Structure Refinement Method Research Articles

Molecular structure refinement based on residual dipolar couplings using magnetic-field rotational sampling.

A method for structure refinement of molecules based on residual dipolar coupling (RDC) data is proposed. It calculates RDC values using magnetic-field rotational sampling of the rotational degrees of freedom of a molecule in conjunction with molecule-internal configurational sampling. By applying rotational sampling, as is occurring in the experiment, leading to observable RDCs, the method stays close to the experiment. It avoids the use of an alignment tensor and, therefore, the assumptions that the overall rotation of the molecule is decoupled from its internal motions and that the molecule is rigid. Two simple molecules, a relatively rigid and a very flexible cyclo-octane molecule with eight aliphatic side chains containing 24 united atoms, serve as so-called "toy model" test systems. The method demonstrates the influence of molecular flexibility, force-field dominance, and the number of RDC restraints available on the outcome of structure refinement based on RDCs. Magnetic-field rotational sampling is basically equivalent but more efficient than explicitly sampling the rotational degrees of freedom of the molecule. In addition, the performance of the method is less dependent on the number NRDC of measured RDC-values available. The restraining forces bias the overall orientation distribution of the molecule correctly. This study suggests that the information content of RDCs with respect to molecular structure is limited.

In some cases more complicated approaches to refinement of macromolecular structures are not necessary.

The manuscript `Modeling a unit cell: crystallographic refinement procedure using the biomolecular MD simulation platform Amber' presents a novel protein structure refinement method claimed to offer improvements over traditional techniques like Refmac5 and Phenix. Our re-evaluation suggests that while the new method provides improvements, traditional methods achieve comparable results with less computational effort.

Cryo-EM structure and B-factor refinement with ensemble representation

Cryo-EM experiments produce images of macromolecular assemblies that are combined to produce three-dimensional density maps. Typically, atomic models of the constituent molecules are fitted into these maps, followed by a density-guided refinement. We introduce TEMPy-ReFF, a method for atomic structure refinement in cryo-EM density maps. Our method represents atomic positions as components of a Gaussian mixture model, utilising their variances as B-factors, which are used to derive an ensemble description. Extensively tested on a substantial dataset of 229 cryo-EM maps from EMDB ranging in resolution from 2.1-4.9 Å with corresponding PDB and CERES atomic models, our results demonstrate that TEMPy-ReFF ensembles provide a superior representation of cryo-EM maps. On a single-model basis, it performs similarly to the CERES re-refinement protocol, although there are cases where it provides a better fit to the map. Furthermore, our method enables the creation of composite maps free of boundary artefacts. TEMPy-ReFF is useful for better interpretation of flexible structures, such as those involving RNA, DNA or ligands.

Growth, structure and spectroscopic properties of Er:YSr3(PO4)3 disordered crystal for mid-infrared laser applications

Mid-infrared lasers in the ⁓ 3 µm region activated by Er3+ ion has attracted considerable attention due to their important applications. Herein, a heavy concentration (30 mol%) Er3+ ion doped YSr3(PO4)3 (Er:YSP) single crystal with a high crystalline quality was grown through the Czochralski pulling method. The structure of single crystal was ascertained to be cubic system with the point group 4¯3m using the powder X−ray diffraction and Rietveld structural refinement methods. Furthermore, the band structure and density of states of the crystal were analyzed by the first principal calculations. The absorption and fluorescence spectra were also investigated. An intense absorption band located at 974 nm with a full width half-maximum of 18 nm, where the absorption cross section was obtained to be 3.72 × 10−21 cm2. The full width half-maximum value of emission band centered at about 3090 nm is up to be 140 nm, which is very suitable for realizing ultrashort pulses and tunable lasers. In addition, the fluorescence lifetime of the upper 4I11/2 and lower 4I13/2 levels were obtained to be 0.65 ms and 5.37 ms, respectively. All the results show that the disordered structure crystal Er:YSP could potentially serve as a laser medium for the ⁓ 3µm region.

Atomic protein structure refinement using all-atom graph representations and SE(3)-equivariant graph transformer.

