Biomolecular structure refinement based on adaptive restraints using local-elevation simulation

Introducing experimental values as restraints into molecular dynamics (MD) simulation to bias the values of particular molecular properties, such as nuclear Overhauser effect intensities or distances, dipolar couplings, ³ J-coupling constants, chemical shifts or crystallographic structure factors, towards experimental values is a widely used structure refinement method. Because multiple torsion angle values ϕ correspond to the same ³ J-coupling constant and high-energy barriers are separating those, restraining ³ J-coupling constants remains difficult. A method to adaptively enforce restraints using a local elevation (LE) potential energy function is presented and applied to ³ J-coupling constant restraining in an MD simulation of hen egg-white lysozyme (HEWL). The method succesfully enhances sampling of the restrained torsion angles until the 37 experimental ³ J-coupling constant values are reached, thereby also improving the agreement with the 1,630 experimental NOE atom–atom distance upper bounds. Afterwards the torsional angles ϕ are kept restrained by the built-up local-elevation potential energies.     

NMR refinement and peptide folding using the GROMACS software

Journal of Biomolecular NMR - Nuclear magnetic resonance spectroscopy is used routinely for studying the three-dimensional structures and dynamics of proteins and nucleic acids. Structure...     

Atomic-level protein structure refinement using fragment-guided molecular dynamics conformation sampling

One of critical difficulties of molecular dynamics (MD)?simulations in protein structure refinement is that the?physics-based energy landscape lacks?a middle-range funnel to guide nonnative conformations toward near-native states. We propose to use the target model as a probe to identify fragmental analogs from PDB. The distance maps are then used to reshape the MD energy funnel. The protocol was tested on 181 benchmarking and 26 CASP targets. It was found that structure models of correct folds with TM-score >0.5 can be often pulled closer to native with higher GDT-HA score, but improvement for the models of incorrect folds (TM-score <0.5) are much less pronounced. These data indicate that template-based fragmental distance maps essentially reshaped the MD energy landscape from golf-course-like to funnel-like ones in the successfully refined targets with a radius of TM-score ～0.5. These results demonstrate a new avenue to improve high-resolution structures by combining knowledge-based template information with physics-based MD simulations.     

Unified 3-D structure and projection orientation refinement using quasi-Newton algorithm

We describe an algorithm for simultaneous refinement of a three-dimensional (3-D) density map and of the orientation parameters of two-dimensional (2-D) projections that are used to reconstruct this map. The application is in electron microscopy, where the 3-D structure of a protein has to be determined from a set of 2-D projections collected at random but initially unknown angles. The design of the algorithm is based on the assumption that initial low resolution approximation of the density map and reasonable guesses for orientation parameters are available. Thus, the algorithm is applicable in final stages of the structure refinement, when the quality of the results is of main concern. We define the objective function to be minimized in real space and solve the resulting nonlinear optimization problem using a Quasi-Newton algorithm. We calculate analytical derivatives with respect to density distribution and the finite difference approximations of derivatives with respect to orientation parameters. We demonstrate that calculation of derivatives is robust with respect to noise in the data. This is due to the fact that noise is annihilated by the back-projection operations. Our algorithm is distinguished from other orientation refinement methods (i) by the simultaneous update of the density map and orientation parameters resulting in a highly efficient computational scheme and (ii) by the high quality of the results produced by a direct minimization of the discrepancy between the 2-D data and the projected views of the reconstructed 3-D structure. We demonstrate the speed and accuracy of our method by using simulated data.     

An automated iterative approach for protein structure refinement using pseudocontact shifts

Journal of Biomolecular NMR - NMR structure calculation using NOE-derived distance restraints requires a considerable number of assignments of both backbone and sidechains resonances, often...     

Biomolecular imaging using atomic force microscopy

Atomic force microscopy (AFM) has become a well-established technique for imaging single biomacromolecules under physiological conditions. The exceptionally high spatial resolution and signal-to-noise ratio of the AFM enables the substructure of individual molecules to be observed. In contrast to other methods, specimens prepared for AFM remain in a plastic state, which enables direct observation of the dynamic molecular response, creating unique opportunities for studying the structure–function relationships of proteins and their functionally relevant assemblies. This review presents recent advances in methods and applications of AFM to imaging biological samples. It is clear that AFM will become an increasingly important tool for probing both the structural and kinetic properties of biological macromolecules.     

