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At least 199 records · Page 11

FLAMES─Fast, Low-Storage, Accurate, and Memory-Efficient Adaptive Sampling─Approach to Resolve Spatially Dependent Dynamics of Molecular Liquids

Many critical phenomena in soft matter occur at large length scales, necessitating the resolution of their structure and dynamics at low wavenumbers. However, resolving wavenumber-dependent dynamics computationally via molecular dynamics simulations presents significant challenges, as these phenomena span several orders of magnitude in both time and length scales, resulting in high computational costs and memory demands. Here, this work highlights the computational and memory challenges associated with analyzing molecular trajectories in reciprocal space and demonstrates a method to address them. We introduce FLAMESFast, Low-storage, Accurate, and Memory-Efficient adaptive Sampling, which is a direct method for calculation of structure factors, allowing us to select only the required number of wavevectors for binning. We also use wavenumber-dependent time steps to extract dynamics. Our FLAMES approach effectively mitigates computational and memory/storage bottlenecks. We demonstrate the method using simulations of a model system, liquid octane, at various temperatures. Comparisons with experimental data and real space computation show that the FLAMES technique achieves high accuracy in resolving temperature- and spatially dependent dynamics while being significantly more computationally efficient and requiring less memory and storage than methods based on a uniform wavevector grid and fixed temporal spacing.

Chen, Guang [Argonne National Laboratory (ANL), Ar↗

Effects of Salt Aggregation in Perfluoroether Electrolytes

Electrolytes comprised of polymers mixed with salts have great potential for enabling the use of Li metal anodes in batteries for increased safety. Ionic conductivity is one of the key performance metrics of these polymer electrolytes and achieving high room-temperature conductivity remains a challenge to date. For a bottom-up design of the polymer electrolytes, we must first understand how the structure of polyelectrolytes on a molecular level determines their properties. Here, we use classical molecular dynamics to study the solvation structure and ion diffusion in electrolytes composed of a short-chain perfluoroether with LiFSI or LiTFSI salts. Density functional theory is also used to provide some insights into the structures and energies of the salt interactions with the perfluoroether. We observe the formation of aggregates of salts in the fluorinated systems even at low salt concentrations. The fluorine-fluorine attraction in the solvent is the governing factor for creating the salt aggregates. The aggregates’ size and lifetime change with concentration and anion. These simulations provide an insight into the structure and dynamics of perfluoroether based electrolytes that can be used to improve Li-ion batteries.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Probing remdesivir nucleotide analogue insertion to SARS-CoV-2 RNA dependent RNA polymerase in viral replication

Remdesivir (RDV) prodrug can be metabolized into a triphosphate form nucleotide analogue (RDV-TP) to bind and insert into the active site of viral RNA dependent RNA polymerase (RdRp) to further interfere with viral genome replication. Here in this work, we computationally studied how RDV-TP binds and inserts to the SARS-CoV-2 RdRp active site, in comparison with natural nucleotide substrate adenosine triphosphate (ATP). To do that, we first constructed atomic structural models of an initial binding complex (active site open) and a substrate insertion complex (active site closed), based on high-resolution cryo-EM structures determined recently for SARS-CoV-2 RdRp or non-structural protein (nsp) 12, in complex with accessory protein factors nsp7 and nsp8. By conducting all-atom molecular dynamics simulation with umbrella sampling strategies on the nucleotide insertion between the open and closed state RdRp complexes, our studies show that RDV-TP can initially bind in a comparatively stabilized state to the viral RdRp active site, as it primarily forms base stacking with the template uracil nucleotide (nt +1), which under freely fluctuations supports a low free energy barrier of the RDV-TP insertion (~1.5 kcal mol -1 ). In comparison, the corresponding natural substrate ATP binds initially to the RdRp active site in Watson–Crick base pairing with the template nt, and inserts into the active site with a medium low free energy barrier (~2.6 kcal mol -1 ), when the fluctuations of the template nt are well quenched. The simulations also show that the initial base stacking of RDV-TP with the template can be specifically stabilized by motif C-S759, S682 (near motif B) with the base, and motif G-K500 with the template backbone. Although the RDV-TP insertion can be hindered by motif F-R555/R553 interaction with the triphosphate, the ATP insertion seems to be facilitated by such interactions. The inserted RDV-TP and ATP can be further distinguished by specific sugar interaction with motif B-T687 and motif A-D623, respectively.