The state-of-art protein structure prediction methods such as AlphaFold are being widely used to predict structures of uncharacterized proteins in biomedical research. There is a significant need to further improve the quality and nativeness of the predicted structures to enhance their usability. In this work, we develop ATOMRefine, a deep learning-based, end-to-end, all-atom protein structural model refinement method. It uses a SE(3)-equivariant graph transformer network to directly refine protein atomic coordinates in a predicted tertiary structure represented as a molecular graph. The method is first trained and tested on the structural models in AlphaFoldDB whose experimental structures are known, and then blindly tested on 69 CASP14 regular targets and 7 CASP14 refinement targets. ATOMRefine improves the quality of both backbone atoms and all-atom conformation of the initial structural models generated by AlphaFold. It also performs better than two state-of-the-art refinement methods in multiple evaluation metrics including an all-atom model quality score-the MolProbity score based on the analysis of all-atom contacts, bond length, atom clashes, torsion angles, and side-chain rotamers. As ATOMRefine can refine a protein structure quickly, it provides a viable, fast solution for improving protein geometry and fixing structural errors of predicted structures through direct coordinate refinement. The source code of ATOMRefine is available in the GitHub repository (https://github.com/BioinfoMachineLearning/ATOMRefine). All the required data for training and testing are available at https://doi.org/10.5281/zenodo.6944368.

NSRGRN: a network structure refinement method for gene regulatory network inference.

The elucidation of gene regulatory networks (GRNs) is one of the central challenges of systems biology, which is crucial for understanding pathogenesis and curing diseases. Various computational methods have been developed for GRN inference, but identifying redundant regulation remains a fundamental problem. Although considering topological properties and edge importance measures simultaneously can identify and reduce redundant regulations, how to address their respective weaknesses whilst leveraging their strengths is a critical problem faced by researchers. Here, we propose a network structure refinement method for GRN (NSRGRN) that effectively combines the topological properties and edge importance measures during GRN inference. NSRGRN has two major parts. The first part constructs a preliminary ranking list of gene regulations to avoid starting the GRN inference from a directed complete graph. The second part develops a novel network structure refinement (NSR) algorithm to refine the network structure from local and global topology perspectives. Specifically, the Conditional Mutual Information with Directionality and network motifs are applied to optimise the local topology, and the lower and upper networks are used to balance the bilateral relationship between the local topology's optimisation and the global topology's maintenance. NSRGRN is compared with six state-of-the-art methods on three datasets (26 networks in total), and it shows the best all-round performance. Furthermore, when acting as a post-processing step, the NSR algorithm can improve the results of other methods in most datasets.

Stroboscopic in situ neutron diffraction approach to elucidate the kinetics of strain mechanisms in ferroelectric materials

The electromechanical properties of ferroelectrics are often strongly frequency-dependent, but the underlying structural kinetics are not well known or understood. Here, we use in situ stroboscopic neutron diffraction combined with a comprehensive structural refinement method to examine the frequency-dependent structural change in the commercial actuator material PIC 151 at realistic operating frequencies. A broad range of frequencies was measured and analyzed in detail. This work further underlines the crucial role of the field-induced phase transformation for explaining the kinetics in ferroelectric materials. Both the tetragonal majority phase and the rhombohedral minority phase contribute with different effects to the frequency dependence of the strain mechanisms. Even creep effects well beyond the probed frequencies can be explained with the observations.

Revealing atomic structure evolution of an Al-1.5Fe alloy in the liquid state using X-ray total scattering and empirical potential structure refinement

We used in-situ real-time synchrotron X-ray total scattering and empirical potential structure refinement method to study the evolution of atomic structure of an Al-1.5Fe alloy melt from 750°C to 630 °C. Detailed data normalization and analyses for the total scattering data were presented in order to achieve sensible atomic structure simulation using the empirical potential structure refinement (EPSR) method with constraints of R-factor is <10-3. Reliable construction of 3D atomic structure of Al-Fe melt in the temperature range reveals that more Al atoms coordinate Fe atoms and the Fe-centered clusters get more compact with the temperature decreases. More systematic work linking the liquid structure to the nucleation structure is under way.

Accelerating simulated annealing of glassy materials with data assimilation

The ultra-long relaxation time of glass transition makes it difficult to construct atomic models of amorphous materials by conventional methods. We propose a novel method for building such atomic models using data assimilation method by simulated annealing with an accurately computed interatomic potential augmented by penalty from experimental data. The advantage of this method is that not only can it reproduce experimental data as the structure refinement methods like reverse Monte Carlo but also obtain the reasonable structure in terms of interatomic potential energy. In addition, thanks to the interatomic potential, we do not need high Q range diffraction data, which is necessary to take into account the short-range order. Persistent homology analysis shows that the amorphous ice obtained by the new method is indeed more ordered at intermediate range.

