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At least 91 records · Page 5

Adaptive Conformer Sampling for Property Prediction Using the Conductor-like Screening Model for Real Solvents

The valorization of lignocellulose-derived bioproducts requires effective separation from excessive water. Liquid–liquid extraction is a promising low-energy separation technology, but effective extraction requires solvent selection based on the thermodynamic properties of the bioproduct and solvent components. We propose a computational framework for predicting such properties by developing an adaptive conformer selection approach for use with COSMO-RS (conductor-like screening model for real solvents) calculations. In this framework, molecular dynamics simulations are used to generate many molecular structures (conformers) at representative temperatures in varying solvent environments. Conformers are then clustered based on structural metrics in a low-dimensional space and selected using a mixed-integer quadratic programming problem to iteratively insert a sampled conformer. At each iteration, we determine bioproduct properties using COSMO-RS. Here, we demonstrate the capability of the proposed framework on representative bioproducts to show convergence of the adaptive sampling toward experimentally measured properties with fewer calculations than required by random conformer sampling, enabling the improved screening of solvent systems for liquid-phase separation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Paired Simulations and Experimental Investigations into the Calcium-Dependent Conformation of Albumin

Serum albumin is the most abundant protein in blood plasma, and it is involved in multiple biological processes. Serum albumin has recently been adapted for improving biomaterial integration with bone tissue, and studies have shown the importance of this protein in bone repair and regeneration. However, the mechanism of action is not yet clear. In stark contrast, other studies have demonstrated that albumin blocks cell adhesion to surfaces, which is seen as a limitation to its bone healing role. These apparent contradictions suggest that the conformation of albumin facilitates its bioactivity, leading to enhanced bone repair. Serum albumin is known to play a major role in maintaining the calcium ion concentration in blood plasma. Due to the prevalence of calcium at bone repair and regeneration sites, it has been hypothesized that calcium binding to serum albumin triggers a conformational change, leading to bioactivity. In the current study, molecular modeling approaches including molecular docking, atomic molecular dynamics (MD) simulation, and coarse-grained MD simulation were used to test this hypothesis by investigating the conformational changes induced in bovine serum albumin by interaction with calcium ions. The computational results were qualitatively validated with experimental Fourier-transform infrared spectroscopy analysis. We find that free calcium ions in solution transiently bind with the three major loops in albumin, triggering a conformational change where N-terminal and C-terminal domains separate from each other in a partial unfolding process. The separation distance between these domains was found to correlate with the calcium ion concentration. The experimental data support the simulation results showing that albumin has enhanced conformational heterogeneity upon exposure to intermediate levels of calcium, without any significant secondary structure changes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

CoarsenConf: Equivariant Coarsening with Aggregated Attention for Molecular Conformer Generation

Molecular conformer generation (MCG) is an important task in cheminformatics and drug discovery. The ability to efficiently generate low-energy 3D structures can avoid expensive quantum mechanical simulations, leading to accelerated virtual screenings and enhanced structural exploration. Several generative models have been developed for MCG, but many struggle to consistently produce high-quality conformers for meaningful downstream applications. To address these issues, we introduce CoarsenConf, which coarse-grains molecular graphs based on torsional angles and integrates them into an SE(3)-equivariant hierarchical variational autoencoder. Through equivariant coarse-graining, we aggregate the fine-grained atomic coordinates of subgraphs connected via rotatable bonds, creating a variable-length coarse-grained latent representation. Our model uses a novel aggregated attention mechanism to restore fine-grained coordinates from the coarse-grained latent representation, enabling efficient generation of accurate conformers. Furthermore, we evaluate the chemical and biochemical quality of our generated conformers on multiple downstream applications, including property prediction and large-scale oracle-based protein docking. Overall, CoarsenConf generates more accurate conformer ensembles compared to prior generative models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Two-Color IRMPD Applied to Conformationally Complex Ions: Probing Cold Ion Structure and Hot Ion Unfolding