36 MATERIALS SCIENCE↗

Structural evolution in Au- and Pd-based metallic glass forming liquids and the case for improved molecular dynamics force fields

The results of a combined experimental and computational investigation of the structural evolution of Au 81 Si 19 , Pd 82 Si 18 , and Pd 77 Cu 6 Si 17 metallic glass forming liquids are presented. Electrostatically levitated metallic liquids are prepared, and synchrotron x-ray scattering studies are combined with embedded atom method molecular dynamics simulations to probe the distribution of relevant structural units. Metal–metalloid based metallic glass forming systems are an extremely important class of materials with varied glass forming ability and mechanical processibility. High quality experimental x-ray scattering data are in poor agreement with the data from the molecular dynamics simulations, demonstrating the need for improved interatomic potentials. The first peak in the x-ray static structure factor in Pd 77 Cu 6 Si 17 displays evidence for a Curie–Weiss type behavior but also a peak in the effective Curie temperature. In conclusion, a proposed order parameter distinguishing glass forming ability, 1/(S(T,q 1 )−1, shows a peak in the effective Curie temperature near a crossover temperature established by the behavior of the viscosity, T A .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Nonperturbative aspects of the electromagnetic pion form factor at high energies

The structure of hadronic form factors at high energies and their deviations from perturbative quantum chromodynamics provide insight on nonperturbative dynamics. Using an approach that is consistent with dispersion relations, we construct a model that simultaneously accounts for the pion wave function, gluonic exchanges, and quark Reggeization. In particular, we find that quark Reggeization can be investigated at high energies by studying scaling violation of the form factor.

Form factors↗

Streptococcus pneumoniae HtrA is a dynamic and monomeric virulence factor capable of forming larger oligomeric complexes

Abstract High‐temperature requirement A (HtrA) proteases are a conserved family of serine proteases central to protein quality control and bacterial virulence. While Gram‐negative and human HtrAs are structurally well studied, Gram‐positive homologs remain essentially uncharacterized. Here, we present the first integrated structural and mechanistic analysis of a Gram‐positive HtrA, from Streptococcus pneumoniae , a virulence factor essential for adhesion and infection in vivo. Proteomic profiling of an htrA knockout and cleavage assays demonstrate that S. pneumoniae HtrA is required for protein quality control, with the PDZ domain mediating substrate recognition. Biochemically, S. pneumoniae HtrA exists exclusively as a monomer in solution, a striking divergence from canonical trimeric HtrAs that we show is shared with other Gram‐positive homologs. NMR analyses reveal that the monomer dynamically samples open and closed conformations, while cryo‐EM of a catalytic mutant identifies a hexamer stabilized by a unique LoopA–PDZ interaction. Together, these findings define S. pneumoniae HtrA as a dynamic monomer with interdomain coupling between its protease and PDZ domains, establishing Gram‐positive HtrAs as a mechanistically divergent subgroup within the HtrA family.

Lee, Eunjeong [Department of Biochemistry and Mole↗

Structural Heterogeneity and Hydrodynamics of an Intrinsically Disordered Protein Condensate

Biology demonstrates precise control over the free-energy landscape through the selective partitioning of biomacromolecules into membraneless organelles, enabling essential functions such as biochemical transformations, signaling cascades, and mechanical reinforcement. Although the function of these condensates depends on their underlying structure and hydrodynamics, molecular-scale information on these systems remains sparse. Here, in this study, neutron scattering is used to probe the organization and dynamics of the intrinsically disordered N-terminal domain of Galectin-3, an extracellular lectin responsible for facilitating liquid–liquid phase separation on the cellular surface, in both dilute and condensed phases. Dilute solutions contain isolated protein chains in equilibrium with mesoscopic clusters, whereas the condensed phase adopts a bicontinuous, microemulsion-like morphology. The dilute phase behavior is quantitatively described by coarse-grained polymer models from soft-matter physics, demonstrating their predictive power for complex biological proteins. At elevated concentrations, the proteins self-assemble akin to block copolymers, microphase separating through the aggregation of hydrophobic domains along the protein contour. The resulting condensate remains fluid-like despite a 25-fold increase in concentration; its internal hydrodynamics slow by only a factor of 3 relative to dilute protein chains. These results provide a molecular-level framework for how disordered proteins achieve both the structural complexity and dynamic fluidity of biomolecular condensates.