Neutron scattering on an aqueous sodium chloride solution in the gigapascal pressure range

An aqueous 3 m (=mol kg−1) NaCl solution in D2O is investigated at 0.1 MPa (hereafter denoted as 0 GPa)/298 K, 1 GPa/298 K, 1 GPa/523 K, and 4 GPa/523 K by neutron scattering combined with an empirical potential structure refinement (EPSR) method. The pressure and temperature dependence of the ion solvation and association and solvent water structure is discussed in pair correlation functions, coordination number distributions, angular distributions (orientational correlation), and spatial density functions (3D structure). The Na+ solvation is characterized as nearly octahedral coordination with about five water molecules and one Cl− over a pressure range measured. The Na–Ow (water oxygen) and Na–Dw (water hydrogen) distances are 2.34–2.37 Å and 2.82–3.00 Å, respectively. The water dipole is tilted by about 31° from the Na–O bond direction and the angle distribution becomes broader with an increase in pressure and temperature. The Cl− solvation shows a change in the coordination number of a water oxygen atom from 11 at 0 GPa to 15 at 4 GPa. An increase in the coordination number of a water hydrogen atom with pressure is observed; the values fall within five to six. The first neighbor Cl–Dw and Cl–Ow distances are 2.19–2.28 Å and 3.10–3.21 Å, respectively. The hydrogen-bonded angle Cl−···Dw–Ow is almost linear over a whole pressure range, but the angle distribution becomes broader upon compression. Another interesting finding of the Cl− solvation is the formation of extended solvation shells of Cl− in the gigapascal pressure range as if they behave as a structure making ion as Na+. The extended solvation shell of Cl– is caused by the breakdown or distortion of the hydrogen-bonded network of solvent water under compression. The coordination number of water oxygen increases from 4.7 at 0 GPa to 12–13, close to a value seen in simple liquids like Ar at 1–4 GPa. Despite such a drastic increase in water oxygen coordination number, the coordination number of the water hydrogen decreases from 2.2 at 0 GPa to 1.8 at 4 GPa, with the Ow–Dw distance lengthening from 1.77 Å to 1.95 Å, i.e., the hydrogen bonds between water molecules are retained in the gigapascal pressure range. The hydrogen bond angle Ow···Dw–Ow is almost linear, but the angle distribution is broadened upon compression, suggesting the distortion of the hydrogen bonds. Thus, it is concluded that compression of an aqueous NaCl solution to the gigapascal pressure causes the distortion of the hydrogen bonds between water molecules, resulting in the formation of the second and extended shells of a structure breaking Cl−.

A Method to Derive Structural Information on Molecules from Residual Dipolar Coupling NMR Data.

A method for structure refinement of molecules based on residual dipolar coupling (RDC) data is proposed. It calculates RDC values using rotational and molecule-internal configurational sampling instead of the common refinement procedure that is based on the approximation of the nonuniform rotational distribution of the molecule by a single alignment tensor representing the average nonuniformity of this distribution. Using rotational sampling, as is occurring in the experiment leading to observable RDCs, the method stays close to the experiment. It avoids the use of an alignment tensor and thus the assumption that the overall rotation of the molecule is decoupled from its internal motions and that the molecule be rigid. Two simple molecules, two-united-atomic ethane and a cyclooctane molecule with eight side chains, containing 24 united atoms, serve as the so-called "toy model" test systems. The method demonstrates the influence of molecular flexibility and force-field deficiencies on the outcome of structure refinement based on RDCs. For a molecule of a given size (number of atoms Nat), there must be a sufficiently large number NRDC of measured RDC values available to allow the restraining forces to bias the overall orientation distribution of the molecule. If the ratio NRDC/Nat gets too small, the RDC-restraining forces will either not be strong enough to change the overall rotational direction of the molecule such that the target RDC values are approximated well or will be so strong that they induce a local deformation of the molecule. In the latter case, the size or inertia of the molecule hinders a restraining-induced overall rotation and the internal structure of the molecule is not strong enough to avoid local deformation due to the restraining forces.

