unbounded weight near the observation points is incorporated into the formulation. Optimality conditions and conditions for recovery in the small noise case are discussed, which motivates concrete choices of the weight. The numerical realization is based on an accelerated conditional gradient method in measure space and a finite element discretization.
97 MATHEMATICS AND COMPUTING↗
Synchronous and asynchronous optimized Schwarz methods for one-way subdivision of bounded domains
Convergence of both synchronous and asynchronous optimized Schwarz algorithms for the shifted Laplacian operator on a bounded rectangular domain, in a one-way subdivision of the computational domain, with overlap, is shown. Convergence results are obtained under very mild conditions on the size of the subdomains and on the amount of overlap. A couple of results are also given, relating the convergence rate of the asynchronous method to changes in the size of the domain. Numerical experiments illustrate the theoretical results.
97 MATHEMATICS AND COMPUTING↗
Crystal structure of the CDK11 kinase domain bound to the small-molecule inhibitor OTS964
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Kelso, Susan↗
A Particle-in-Cell Method for Plasmas with a Generalized Momentum Formulation, Part I: Model Formulation
Here, this paper formulates a new particle-in-cell method for the Vlasov–Maxwell system. Under the Lorenz gauge condition, Maxwell’s equations for the electromagnetic fields can be written as a collection of scalar and vector wave equations. The use of potentials for the fields motivates the adoption of a Hamiltonian formulation for particles that employs the generalized (conjugate) momentum. A notable advantage offered by the Hamiltonian formulation is the elimination of time derivatives in the Lorenz gauge formulation that are required by the standard Newton–Lorentz treatment of the particles. This allows the fields to retain the full time-accuracy guaranteed by the field solver. The resulting updates for particles require only knowledge of the fields and their spatial derivatives. An analytical method for constructing these spatial derivatives is presented that exploits the underlying integral solution used in the field solver for the wave equations. Moreover, these derivatives are demonstrated to converge at the same rate as the fields in both time and space. The Method of Lines Transpose field solver we consider in this work is globally first-order accurate in time and high-order accurate in space (e.g., fourth- and fifth-order) and belongs to a larger class of methods which are unconditionally stable, can address geometry, and leverage $\mathcal {O}(N)$ fast summation methods for efficiency. We demonstrate the method on several well-established benchmark problems on bounded domains, including a plasma sheath as well as a relativistic particle beam. The efficacy of the proposed formulation is established by comparing with a second-order accurate finite-difference time-domain method that employs a leapfrog time advance for particles and a charge conserving map suitable for bounded domains. The new method shows mesh-independent numerical heating properties even in cases where the plasma Debye length is smaller than the grid spacing. This is an important feature of the new method for problems defined on bounded domains, because it permits the use of coarser grids in space in the representation of the fields. Such a capability has significant implications for the simulation of plasmas in bounded domains with complex geometry, where the ratio between the largest and smallest cells can vary significantly. The use of high-order spatial approximations in the new method also means that fewer grid points are required in order to achieve a fixed accuracy. Our results also suggest that the new method can be used with fewer simulation particles per cell compared to the benchmark explicit method, which permits further computational savings.
97 MATHEMATICS AND COMPUTING↗
Crescendo beyond the horizon: More gravitational waves from domain walls bounded by inflated cosmic strings
Gravitational-wave (GW) signals offer a unique window into the dynamics of the early universe. GWs may be generated by the topological defects produced in the early universe, which contain information on the symmetry of UV physics. We consider the case in which a two-step phase transition produces a network of domain walls bounded by cosmic strings. Specifically, we focus on the case in which there is a hierarchy in the symmetry-breaking scales, and a period of inflation pushes the cosmic string generated in the first phase transition outside the horizon before the second phase transition. We show that the GW signal from the evolution and collapse of this string-wall network has a unique spectrum, and the resulting signal strength can be sizeable. In particular, depending on the model parameters, the resulting signal can show up in a broad range of frequencies and can be discovered by a multitude of future probes, including the pulsar timing arrays and space- and ground-based GW observatories. As an example that naturally gives rise to this scenario, we present a model with the first phase transition followed by a brief period of thermal inflation driven by the field responsible for the second stage of symmetry breaking. Here, the model can be embedded into a supersymmetric setup, which provides a natural realization of this scenario. In this case, the successful detection of the peak of the GW spectrum probes the soft supersymmetry breaking scale and the wall tension.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
A Particle-in-Cell Method for Plasmas with a Generalized Momentum Formulation, Part II: Enforcing the Lorenz Gauge Condition