Carrick, Brian R. [Massachusetts Inst. of Technolo↗

Solvent-Dependent Dynamics of Cellulose Nanocrystals in Process-Relevant Flow Fields

Flow-assisted alignment of anisotropic nanoparticles is a promising route for the bottom-up assembly of advanced materials with tunable properties. While aligning processes could be optimized by controlling factors such as solvent viscosity, flow deformation, and the structure of the particles themselves, it is necessary to understand the relationship between these factors and their effect on the final orientation. In this study, we investigated the flow of surface-charged cellulose nanocrystals (CNCs) with the shape of a rigid rod dispersed in water and propylene glycol (PG) in an isotropic tactoid state. In situ scanning small-angle X-ray scattering (SAXS) and rheo-optical flow-stop experiments were used to quantify the dynamics, orientation, and structure of the assigned system at the nanometer scale. The effects of both shear and extensional flow fields were revealed in a single experiment by using a flow-focusing channel geometry, which was used as a model flow for nanomaterial assembly. Due to the higher solvent viscosity, CNCs in PG showed much slower Brownian dynamics than CNCs in water and thus could be aligned at lower deformation rates. Moreover, CNCs in PG also formed a characteristic tactoid structure but with less ordering than CNCs in water owing to weaker electrostatic interactions. The results indicate that CNCs in water stay assembled in the mesoscale structure at moderate deformation rates but are broken up at higher flow rates, enhancing rotary diffusion and leading to lower overall alignment. Albeit being a study of cellulose nanoparticles, the fundamental interplay between imposed flow fields, Brownian motion, and electrostatic interactions likely apply to many other anisotropic colloidal systems.

36 MATERIALS SCIENCE↗

Unsteady- and Steady-State Relative Permeability Study with X-ray and Acoustic Monitoring for CO 2 Storage in Deep Saline Aquifers

In this study, we link the multiphase flow measurements with controls of sedimentary structures (e.g., heterogeneity and anisotropy) on relative permeability to variations in ultrasonic velocities for two deep saline aquifer formations (Entrada and Bluff Sandstones) in the San Juan Basin of the Southwestern USA. The rock specimens were extracted from outcrop sites near Durango, CO, USA. They have distinct differences in grain size, cementation composition, and individual chemical amounts, despite both formations being eolian sandstones. We performed a series of unsteady- and steady-state CO 2 -brine relative permeability experiments under capillary-controlled displacement rates. Unsteady-state experiments were conducted at 71 °C and 9.65 MPa; steady-state experiments were conducted at 85 °C and 22.8 MPa and 89 °C and 24.1 MPa for the Bluff and Entrada Sandstones, respectively. During the unsteady experiments, X-ray computed tomography was used to visualize multiphase flow in porous media and quantify saturations during brine drainage under various flow rates. Scan images and saturation profiles indicate that the CO 2 distribution in the pore volume was strongly impacted by the presence of high-angle cross-laminations, heterogeneous rock structure, and direction of bedding orientation. Those factors contribute to dramatic and quick initial breakthroughs and affect the overall saturation dynamics. Steady-state relative permeability tests were conducted at net flow rates of 1 mL/min for both brine drainage and imbibition. During the experimental steps, the CO 2 fractional flow was increased and decreased for both drainage and imbibition scenarios to mimic the front when CO 2 contacts brine and behind the front when brine enters space previously occupied by CO 2 . It was found that compressional velocity decreased, while shear waves slightly increased as brine saturation decreased. The hysteresis effects for the relative permeability and acoustic velocities were distinct. Furthermore, the CO 2 /brine front stability is quantified by applying a mobility ratio approach to spot saturations at which the boundary line between fluids becomes uneven. The results presented in this work can potentially boost the quality and precision of forecasts for the CO 2 storage projects in which the vertical and horizontal core-scale heterogeneity and anisotropy impact the plume migration within host reservoirs.

carbon dioxide (CO2)↗

Atomistic Insights into Lithium–Glyme Solvate Ionic Liquids: Effects of Chain Length and Anion Coordination