Biomolecular energy calculations using transputer technology

We report an application of current parallel processing transputer technology which has readily achieved a 25-fold reduction in computational time of peptide-solvent interactions.     

Computational design,structure refinement and molecular dynamics simulation of novel engineered serratiopeptidase analogs

Communicated by Ramaswamy H. Sarma     

Protein structure refinement by optimization

Knowledge‐based protein potentials are simplified potentials designed to improve the quality of protein models, which is important as more accurate models are more useful for biological and pharmaceutical studies. Consequently, knowledge‐based potentials often are designed to be efficient in ordering a given set of deformed structures denoted decoys according to how close they are to the relevant native protein structure. This, however, does not necessarily imply that energy minimization of this potential will bring the decoys closer to the native structure. In this study, we introduce an iterative strategy to improve the convergence of decoy structures. It works by adding energy optimized decoys to the pool of decoys used to construct the next and improved knowledge‐based potential. We demonstrate that this strategy results in significantly improved decoy convergence on Titan high resolution decoys and refinement targets from Critical Assessment of protein Structure Prediction competitions. Our potential is formulated in Cartesian coordinates and has a fixed backbone potential to restricts motions to be close to those of a dihedral model, a fixed hydrogen‐bonding potential and a variable coarse grained carbon alpha potential consisting of a pair potential and a novel solvent potential that are b‐spline based as we use explicit gradient and Hessian for efficient energy optimization. Proteins 2015; 83:1616–1624. © 2015 Wiley Periodicals, Inc.     

Biomolecular structure prediction at a low resolution using a neural network and the double-iterated kalman filter technique

We report the application of an integrated computational approach for biomolecular structure determination at a low resolution. In particular, a neural network is trained to predict the spatial proximity of C-alpha atoms that are less than a given threshold apart, whereas a Kalman filter algorithm is employed to outline the biomolecular fold, with a constraints set that includes these pairwise atomic distances, and the distances and angles that define the structure as it is known from the protein's sequence. The results for Crambin demonstrate that this integrated approach is useful for molecular structure prediction at a low resolution and may also complement existing experimental distance data for a protein structure determination. © 1996 John Wiley & Sons, Inc.     

Deriving correlated motions in proteins from X-ray structure refinement by using TLS parameters

Dynamic information in proteins may provide valuable information for understanding allosteric regulation of protein complexes or long-range effects of the mutations on enzyme activity. Experimental data such as X-ray B-factors or NMR order parameters provide a convenient estimate of atomic fluctuations (or atomic auto-correlated motions) in proteins. However, it is not as straightforward to obtain atomic cross-correlated motions in proteins — one usually resorts to more sophisticated computational methods such as Molecular Dynamics, normal mode analysis or atomic network models. In this report, we show that atomic cross-correlations can be reliably obtained directly from protein structure using X-ray refinement data. We have derived an analytic form of atomic correlated motions in terms of the original TLS parameters used to refine the B-factors of X-ray structures. The correlated maps computed using this equation are well correlated with those of the method based on a mechanical model (the correlation coefficient is 0.75) for a non-homologous dataset comprising 100 structures. We have developed an approach to compute atomic cross-correlations directly from X-ray protein structure. Being in analytic form, it is fast and provides a feasible way to compute correlated motions in proteins in a high throughput way. In addition, avoiding sophisticated computational operations; it provides a quick, reliable way, especially for non-computational biologists, to obtain dynamics information directly from protein structure relevant to its function.     

Evaluation and refinement of tmRNA structure using gene sequences from natural microbial communities

DNA harvested directly from complex natural microbial communities by PCR has been successfully used to predict RNase P RNA structure, and can potentially provide an abundant source of information for structural predictions of other RNAs. In this study, we utilized genetic variation in natural communities to test and refine the secondary and tertiary structural model for the bacterial tmRNA. The variability of proposed tmRNA secondary structures in different organisms and the lack of any predicted tertiary structure suggested that further refinement of the tmRNA could be useful. To increase the phylogenetic representation of tmRNA sequences, and thereby provide additional data for statistical comparative analysis, we amplified, sequenced, and compared tmRNA sequences from natural microbial communities. Using primers designed from gamma proteobacterial sequences, we determined 44 new tmRNA sequences from a variety of environmental DNA samples. Covariation analyses of these sequences, along with sequences from cultured organisms, confirmed most of the proposed tmRNA model but also provided evidence for a new tertiary interaction. This approach of gathering sequence information from natural microbial communities seems generally applicable in RNA structural analysis.     