In a previous paper Christlieb et al. (A particle-in-cell method for plasmas with a generalized momentum formulation, part I: Model formulation, 2024), we developed a new particle-in-cell (PIC) method for the relativistic Vlasov–Maxwell system in which the electromagnetic fields and the equations of motion for the particles were cast in terms of scalar and vector potentials through a Hamiltonian formulation. This new method evolved the potentials under the Lorenz gauge using integral equation methods. New methods to construct spatial derivatives of the potentials that converge at the same rates as the fields were also presented. The new particle method was compared against standard explicit discretizations, including the well-known FDTD-PIC method, for a range of applications involving sheaths and particle beams. Here, this paper extends this new class of methods by focusing on the enforcement the Lorenz gauge condition in both exact and approximate forms using co-located meshes. A time-consistency property of the proposed field solver for the vector potential form of Maxwell’s equations is established, which is shown to preserve the equivalence between the semi-discrete Lorenz gauge condition and the analogous semi-discrete continuity equation. Using this property, we present three methods to enforce a semi-discrete gauge condition. The first method introduces an update for the continuity equation that is consistent with the discretization of the Lorenz gauge condition. Both the finite difference and spectral implementations satisfy this discrete gauge condition to machine precision. The second approach we propose enforces a semi-discrete continuity equation using the boundary integral solution to the field equations. The potential benefit of this approach is that it eliminates spatial derivatives that appear on the particle data, namely the current density, which is often calculated by linear combinations of low-order spline basis functions. This method is ideally suited to boundary integral equation methods that invert multi-dimensional operators without dimensional splitting techniques and will be the subject of future work. The third approach introduces a gauge correcting method that makes direct use of the gauge condition to modify the scalar potential and uses local maps for both the charge and current densities. This results in a gauge error, as the maps do not enforce the continuity equation. The vector potential coming from the current density is taken to be exact, and using the Lorenz gauge, we compute a correction to the scalar potential that makes the two potentials satisfy the gauge condition. This method also enforces the gauge condition to machine precision. We demonstrate two of the proposed methods in the context of periodic domains. Problems defined on bounded domains, including those with complex geometric features remain an ongoing effort. However, this work shows that it is possible to design computationally efficient methods that can effectively enforce the Lorenz gauge condition in a non-staggered PIC formulation.
97 MATHEMATICS AND COMPUTING↗
ALS mutations disrupt self-association between the ubiquilin STI1 hydrophobic groove and internal placeholder sequences
Ubiquilins are molecular chaperones that play multifaceted roles in proteostasis, with point mutations in UBQLN2 leading to altered phase-separation properties and amyotrophic lateral sclerosis (ALS). Our mechanistic understanding of this essential process has been hindered by a lack of structural information on the STI1 domain, which is essential for ubiquilin chaperone activity and phase separation. Here, we present the first crystal structure of a ubiquilin-family STI1 domain bound to a transmembrane domain (TMD), and show that ALS mutations disrupt the STI1-TMD interaction. We further demonstrate that ubiquilins contain multiple conserved internal sequences that bind to the STI1 domain, including the PXX-repeat region that is a hotspot for ALS mutations. We propose that these placeholder sequences prevent solvent exposure of the STI1 hydrophobic groove and contribute to the multivalency that drives ubiquilin phase-separation. Together, this work provides a new paradigm for understanding how STI1 domains modulate ubiquilin chaperone activity and phase separation, and offers insights into the molecular basis of ALS pathogenesis.
Onwunma, Joan [Univ. of Toledo, OH (United States)↗
Structure-function studies of Vibrio cholerae quorum-sensing receptor CqsR signal recognition
Ethanolamine signaling through the transmembrane quorum-sensing receptor CqsR influencesVibrio choleraeniche recognition and host colonization. In this study, we present a comprehensive structure-function analysis of CqsR. Specifically, we have determined X-ray crystal structures of the CqsR periplasmic domain bound to the signaling agonist ethanolamine and its analogs, serinol and L-alaninol, as well as the ligand-free (apo) form of CqsR. The periplasmic ligand-binding domain of CqsR is a Cache domain, the most prevalent extracellular sensory module in prokaryotes. Our findings provide a rare structural comparison of ligand-bound and unbound states of a Cache domain receptor. Coupled with thermodynamic binding assays and genetic analyses, these structures elucidate the molecular basis of CqsR ligand specificity. This study not only advances the understanding of Cache domain function but also informs the identification of ligands for orphan Cache receptors and the rational design of signaling agonists and antagonists. Lastly, we discuss ligand-induced conformational changes in the CqsR Cache domains and explore the potential for the existence of additional regulatory ligands.