Two-color infrared multiphoton dissociation (2C-IRMPD) spectroscopy is a technique that mitigates spectral distortions due to nonlinear absorption that is inherent to one-color IRMPD. We use a 2C-IRMPD scheme that incorporates two independently tunable IR sources, providing considerable control over the internal energy content and type of spectrum obtained by varying the trap temperature, the time delays and fluences of the two infrared lasers, and whether the first or second laser wavelength is scanned. In this work, we describe the application of this variant of 2C-IRMPD to conformationally complex peptide ions. The 2C-IRMPD technique is used to record near-linear action spectra of both cations and anions with temperatures ranging from 10 to 300 K. In this work, we also determine the conditions under which it is possible to record IR spectra of single conformers in a conformational mixture. Furthermore, we demonstrate the capability of the technique to explore conformational unfolding by recording IR spectra with widely varying internal energy in the ion. The protonated peptide ions YGGFL (NH 3 + -Tyr-Gly-Gly-Phe-Leu, Leu-enkephalin) and YGPAA (NH 3 + -Tyr-Gly-Pro-Ala-Ala) are used as model systems for exploring the advantages and disadvantages of the method when applied to conformationally complex ions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Evaluating the Importance of Conformers for Understanding the Vacuum-Ultraviolet Spectra of Oxiranes: Experiment and Theory

Vacuum-ultraviolet (VUV) absorption spectroscopy enables electronic transitions that offer the unambiguous identification of molecules. As target molecules become more complex, multifunctional species present a great challenge to both experimental and computational spectroscopy. This research reports both experimental and theoretical studies of oxiranes. Computationally, the nuclear ensemble approach has been used to accurately predict experimental spectra for a variety of molecules. However, this approach incurs great computational cost, as ensembles generally consist of thousands of geometries. The present study aims to drastically reduce the ensemble by evaluating the significance of the conformers to the predicted spectra. This approach was applied to 11 substituted oxiranes using the Conformer Rotamer Ensemble Sampling Tool (CREST) of Grimme to generate an ensemble of unique conformers determined by their Boltzmann populations. Five TD-DFT functionals (BMK, CAM-B3LYP, M06-2X, MN15, ωB97X-D) and EOM-CCSD were used to simulate the spectrum of each substituted oxirane ensemble. Computed spectra were then compared to the experiment using both qualitative and quantitative metrics. Based on these metrics, it was observed that certain conformers may not be necessary to characterize this set of oxiranes despite the temperature (323 K) of the experiment. A single conformer can then be used with TD-DFT and EOM-CCSD to replicate the experimental spectra of these medium-sized combustion species.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Distinguishing Potassium Channel Resting State Conformations in Live Cells with Environment-Sensitive Fluorescence

Ion channels are polymorphic membrane proteins whose high-resolution structures offer images of individual conformations, giving us starting points for identifying the complex and transient allosteric changes that give rise to channel physiology. Here, we report live-cell imaging of voltage-dependent structural changes of voltage-gated Kv2.1 channels using peptidyl tarantula toxins labeled with an environment-sensitive fluorophore, whose spectral shifts enable identification of voltage-dependent conformation changes in the resting voltage sensing domain (VSD) of the channel. We synthesize a new environment-sensitive, far-red fluorophore, julolidine phenoxazone (JP) azide, and conjugate it to tarantula toxin GxTX to characterize Kv2.1 VSD allostery during membrane depolarization. JP has an inherent response to the polarity of its immediate surroundings, offering site-specific structural insight into each channel conformation. Using voltage-clamp spectroscopy to collect emission spectra as a function of membrane potential, we find that they vary with toxin labeling site, the presence of Kv2 channels, and changes in membrane potential. With a high-affinity conjugate in which the fluorophore itself interacts closely with the channel, the emission shift midpoint is 50 mV more negative than the Kv2.1 gating current midpoint. This suggests that substantial conformational changes at the toxin-channel interface are associated with early gating charge transitions and these are not concerted with VSD motions at more depolarized potentials. These fluorescent probes enable study of conformational changes that can be correlated with electrophysiology, putting channel structures and models into a context of live-cell membranes and physiological states.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Ligand-induced transmembrane conformational coupling in monomeric $\mathrm{EGFR}$