For this study, mixtures of lithium bis(trifluoromethanesulfonyl)imide (LiTFSI) in diglyme (G2), triglyme (G3) and tetraglyme (G4) at solvate ionic liquid (SIL) concentrations were investigated using classical molecular dynamics (cMD) simulations with a physically motivated force-field specifically developed for modeling these systems. The structural and dynamical properties of the mixtures were computed and analyzed. Lithium solvation shells, radial distribution functions, and X-ray structure factors were studied across the different SIL systems. Translational diffusion and rotational relaxation times were also evaluated, exhibiting similar trends with increasing glyme chain length. The results are consistent with experimental data and in good agreement with previous computational studies on G3 and G4. These findings validate the accuracy of the force field in modeling glyme systems and its use for describing the [Li(G2) 4/3 ][TFSI] mixture. Additionally, the thermal and electrochemical stability of these electrolytes were systematically examined. The thermal stability appears to be governed by cooperative interactions among glyme molecules, while the electrochemical stability is primarily influenced by Li + -anion interactions, which vary significantly with glyme chain length. Overall, the study sheds light on the crucial role of the anion in these glyme-based SILs and offers valuable insights into Li + -glyme systems at SIL concentrations, highlighting their promise as potential Li-ion battery electrolytes.

anions↗

The changing mouse embryo transcriptome at whole tissue and single-cell resolution

During mammalian embryogenesis, differential gene expression gradually builds the identity and complexity of each tissue and organ system 1 . Here we systematically quantified mouse polyA-RNA from day 10.5 of embryonic development to birth, sampling 17 tissues and organs. The resulting developmental transcriptome is globally structured by dynamic cytodifferentiation, body-axis and cell-proliferation gene sets that were further characterized by the transcription factor motif codes of their promoters. We decomposed the tissue-level transcriptome using single-cell RNA-seq (sequencing of RNA reverse transcribed into cDNA) and found that neurogenesis and haematopoiesis dominate at both the gene and cellular levels, jointly accounting for one-third of differential gene expression and more than 40% of identified cell types. By integrating promoter sequence motifs with companion ENCODE epigenomic profiles, we identified a prominent promoter de-repression mechanism in neuronal expression clusters that was attributable to known and novel repressors. Focusing on the developing limb, single-cell RNA data identified 25 candidate cell types that included progenitor and differentiating states with computationally inferred lineage relationships. We extracted cell-type transcription factor networks and complementary sets of candidate enhancer elements by using single-cell RNA-seq to decompose integrative cis -element (IDEAS) models that were derived from whole-tissue epigenome chromatin data. These ENCODE reference data, computed network components and IDEAS chromatin segmentations are companion resources to the matching epigenomic developmental matrix, and are available for researchers to further mine and integrate.

59 BASIC BIOLOGICAL SCIENCES↗

Comparison of the Arrhenius parameters between conventional hydrothermal and microwave-assisted synthesis methods for tin oxide nanoparticles

Microwave (MW) irradiation has emerged as a powerful tool for accelerating materials synthesis, yet the origins of its specific influence on reaction kinetics remain elusive. While multiple studies have attributed the observed enhancements in reaction rates under MW heating to reduced activation energies, other accounts have suggested modifications to the Arrhenius pre-exponential factor as the predominant cause. Distinguishing between these parameters in modern applications of MW processing in nanomaterials requires experimental approaches capable of resolving the dynamic and nuanced structural kinetics that govern MW-assisted chemistry. Here, we combine in-situ synchrotron X-ray total scattering with pair distribution function (PDF) analysis to track the structural evolution of SnO 2 nanoparticles synthesized via MW-assisted and conventional hydrothermal conditions. Avrami modeling and Arrhenius analysis suggest that although MW irradiation yields a higher apparent activation energy, the enhanced crystallization is better explained by a pre-exponential factor several orders of magnitude larger than that of conventional heating. These findings suggest that the MW field induces a higher frequency of successful molecular rearrangements rather than lowering the intrinsic activation barrier. The results contribute further insights clarifying the role of the applied MW field for materials design where MW-specific effects can be deliberately harnessed. Furthermore, this work presents a framework promoting the utility of in-situ PDF characterization coupled with kinetic analysis for developing more sophisticated descriptions of nanoscale transformations for MW-driven reaction kinetics.