NMR: prediction of molecular alignment from structure using the PALES software

Orientational restraints such as residual dipolar couplings promise to overcome many of the problems that traditionally limited liquid-state nuclear magnetic resonance spectroscopy. Recently, we developed methods to predict a molecular alignment tensor and thus residual dipolar couplings for a given molecular structure. This provides many new opportunities for the study of the structure and dynamics of proteins, nucleic acids, oligosaccharides and small molecules. This protocol details the use of the software PALES (Prediction of AlignmEnt from Structure) for prediction of an alignment tensor from a known three-dimensional (3D) coordinate file of a solute. The method is applicable to alignment of molecules in many neutral and charged orienting media and takes into account the molecular shape and 3D charge distribution of the molecule.     

Low-resolution structure refinement in electron microscopy

A real-space structure refinement method, originally developed for macromolecular X-ray crystallography, has been applied to protein structure analysis by electron microscopy (EM). This method simultaneously optimizes the fit of an atomic model to a density map and the stereo-chemical properties of the model by minimizing an energy function. The performance of this method is characterized at different resolution and signal-to-noise ratio conditions typical for EM electron density maps. A multi-resolution scheme is devised to improve the convergence of the refinement on the global energy minimum. Applications of the method to various model systems are demonstrated here. The first case is the arrangement of FlgE molecules in the helical filament of flagellar hook, in which refinement with segmented rigid bodies improves the density correlation and reduces severe van der Waals contacts among the symmetry-related subunits. The second case is a conformational analysis of the NSF AAA ATPase in which a multi-conformer model is used in the refinement to investigate the arrangement of the two ATPase domains in the molecule. The third case is a docking simulation in which the crystal structure of actin and the NOE data from NMR experiments on the dematin headpiece are combined with a low-resolution EM density map to generate an atomic model of the F-actin-dematin headpiece structure.     

Detecting the number of clusters of individuals using the software STRUCTURE: a simulation study

The identification of genetically homogeneous groups of individuals is a long standing issue in population genetics. A recent Bayesian algorithm implemented in the software STRUCTURE allows the identification of such groups. However, the ability of this algorithm to detect the true number of clusters (K) in a sample of individuals when patterns of dispersal among populations are not homogeneous has not been tested. The goal of this study is to carry out such tests, using various dispersal scenarios from data generated with an individual-based model. We found that in most cases the estimated 'log probability of data' does not provide a correct estimation of the number of clusters, K. However, using an ad hoc statistic DeltaK based on the rate of change in the log probability of data between successive K values, we found that STRUCTURE accurately detects the uppermost hierarchical level of structure for the scenarios we tested. As might be expected, the results are sensitive to the type of genetic marker used (AFLP vs. microsatellite), the number of loci scored, the number of populations sampled, and the number of individuals typed in each sample.     

Correction to: An automated iterative approach for protein structure refinement using pseudocontact shifts

Journal of Biomolecular NMR -     

Further refinement of the structure of yeast tRNAPhe.

We have refined the monoclinic crystal structure of yeast tRNA^Phe against a complete set of X-ray data at 2.5 Å resolution, using real-space refinement and a combination of energy minimisation and crystallographic least-squares. This refinement has allowed us to define the conformation of residue D16, and to make corrections to Y37 and A76. We have found an additional magnesium binding site (making a total of four), a number of water molecules, and a possible spermine molecule.A revised list of torsion angles is given.     

Protein structure prediction by all-atom free-energy refinement

Background  

The reliable prediction of protein tertiary structure from the amino acid sequence remains challenging even for small proteins. We have developed an all-atom free-energy protein forcefield (PFF01) that we could use to fold several small proteins from completely extended conformations. Because the computational cost of de-novo folding studies rises steeply with system size, this approach is unsuitable for structure prediction purposes. We therefore investigate here a low-cost free-energy relaxation protocol for protein structure prediction that combines heuristic methods for model generation with all-atom free-energy relaxation in PFF01.