Single pass cell surface receptors regulate cellular processes by transmitting ligand-encoded signals across the plasma membrane via changes to their extracellular and intracellular conformations. This transmembrane signaling is generally initiated by ligand binding to the receptors in their monomeric form. While subsequent receptor-receptor interactions are established as key aspects of transmembrane signaling, the contribution of monomeric receptors has been challenging to isolate due to the complexity and ligand-dependence of these interactions. By combining membrane nanodiscs produced with cell-free expression, single-molecule Förster Resonance Energy Transfer measurements, and molecular dynamics simulations, we report that ligand binding induces intracellular conformational changes within monomeric, full-length epidermal growth factor receptor (EGFR). Our observations establish the existence of extracellular/intracellular conformational coupling within a single receptor molecule. We implicate a series of electrostatic interactions in the conformational coupling and find the coupling is inhibited by targeted therapeutics and mutations that also inhibit phosphorylation in cells. Collectively, these results introduce a facile mechanism to link the extracellular and intracellular regions through the single transmembrane helix of monomeric EGFR, and raise the possibility that intramolecular transmembrane conformational changes upon ligand binding are common to single-pass membrane proteins.

59 BASIC BIOLOGICAL SCIENCES↗

An active site loop toggles between conformations to control antibiotic hydrolysis and inhibition potency for CTX-M β-lactamase drug-resistance enzymes

Abstract β-lactamases inactivate β-lactam antibiotics leading to drug resistance. Consequently, inhibitors of β-lactamases can combat this resistance, and the β-lactamase inhibitory protein (BLIP) is a naturally occurring inhibitor. The widespread CTX-M-14 and CTX-M-15 β-lactamases have an 83% sequence identity. In this study, we show that BLIP weakly inhibits CTX-M-14 but potently inhibits CTX-M-15. The structure of the BLIP/CTX-M-15 complex reveals that binding is associated with a conformational change of an active site loop of β-lactamase. Surprisingly, the loop structure in the complex is similar to that in a drug-resistant variant (N106S) of CTX-M-14. We hypothesized that the pre-established favorable loop conformation of the N106S mutant would facilitate binding. The N106S substitution results in a ~100- and 10-fold increase in BLIP inhibition potency for CTX-M-14 and CTX-M-15, respectively. Thus, this indicates that an active site loop in β-lactamase toggles between conformations that control antibiotic hydrolysis and inhibitor susceptibility. These findings highlight the role of accessible active site conformations in controlling enzyme activity and inhibitor susceptibility as well as the influence of mutations in selectively stabilizing discrete conformations.

59 BASIC BIOLOGICAL SCIENCES↗

A conformational equilibrium in the nitrogenase MoFe protein with an α-V70I amino acid substitution illuminates the mechanism of H 2 formation

Study of α-V70I-substituted nitrogenase MoFe protein identified Fe6 of FeMo-cofactor (Fe 7 S 9 MoC-homocitrate) as a critical N 2 binding/reduction site. Freeze-trapping this enzyme during Ar turnover captured the key catalytic intermediate in high occupancy, denoted E 4 (4H), which has accumulated 4[e — /H + ] as two bridging hydrides, Fe2–H–Fe6 and Fe3–H–Fe7, and protons bound to two sulfurs. E 4 (4H) is poised to bind/reduce N 2 as driven by mechanistically-coupled H 2 reductive-elimination of the hydrides. This process must compete with ongoing hydride protonation (HP), which releases H 2 as the enzyme relaxes to state E 2 (2H), containing 2[e — /H + ] as a hydride and sulfur-bound proton; accumulation of E 4 (4H) in α-V70I is enhanced by HP suppression. EPR and 95 Mo ENDOR spectroscopies now show that resting-state α-V70I enzyme exists in two conformational states, both in solution and as crystallized, one with wild type (WT)-like FeMo-co and one with perturbed FeMo-co. These reflect two conformations of the Ile residue, as visualized in a reanalysis of the X-ray diffraction data of α-V70I and confirmed by computations. EPR measurements show delivery of 2[e — /H + ] to the E 0 state of the WT MoFe protein and to both α-V70I conformations generating E 2 (2H) that contains the Fe3–H–Fe7 bridging hydride; accumulation of another 2[e — /H + ] generates E 4 (4H) with Fe2–H–Fe6 as the second hydride. E 4 (4H) in WT enzyme and a minority α-V70I E 4 (4H) conformation as visualized by QM/MM computations relax to resting-state through two HP steps that reverse the formation process: HP of Fe2–H–Fe6 followed by slower HP of Fe3–H–Fe7, which leads to transient accumulation of E 2 (2H) containing Fe3–H–Fe7. In the dominant α-V70I E 4 (4H) conformation, HP of Fe2–H–Fe6 is passively suppressed by the positioning of the Ile sidechain; slow HP of Fe3–H–Fe7 occurs first and the resulting E 2 (2H) contains Fe2–H–Fe6. Importantly, it is this HP suppression in E 4 (4H) that enables α-V70I MoFe to accumulate E 4 (4H) in high occupancy. In addition, HP suppression in α-V70I E 4 (4H) kinetically unmasks hydride reductive-elimination without N 2 -binding, a process that is precluded in WT enzyme.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Transient hydroperoxyalkyl intermediates (•QOOH) in isopentane oxidation. I. Conformer- and isomer-resolved infrared spectra