36 MATERIALS SCIENCE↗

Forward and Off-Forward Parton Distributions from Lattice QCD

The interpretation of (semi-)inclusive and certain exclusive scattering processes relies on the factorization of hard parton level cross sections from long-range and non-perturbative parton correlations. The familiar Parton Distribution Functions (PDFs) and Generalized Parton Distributions quantify the non-perturbative dynamics in these situations and address a number of key questions surrounding the structure of hadrons. A certain class of matrix elements accessible in lattice QCD, so called Lattice Cross Sections, have been shown to factorize into these collinear distributions in a manner akin to the factorization of hadronic cross sections. In the short-distance regime, matrix elements of space-like separated two-current operators and parton bilinears can be expressed as the convolution of perturbative coefficient functions and the PDFs. Matrix elements of this type are isolated in the pion and nucleon, each offering a glimpse of the unpolarized valence quark content of these phenomenologically important hadronic states. The calculations within the nucleon represent the first application of the distillation spatial smearing paradigm to the collinear structure of hadrons, and is found to offer higher precision data compared to similar calculations in the literature. A novel method to obtain PDFs from these lattice data, while simultaneously controlling systematic effects, is developed and applied to the nucleon dataset. The coordinate space factorization of space-like separated parton bilinears has also recently been extended to include Generalized Parton Distributions. Preliminary results in off-forward nucleon matrix elements using distillation are explored.

Egerer, Colin↗

Stress Intensity Thresholds for Development of Reliable Brittle Materials

Brittle material failure in high consequence systems can appear random and unpredictable at subcritical stresses. Gaps in our understanding of how structural flaws and environmental factors (humidity, temperature) impact fracture propagation need to be addressed to circumvent this issue. A combined experimental and computational approach composed of molecular dynamics (MD) simulations, numerical modeling, and atomic force microscopy (AFM) has been undertaken to identify mechanisms of slow crack growth in silicate glasses. AFM characterization of crack growth as slow as 10 -13 m/s was observed, with some stepwise crack growth. MD simulations have identified the critical role of inelastic relaxation in crack propagation, including evolution of the structure during relaxation. A numerical model for the existence of a stress intensity threshold, a stress intensity below which a fracture will not propagate, was developed. This transferrable model for predicting slow crack growth is being incorporated into mission-based programs.

36 MATERIALS SCIENCE↗

Measurement of the Neutron Elastic Electromagnetic Form Factor Ratio at Large Momentum Transfer

Exploring nucleon structure is vital both for understanding its origin and existence as well as for the advancement of the sciences. It helps us answer key questions such as how quark and gluon dynamics create 99% of the nucleon mass. Electron- nucleon scattering has been widely used for precision studies of the nucleon and nuclear structure since the Nobel Prize winning investigations by Robert Hofstadter and collaborators in the 1950s. These studies provide information about the spatial charge and current densities of the nucleon in terms of the electromagnetic form factors. The form factors are functions of four momentum transfer squared (Q2). Extending the electromagnetic form factor measurements to higher Q2 plays a critical role in furthering the understanding of nucleon structure. This motivated the Super BigBite Spectrometer (SBS) program at Jefferson Lab. The open nature of the spectrometers and the direct line of sight from the target to the tracking detector locations in experimental setups such as SBS creates high levels of background at the detectors. This necessitates the use of tracking detectors with high rate capability and good position resolution. Gas Electron Multiplier (GEM) detectors are an excellent choice for tracking detectors in such experiments. Understanding the performance of the GEM detectors is important not just for SBS experiments but also for future high-luminosity experiments. This thesis reports the exploratory results from the measurement of the neutron elastic electromagnetic form factor ratio (Gn E/Gn M) at high momentum transfer. A longitudinally polarized electron beam was scattered off a polarized 3He target, used as an effective polarized neutron target. In this experiment, the polarized 3He target achieved a world record polarization weighted luminosity at a beam current of 45 µA. Double spin asymmetry of the scattered neutron events is used to extract the neutron form factor ratio. Measurements were taken at Q2 = 3.0, 6.8, 9.8 (GeV/c)2. The lowest Q2 measurement is in good agreement with the existing world data, and the higher-Q2 measurements extend the Q2 reach well beyond the existing world data and are expected to remain unmatched for a long time.