Microbiology↗
Compositions and methods for regulating proteins and nucleic acids activities
Compositions and methods for conditionally regulating activities of CRISPR-Cas systems. In some embodiments, the methods comprise providing an inactive guide RNA comprising a regulatory domain bound by a lock nucleic acid different from the guide RNA; and displacing the lock nuclei acid from the regulatory domain by a trigger nucleic acid, thereby activating the guide RNA, wherein the activated guide RNA forms a complex with a Cas enzyme.
Choudhary, Amit↗
Structures of Two Human Astrovirus Capsid/Neutralizing Antibody Complexes Reveal Distinct Epitopes and Inhibition of Virus Attachment to Cells
Human astrovirus is an important cause of viral gastroenteritis worldwide. Young children, the elderly, and the immunocompromised are especially at risk for contracting severe disease. However, no vaccines exist to combat human astrovirus infection. Evidence points to the importance of antibodies in protecting healthy adults from reinfection. To develop an effective subunit vaccine that broadly protects against diverse astrovirus serotypes, we must understand how neutralizing antibodies target the capsid surface at the molecular level. Here, we report the structures of the human astrovirus capsid spike domain bound to two neutralizing monoclonal antibodies. These antibodies bind two distinct conformational epitopes on the spike surface. We add to existing evidence that the human astrovirus capsid spike contains a receptor-binding domain and demonstrate that both antibodies neutralize human astrovirus by blocking virus attachment to host cells. We identify patches of conserved amino acids which overlap or border the antibody epitopes and may constitute a receptor-binding site. Our findings provide a basis for developing therapies to prevent and treat human astrovirus gastroenteritis.
59 BASIC BIOLOGICAL SCIENCES↗
Stable binding to phosphatidylserine-containing membranes requires conserved arginine residues in tandem C domains of blood coagulation factor VIII
At sites of vascular damage, factor VIII (fVIII) is proteolytically activated by thrombin and binds to activated platelet surfaces with activated factor IX (fIXa) to form the intrinsic “tenase” complex. Previous structural and mutational studies of fVIII have identified the C1 and C2 domains in binding to negatively charged membrane surfaces through β-hairpin loops with solvent-exposed hydrophobic residues and a ring of positively charged basic residues. Several hemophilia A-associated mutations within the C domains are suggested to disrupt lipid binding, preventing formation of the intrinsic tenase complex. In this study, we devised a novel platform for generating recombinant C1, C2, and C1C2 domain constructs and performed mutagenesis of several charged residues proximal to the putative membrane binding region of each C domain. Binding measurements between phosphatidylserine (PS)-containing lipid membrane surfaces and fVIII C domains demonstrated an ionic strength dependence on membrane binding affinity. Mutations to basic residues adjacent to the surface-exposed hydrophobic regions of C1 and C2 differentially disrupted membrane binding, with abrogation of binding occurring for mutations to conserved arginine residues in the C1 (R2163) and C2 (R2320) domains. Lastly, we determined the X-ray crystal structure of the porcine fVIII C2 domain bound to o-phospho-L-serine, the polar headgroup of PS, which binds to a basic cleft and makes charge-charge contact with R2320. We conclude that basic clefts in the fVIII C domains bind to PS-containing membranes through conserved arginine residues via a C domain modularity, where each C domain possesses modest electrostatic-dependent affinity and tandem C domains are required for high affinity binding.
59 BASIC BIOLOGICAL SCIENCES↗
Analysis of nonlinear features associated with radio-frequency sheaths
An analytic study is conducted of nonlinear features that arise when radio-frequency (RF) sheath boundary conditions are solved self-consistently with the electromagnetic fields in a magnetized plasma. An instability associated with RF sheath–plasma interactions is identified and shown to be closely linked with sheath–plasma resonance and the occurrence of multiple solutions. It is proposed that this instability serves as a physical mechanism that enables jumping from one solution branch to another, providing a physical basis for the prediction of an RF sheath hysteresis in the time domain. It is further shown that this instability can lead to non-intuitive features such as spontaneous symmetry breaking in an otherwise completely symmetric problem. In plane-stratified geometry, two analytically solvable examples are considered for the cases of an unbounded half-space and a bounded domain
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Structural basis of SARS-CoV-2 Omicron immune evasion and receptor engagement
The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) Omicron variant of concern evades antibody-mediated immunity that comes from vaccination or infection with earlier variants due to accumulation of numerous spike mutations. To understand the Omicron antigenic shift, we determined cryo–electron microscopy and x-ray crystal structures of the spike protein and the receptor-binding domain bound to the broadly neutralizing sarbecovirus monoclonal antibody (mAb) S309 (the parent mAb of sotrovimab) and to the human ACE2 receptor. We provide a blueprint for understanding the marked reduction of binding of other therapeutic mAbs that leads to dampened neutralizing activity. Remodeling of interactions between the Omicron receptor-binding domain and human ACE2 likely explains the enhanced affinity for the host receptor relative to the ancestral virus.