Transient carbon-centered hydroperoxyalkyl intermediates (•QOOH) in isopentane oxidation are characterized by infrared (IR) action spectroscopy under jet-cooled conditions with selective detection of hydroxyl (OH) radical products. Two distinct •QOOH isomers with radical sites at a primary carbon of one of the methyl groups (β-Me) or a secondary carbon (β-Et) of the ethyl group are identified by comparison with theoretically calculated IR absorption features for multiple conformers, including C–O, ethyl, and O–O torsions of the two isomers. Here, a master-equation analysis is developed and utilized to explore the conformational cooling process and the resultant conformer population distributions of the two isomers. Most of the IR features observed, including those in the strong fundamental and first overtone OH stretch regions as well as weaker combination bands involving OH stretch with torsion or OOH bend, are in good accord with computed anharmonic frequencies for the most populated conformers of the •QOOH_Et isomer. Relatively weak IR features most evident in the fundamental and first overtone OH stretch regions are ascribed to multiple conformers of the less stable •QOOH_Me isomer, along with a weak feature that is uniquely attributed to a combination band involving asymmetric CH 2 stretch and HCH bend of •QOOH_Me.

Chemical reaction jet spectroscopy↗

Properties of protein unfolded states suggest broad selection for expanded conformational ensembles

Much attention is being paid to conformational biases in the ensembles of intrinsically disordered proteins. However, it is currently unknown whether or how conformational biases within the disordered ensembles of foldable proteins affect function in vivo. Recently, we demonstrated that water can be a good solvent for unfolded polypeptide chains, even those with a hydrophobic and charged sequence composition typical of folded proteins. These results run counter to the generally accepted model that protein folding begins with hydrophobicity-driven chain collapse. Here we investigate what other features, beyond amino acid composition, govern chain collapse. We found that local clustering of hydrophobic and/or charged residues leads to significant collapse of the unfolded ensemble of pertactin, a secreted autotransporter virulence protein from Bordetella pertussis , as measured by small angle X-ray scattering (SAXS). Sequence patterns that lead to collapse also correlate with increased intermolecular polypeptide chain association and aggregation. Crucially, sequence patterns that support an expanded conformational ensemble enhance pertactin secretion to the bacterial cell surface. Similar sequence pattern features are enriched across the large and diverse family of autotransporter virulence proteins, suggesting sequence patterns that favor an expanded conformational ensemble are under selection for efficient autotransporter protein secretion, a necessary prerequisite for virulence. More broadly, we found that sequence patterns that lead to more expanded conformational ensembles are enriched across water-soluble proteins in general, suggesting protein sequences are under selection to regulate collapse and minimize protein aggregation, in addition to their roles in stabilizing folded protein structures.