Synchrotron x-ray total scattering and modeling study of high-pressure-induced inhomogeneous atom reconfiguration in an equiatomic Zr50Cu50 metallic glassy alloy

We studied in situ the local atomic structure evolution of an equiatomic ${\mathrm{Zr}}_{50}{\mathrm{Cu}}_{50}$ metallic glassy alloy under high pressure compression inside a diamond anvil cell using synchrotron x-ray total scattering. The empirical potential structure refinement method was used to reconstruct the three-dimensional atomic models at each pressure step, and to analyze the spatially averaged local atomic structure configurations. The interatomic distances of different atomic pairs are reduced at different rates with increasing pressure and the Cu-Cu pairs exhibit the highest percentage reduction. Between ambient pressure and 36.85 GPa, the atomic separation of the Cu-Cu pairs is reduced by \ensuremath{\sim}12% compared to \ensuremath{\sim}5% for Zr-Zr and Zr-Cu pairs. Such disproportional decrease in interatomic distance results in inhomogeneous atom reconfiguration in the short atomic range. With the increase of pressure, the Zr atoms move preferentially towards the Zr-Zr pairs, while the Cu atoms move preferentially towards the Cu-Cu pairs, creating inhomogeneous atom reconfiguration with positive short-range order coefficients of 0.0309 and 0.0464 for Zr-Zr and Cu-Cu respectively, but a negative value of \ensuremath{-}0.0464 for Zr-Cu pairs. Voronoi tessellation method was also used to study the evolution of the short-range atom packing versus pressure, elucidating the cause for the bimodal distribution of the bond angle distributions. The research sheds light on understanding of the atomic reconfiguration of equiatomic alloys under high pressure.

Benchmarking of structure refinement methods for protein complex models.

Protein structure docking is the process in which the quaternary structure of a protein complex is predicted from individual tertiary structures of the protein subunits. Protein docking is typically performed in two main steps. The subunits are first docked while keeping them rigid to form the complex, which is then followed by structure refinement. Structure refinement is crucial for a practical use of computational protein docking models, as it is aimed for correcting conformations of interacting residues and atoms at the interface. Here, we benchmarked the performance of eight existing protein structure refinement methods in refinement of protein complex models. We show that the fraction of native contacts between subunits is by far the most straightforward metric to improve. However, backbone dependent metrics, based on the Root Mean Square Deviation proved more difficult to improve via refinement.

Ultrafast coherent motion and helix rearrangement of homodimeric hemoglobin visualized with femtosecond X-ray solution scattering

Ultrafast motion of molecules, particularly the coherent motion, has been intensively investigated as a key factor guiding the reaction pathways. Recently, X-ray free-electron lasers (XFELs) have been utilized to elucidate the ultrafast motion of molecules. However, the studies on proteins using XFELs have been typically limited to the crystalline phase, and proteins in solution have rarely been investigated. Here we applied femtosecond time-resolved X-ray solution scattering (fs-TRXSS) and a structure refinement method to visualize the ultrafast motion of a protein. We succeeded in revealing detailed ultrafast structural changes of homodimeric hemoglobin involving the coherent motion. In addition to the motion of the protein itself, the time-dependent change of electron density of the hydration shell was tracked. Besides, the analysis on the fs-TRXSS data of myoglobin allows for observing the effect of the oligomeric state on the ultrafast coherent motion.

Anomalous Behavior in the Atomic Structure of Nb3Sn under High Pressure

In the present study, the local atomic structure of a Nb3Sn superconductor sample has been probed by X-ray absorption fine structure (XAFS) as a function of hydrostatic pressure (from ambient up to 26 GPa) using a diamond anvil cell set-up. The analysis of the Nb-K edge extended X-ray absorption fine structure (EXAFS) data was carried out combining standard multi shell structural refinement and reverse Monte Carlo method to provide detailed in situ characterization of the pressure-induced evolution of the Nb local structure in Nb3Sn. The results highlight a complex evolution of Nb chains at the local atomic scale, with a peculiar correlated displacement of Nb–Nb and Nb–Nb–Nb configurations. Such a local effect appears related to anomalies evidenced by X-ray diffraction in other superconductors belonging to the same A15 crystallographic structure.

Free Energy Along Transition Pathways from Structure Refinement Simulations

Modern cryo-EM provides high-resolution structures of multiple conformational states of biomolecules and biomolecular complexes from heterogeneous samples, yielding spectacular insights into their conformational heterogeneity and functional mechanisms. This approach is limited, however, to highly populated states and lacks a detailed description of the dynamics and energetics of the transitions between these states. Here we show that molecular dynamics (MD) -based structure refinement methods can be used not only to obtain such information, but also to provide time resolved pathways for each atom of the system.

The structure of aqueous solutions of hexafluoro-iso-propanol studied by neutron diffraction with hydrogen/deuterium isotope substitution and empirical potential structure refinement modeling.