60 APPLIED LIFE SCIENCES↗
Why Seeding Works When Nucleation Barriers Vanish
Crystallization is a process governed by the interplay between nucleation and growth. While crystalline seeds are known to reduce nucleation barriers and accelerate crystallization under nucleation-limited conditions, their influence when nucleation is not the limiting step remains poorly understood. This creates a mechanistic puzzle in systems where nucleation barriers are already negligible, yet seeding still accelerates crystallization. Here, the synthesis of zeolites is a quintessential example of growth-limited crystallization in which seeds accelerate the process despite negligible homogeneous nucleation barriers. Using coarse-grained molecular dynamics simulations─validated across two zeolites and the unrelated case of ice crystallization─we establish that growth-limited crystallization produces many small, misoriented crystallites whose slow coarsening into larger domains controls the emergence of X-ray-detectable crystallinity. Local crystalline order, structural coherence, and X-ray detectability are therefore kinetically decoupled milestones: the first can be reached rapidly while the latter two lag significantly. Seeds resolve this lag by imposing a common orientational registry on nascent crystallites, enabling their coherent coalescence into large seed-bound domains. This early coherence-building step produces a crystallite-size asymmetry that accelerates subsequent coarsening, advancing the onset of X-ray-detectable crystallinity without necessarily increasing the nucleated fraction. We conclude that under growth-limited conditions, the apparent induction period observed in powder X-ray diffraction reflects the time required to build long-range coherence, not the time to form crystalline material. Accordingly, seeds function not primarily by reducing nucleation barriers but by enforcing spatial coherence, thereby shortening the time required to develop long-range order detectable by X-ray diffraction.
Growth-Limited Crystallization↗
Dirichlet absorbing boundary conditions for classical and peridynamic diffusion-type models
Diffusion-type problems in (nearly) unbounded domains play important roles in various fields of fluid dynamics, biology, and materials science. The aim of this paper is to construct accurate absorbing boundary conditions (ABCs) suitable for classical (local) as well as nonlocal peridynamic (PD) diffusion models. The main focus of the present study is on the PD diffusion formulation. The majority of the PD diffusion models proposed so far are applied to bounded domains only. In this study, we propose an effective way to handle unbounded domains both with PD and classical diffusion models. For the former, we employ a meshfree discretization, whereas for the latter the finite element method (FEM) is employed. The proposed ABCs are time-dependent and Dirichlet-type, making the approach easy to implement in the available models. The performance of the approach, in terms of accuracy and stability, is illustrated by numerical examples in 1D, 2D, and 3D.
36 MATERIALS SCIENCE↗
An auto-inhibited state of protein kinase G and implications for selective activation
Cyclic GMP-dependent protein kinases (PKGs) are key mediators of the nitric oxide/cyclic guanosine monophosphate (cGMP) signaling pathway that regulates biological functions as diverse as smooth muscle contraction, cardiac function, and axon guidance. Understanding how cGMP differentially triggers mammalian PKG isoforms could lead to new therapeutics that inhibit or activate PKGs, complementing drugs that target nitric oxide synthases and cyclic nucleotide phosphodiesterases in this signaling axis. Alternate splicing of PRKG1 transcripts confers distinct leucine zippers, linkers, and auto-inhibitory (AI) pseudo-substrate sequences to PKG Iα and Iβ that result in isoform-specific activation properties, but the mechanism of enzyme auto-inhibition and its alleviation by cGMP is not well understood. Here, we present a crystal structure of PKG Iβ in which the AI sequence and the cyclic nucleotide-binding (CNB) domains are bound to the catalytic domain, providing a snapshot of the auto-inhibited state. Specific contacts between the PKG Iβ AI sequence and the enzyme active site help explain isoform-specific activation constants and the effects of phosphorylation in the linker. We also present a crystal structure of a PKG I CNB domain with an activating mutation linked to Thoracic Aortic Aneurysms and Dissections. Similarity of this structure to wildtype cGMP-bound domains and differences with the auto-inhibited enzyme provide a mechanistic basis for constitutive activation. We show that PKG Iβ auto-inhibition is mediated by contacts within each monomer of the native full-length dimeric protein, and using the available structural and biochemical data we develop a model for the regulation and cooperative activation of PKGs.
59 BASIC BIOLOGICAL SCIENCES↗