59 BASIC BIOLOGICAL SCIENCES↗

Zinc binding alters the conformational dynamics and drives the transport cycle of the cation diffusion facilitator YiiP

YiiP is a secondary transporter that couples Zn 2+ transport to the proton motive force. Structural studies of YiiP from prokaryotes and Znt8 from humans have revealed three different Zn 2+ sites and a conserved homodimeric architecture. These structures define the inward-facing and outward-facing states that characterize the archetypal alternating access mechanism of transport. To study the effects of Zn 2+ binding on the conformational transition, we use cryo-EM together with molecular dynamics simulation to compare structures of YiiP from Shewanella oneidensis in the presence and absence of Zn 2+ . To enable single-particle cryo-EM, we used a phage-display library to develop a Fab antibody fragment with high affinity for YiiP, thus producing a YiiP/Fab complex. To perform MD simulations, we developed a nonbonded dummy model for Zn 2+ and validated its performance with known Zn 2+ -binding proteins. Using these tools, we find that, in the presence of Zn 2+ , YiiP adopts an inward-facing conformation consistent with that previously seen in tubular crystals. After removal of Zn 2+ with high-affinity chelators, YiiP exhibits enhanced flexibility and adopts a novel conformation that appears to be intermediate between inward-facing and outward-facing states. This conformation involves closure of a hydrophobic gate that has been postulated to control access to the primary transport site. Comparison of several independent cryo-EM maps suggests that the transition from the inward-facing state is controlled by occupancy of a secondary Zn 2+ site at the cytoplasmic membrane interface. This work enhances our understanding of individual Zn 2+ binding sites and their role in the conformational dynamics that govern the transport cycle.

59 BASIC BIOLOGICAL SCIENCES↗

Mutation-driven RRE stem-loop II conformational change induces HIV-1 nuclear export dysfunction

Abstract The Rev response element (RRE) forms an oligomeric complex with the viral protein Rev to facilitate the nuclear export of intron-retaining viral RNAs during the late phase of HIV-1 (human immunodeficiency virus type 1) infection. However, the structures and mechanisms underlying this process remain largely unknown. Here, we determined the crystal structure of the HIV-1 RRE stem-loop II (SLII), revealing a unique three-way junction architecture in which the base stem (IIa) bifurcates into the stem-loops (IIb and IIc) to compose Rev binding sites. The crystal structures of various SLII mutants demonstrated that while some mutants retain the same “compact” fold as the wild type, other single-nucleotide mutants induce drastic conformational changes, forming an “extended” SLII structure. Through in vitro Rev binding assays and Rev activity measurements in HIV-1-infected cells using structure-guided SLII mutants designed to favor specific conformers, we showed that while the compact fold represents a functional SLII, the alternative extended conformation inhibits Rev binding and oligomerization and consequently stimulates HIV-1 RNA nuclear export dysfunction. The propensity of SLII to adopt multiple conformations as captured in crystal structures and their influence on Rev oligomerization illuminate emerging perspectives on RRE structural plasticity-based regulation of HIV-1 nuclear export and provide opportunities for developing anti-HIV drugs targeting specific RRE conformations.

Biochemistry & Molecular Biology↗

Anti-polyelectrolyte and polyelectrolyte effects on conformations of polyzwitterionic chains in dilute aqueous solutions

Abstract Polyzwitterions (PZs) are considered as model synthetic analogs of intrinsically disordered proteins. Based on this analogy, PZs in dilute aqueous solutions are expected to attain either globular (i.e. molten, compact) or random coil conformations. Addition of salt is expected to open these conformations. To the best of our knowledge, these hypotheses about conformations of PZs have never been verified. In this study, we test these hypotheses by studying effects of added salt [potassium bromide (KBr)] on gyration and hydrodynamic radii of poly(sulfobetaine methacrylate) in dilute aqueous solutions using dynamic light scattering and small-angle X-ray scattering, respectively. Effects of zwitteration are revealed by direct comparisons of the PZs with the polymers of the same backbone but containing (1) no explicit charges on side groups such as poly(2-dimethylaminoethyl methacrylate)s and (2) explicit cationic side groups with tertiary amino bromide pendants. Zeta-potential measurements, transmission electron microscopy, and ab initio molecular dynamics simulations reveal that the PZs acquire net positive charge in near salt-free conditions due to protonation but retain coiled conformations. Added KBr leads to nonmonotonic changes exhibiting an increase followed by a decrease in radius of gyration (and hydrodynamic radius), which are called antipolyelectrolyte and polyelectrolyte effects, respectively. Charge regulation and screening of charge–charge interactions are discussed in relation to the antipolyelectrolyte and polyelectrolyte effects, respectively, which highlight the importance of salt in affecting net charge and conformations of PZs.