Neutron diffraction measurements of H/D isotopic substitution are made at room temperature for seven H/D substituted hexafluoro-iso-propanol (HFIP; 1,1,1,3,3,3-hexafluoro-2-propanol)-water mixtures at 0.1, 0.2, and 0.4 HFIP mole fraction (xHFIP). The eight partial structure factors except for the H(CH)-H(CH) pair obtained are subjected to an empirical potential structure refinement (EPSR) method to derive all site-site pair correlation functions. It is found that with increasing HFIP concentration the ice-like network of water disappears between xHFIP = 0.1 and 0.2, followed by the formation of a chain-like water structure embedded in an intrinsic structure of HFIP evolved at xHFIP = 0.4. The hydroxyl group of HFIP forms hydrogen bonds with the surrounding water molecules at all HFIP mole fractions investigated. There is no evidence that the water structure is well defined around the CF3 groups of HFIP, but water molecules surround tangentially the CF3 groups of HFIP.

Effect on the structural, optical and electrical properties of Mn-doped ZnO nanobelts synthesized via the hydrothermal method

The structural, optical and electrical properties of Mn-doped ZnO samples with different percentages of Mn synthesized using the hydrothermal method were studied. The structural properties were studied using X-ray diffraction (XRD). The XRD patterns analyzed via the Rietveld structure refinement method showed a typical wurtzite structure and no other impurity phases. The lattice parameters calculated for the Mn-doped ZnO from the XRD pattern were found to be slightly larger than those of the ZnO, which indicates the substitution of Mn into the ZnO lattice. Transmission electron microscopy (TEM) revealed the synthesis of ZnO nanobelts. The incorporation of Mn ions into the ZnO lattice was also confirmed by Fourier transform infrared spectroscopy and UV-spectroscopy. Results show that the increase in Mn concentration increases the gap energy. The study of the electrical properties shows two conduction phenomena. The variation of impedance, dielectric constant and dielectric loss tangent is also discussed.

Optimization of Thermal Processes Applied to Hypoeutectic White Cast Iron containing 25% Cr Aimed at Increasing Erosive Wear Resistance

Hypoeutectic white cast irons containing 25% Cr are used in very demanding environments that require high resistance to erosive wear, for instance, the crushing and processing of minerals or the manufacture of cement. This high percentage in Cr, in turn, favors corrosion resistance. The application of a Design of Experiments (DoE) allows the analysis of the effects of modifying certain factors related to the heat treatments applied to these alloys. Among these factors, the influence of prior softening treatment to facilitate the machining of these cast irons and the influence of the factors related to the destabilization of austenite, during both quenching and tempering, were analyzed. The precipitated phases were identified by X-ray diffraction (XRD), while the Rietveld structural refinement method was used to determine their percentages by weight. Erosive wear resistance was calculated using the ASTM G76 standard test method. It is concluded that the thermal softening treatment, consisting of 2 h at 1000 °C and 24 h at 700 °C, does not result in additional softening of the material compared to its as-cast state. Furthermore, it is observed that not only eutectic carbides influence wear resistance, but that the influence of the matrix constituent is also significant. It is also verified that the tempering treatment plays a decisive role in wear resistance. Temperatures of 500 °C and tempering times of 6 h increase the wear resistance and hardness of the aforementioned matrix constituent. Tempering temperatures of 200 °C lead to an increase in retained austenite content and the presence of M3C carbides versus mixed M7C3 and M23C6 carbides. The quench cooling medium is not found to have a significant influence on the hardness or wear resistance.

Luminescence properties of PbF2:Nd3+,Er3+, Yb3+Phosphors and it’s multi-wavelength sensitive bidirectional conversion mechanism

In this paper, PbF2:Nd3+, Er3+, Yb3+ bidirectional conversion phosphors were successfully prepared by high temperature solid-state method, and characterized by X-ray powder diffraction (XRD), general structure analysis system structure refinement, photoluminescence spectra and lifetime analysis methods. X-ray diffraction and refinement results analyzed phase composition and changes in cell parameters. Intense characteristic emissions of the samples were observed when excited under ultraviolet (378 nm) and different infrared wavelengths (808 nm, 980 nm). Under 808 nm excitation, the PbF2:3mol%Nd3+, 1.5mol%Er3+, 13.5mol% Yb3+ phosphors reached the maximum emission intensity among all samples. In order to study the effect of the Nd3+ ion on the luminescence mechanism, the decay curves of the Er3+: 4S3/2 level at 550 nm under pulsed 808 nm and 980 nm excitation were analyzed. Finally, the down-conversion and up-conversion multi-wavelength sensitive luminescence mechanisms were discussed.