Gamage, Vimukthi Haththotuwa [Univ. of Virginia, C↗

Effect of transport mechanism on the coarsening of bicontinuous structures: A comparison between bulk and surface diffusion

Here, coarsening of bicontinuous microstructures is observed in a variety of systems, such as nanoporous metals and mixtures that have undergone spinodal decomposition. To better understand the morphological evolution of these structures during coarsening, we compare the morphologies resulting from two different coarsening mechanisms, surface and bulk diffusion. We perform phase-field simulations of coarsening via each mechanism in a two-phase mixture at nominal volume fractions of 50%-50% and 36%-64%, and the simulated structures are characterized in terms of topology (genus density), the interfacial shape distribution, structure factor, and autocorrelations of phase and mean curvature. We observe self-similar evolution of morphology and topology and agreement with the expected power laws for dynamic scaling, in which the characteristic length scale increases over time proportionally to t 1/4 for surface diffusion and t 1/3 for bulk diffusion. While we observe the expected difference in the coarsening kinetics, we find that differences in self-similar morphology due to coarsening mechanism are relatively small, although typically they are larger at 36% volume fraction than at 50% volume fraction. In particular, we find that bicontinuous structures coarsened via surface diffusion have lower scaled genus densities than structures coarsened via bulk diffusion. We also compare the self-similar morphologies to those in literature and to two model bicontinuous structures, namely, constant-mean-curvature surfaces based on the Schoen G minimal surface and random leveled-wave structures. The average scaled mean curvatures of these model structures agree reasonably with those of the coarsened structures at both 36% and 50%, but we find substantial disagreements in the scaled genus densities and the standard deviations of mean curvature.

36 MATERIALS SCIENCE↗

Stand Age and Climate Change Effects on Carbon Increments and Stock Dynamics

Carbon assimilation and wood production are influenced by environmental conditions and endogenous factors, such as species auto-ecology, age, and hierarchical position within the forest structure. Disentangling the intricate relationships between those factors is more pressing than ever due to climate change’s pressure. We employed the 3D-CMCC-FEM model to simulate undisturbed forests of different ages under four climate change (plus one no climate change) Representative Concentration Pathways (RCP) scenarios from five Earth system models. In this context, carbon stocks and increment were simulated via total carbon woody stocks and mean annual increment, which depends mainly on climate trends. We find greater differences among different age cohorts under the same scenario than among different climate scenarios under the same age class. Increasing temperature and changes in precipitation patterns led to a decline in above-ground biomass in spruce stands, especially in the older age classes. On the contrary, the results show that beech forests will maintain and even increase C-storage rates under most RCP scenarios. Scots pine forests show an intermediate behavior with a stable stock capacity over time and in different scenarios but with decreasing mean volume annual increment. These results confirm current observations worldwide that indicate a stronger climate-related decline in conifers forests than in broadleaves.

Forestry↗

Decoding substrate specificity determining factors in glycosyltransferase-B enzymes – insights from machine learning models

Substrate specificity is an essential characteristic of any enzyme's function and an understanding of the factors that determine this specificity is crucial for enzyme engineering. Unlike the structure of an enzyme which is directly impacted by its sequence, substrate specificity as an enzyme attribute involves a rather indirect relationship with sequence as it also depends on structural aspects that dictate substrate accessibility and active site dynamics. In this study, we explore the performance of classifier-based machine learning models trained on curated sequence and structural data for a class of glycosyltransferases (GTs), namely GT-Bs, to understand their substrate specificity determining factors. GTs enable the transfer of sugar moieties to other biomolecules such as oligosaccharides or proteins and are found in all kingdoms of life. In plants, GTs participate in the biosynthesis of plant cell wall biopolymers (e.g.: hemicelluloses and pectins) and are an integral part of the enzymatic machinery that enables the storage of carbon and energy as plant biomass. To elucidate the substrate specificity of uncharacterized GT-Bs, we constructed multi-label machine learning models (Support Vector Classifier, K-Nearest Neighbors, Gaussian Naïve-Bayes, Random Forest) that incorporate both sequence and structural features. These models achieve good predictive accuracies on test datasets. However, despite our use of structural information, we highlight that there is further scope for improvement in training these models to draw interpretable relationships between sequence, structure and substrate specificity determining motifs in GT-Bs.

97 MATHEMATICS AND COMPUTING↗