36 MATERIALS SCIENCE↗

Hidden conformal symmetry of the discrete series scalars in dS 2

In D dimensional de Sitter space, a scalar field has an infinite tower of special tachyonic mass values at which enhanced shift symmetries appear. After modding out by these shift symmetries, these fields correspond to the unitary irreducible representations of the de Sitter group known as the discrete series. We show that in D = 2 these theories have global conformal symmetry. In all but the massless case, these theories have no stress tensor and the conformal symmetry does not act in the usual way on the scalar field. We find the conformal symmetry by explicitly computing the correlators of the shift invariant local operators and showing that they take conformally invariant forms. We also demonstrate how these fields are self-dual in D = 2 , and dual to the shift invariant massive vector fields, which are therefore also conformally invariant. Published by the American Physical Society 2025

Farnsworth, Kara (ORCID:000000020200078X)↗

Conformer-specific photochemistry imaged in real space and time

Conformation-dependent dynamics play an important role in organic chemistry syntheses such as electrocyclic reactions, as well as in biological processes such as protein folding. However, current time-resolved experimental methods struggle to distinguish conformers from each other, and conformational isomerism is usually analyzed through reactant and product distributions. Using a combination of mega–electron volt ultrafast electron diffraction and quantum wave packet simulations, Champenois et al. directly followed the photochemical electrocyclic ring opening of the molecule α-phellandrene with femtosecond time resolution and confirmed that the transformation of a specific molecular conformer follows the famous Woodward-Hoffmann rules. The proposed method is potentially a powerful tool to follow conformer specificity in various organic and biological systems in real time.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Towards interpretable Cryo-EM: disentangling latent spaces of molecular conformations

Molecules are essential building blocks of life and their different conformations (i.e., shapes) crucially determine the functional role that they play in living organisms. Cryogenic Electron Microscopy (cryo-EM) allows for acquisition of large image datasets of individual molecules. Recent advances in computational cryo-EM have made it possible to learn latent variable models of conformation landscapes. However, interpreting these latent spaces remains a challenge as their individual dimensions are often arbitrary. The key message of our work is that this interpretation challenge can be viewed as an Independent Component Analysis (ICA) problem where we seek models that have the property of identifiability. That means, they have an essentially unique solution, representing a conformational latent space that separates the different degrees of freedom a molecule is equipped with in nature. Thus, we aim to advance the computational field of cryo-EM beyond visualizations as we connect it with the theoretical framework of (nonlinear) ICA and discuss the need for identifiable models, improved metrics, and benchmarks. Moving forward, we propose future directions for enhancing the disentanglement of latent spaces in cryo-EM, refining evaluation metrics and exploring techniques that leverage physics-based decoders of biomolecular systems. Moreover, we discuss how future technological developments in time-resolved single particle imaging may enable the application of nonlinear ICA models that can discover the true conformation changes of molecules in nature. The pursuit of interpretable conformational latent spaces will empower researchers to unravel complex biological processes and facilitate targeted interventions. This has significant implications for drug discovery and structural biology more broadly. More generally, latent variable models are deployed widely across many scientific disciplines. Thus, the argument we present in this work has much broader applications in AI for science if we want to move from impressive nonlinear neural network models to mathematically grounded methods that can help us learn something new about nature.

59 BASIC BIOLOGICAL SCIENCES↗

A finite element-boundary integral method for conformal antenna arrays on a circular cylinder

Conformal antenna arrays offer many cost and weight advantages over conventional antenna systems. In the past, antenna designers have had to resort to expensive measurements in order to develop a conformal array design. This was due to the lack of rigorous mathematical models for conformal antenna arrays. As a result, the design of conformal arrays was primarily based on planar antenna design concepts. Recently, we have found the finite element-boundary integral method to be very successful in modeling large planar arrays of arbitrary composition in a metallic plane. We are extending this formulation to conformal arrays on large metallic cylinders. In doing so, we will develop a mathematical formulation. In particular, we discuss the finite element equations, the shape elements, and the boundary integral evaluation. It is shown how this formulation can be applied with minimal computation and memory requirements.

Kempel, Leo C.↗