Time- and ensemble-averaged direct NOE restraints

Summary NMR data are collected as time- and ensemble-averaged quantities. Yet, in commonly used methods for structure determination of biomolecules, structures are required to satisfy simultaneously a large number of constrainsts. Recently, however, methods have been developed that allow a better fit of the experimental data by the use of time- or ensemble-averaged restraints. Thus far, these methods have been applied to structure refinement using distance and J-coupling restraints. In this paper, time and ensemble averaging is extended to the direct refinement with experimental NOE data. The implementation of time- and ensemble-averaged NOE restraints in DINOSAUR is described and illustrated with experimental NMR data for crambin, a 46-residue protein. Structure refinement with both time- and ensemble-averaged NOE restraints results in lower R-factors, indicating a better fit of the experimental NOE data.     

Modified genetic algorithm resolves ambiguous NOE restraints and reduces unsightly NOE violations

In an ideal world, every NOE cross peak would have a unique assignment. However, the interpretation of NOE peaks is frequently complicated by overlapping resonances. In theory, ambiguous assignments could be resolved by performing separate structure calculations with each possible interpretation. Unfortunately, this would require an astronomical amount of computing time. A modified genetic algorithm has been developed that efficiently resolves hundreds of ambiguous restraints in parallel. Each NOE assignment becomes a gene that can be passed on to a new generation. New individuals are constructed by making a constraint lists from a subset of the genes. The constraint lists are then tested for self-consistency by using molecular dynamics to generate new structures for each list. To a first-degree approximation, there is enough information retained in each list to determine the global fold of the protein. Self-consistent constraint lists receive higher scores and their genes (or NOEs) stand a better chance of surviving into the next generation. The process selects NOEs that are consistent with the global fold. Under normal conditions, the program converges in 3 to 8 generations using 70 structures per generation. The final constraints are self-consistent and contain almost no residual NOE violations.     

Ensemble models of proteins and protein domains based on distance distribution restraints

Conformational ensembles of intrinsically disordered peptide chains are not fully determined by experimental observations. Uncertainty due to lack of experimental restraints and due to intrinsic disorder can be distinguished if distance distributions restraints are available. Such restraints can be obtained from pulsed dipolar electron paramagnetic resonance (EPR) spectroscopy applied to pairs of spin labels. Here, we introduce a Monte Carlo approach for generating conformational ensembles that are consistent with a set of distance distribution restraints, backbone dihedral angle statistics in known protein structures, and optionally, secondary structure propensities or membrane immersion depths. The approach is tested with simulated restraints for a terminal and an internal loop and for a protein with 69 residues by using sets of sparse restraints for underlying well‐defined conformations and for published ensembles of a premolten globule‐like and a coil‐like intrinsically disordered protein. Proteins 2016; 84:544–560. © 2016 Wiley Periodicals, Inc.     

Protein dynamics and distance determination by NOE measurements

Present analysis procedures for NMR structure determination of macromolecules presuppose fixed internuclear distances. Improvement of the precision of the requisite NOE information has stimulated the use of more quantitative distance constraints thus necessitating examination as to whether the assumption of a rigid model systematically biases the distance estimates. Analysis using the simple (r-6) dependence of NOE buildup rates seriously underestimates the correct distance for spatially proximal proton pairs having fluctuations comparable to those observed in X-ray temperature factor analysis. However, by calculating the proper generalized order parameter it is shown that for nuclei undergoing rapid isotropic uncorrelated fluctuations the effective distance is identical to the distance between the mean positions of the nuclei. Similar analysis of molecular dynamics simulation data from bovine pancreatic trypsin inhibitor indicates that the distance obtained from the generalized order parameter predicts the distance between the mean positions to within a few percent regardless of the degree of correlation of the pairwise motion for virtually all main chain and dynamically constrained side chain protons.     

Molecular dynamics simulation using weak-coupling NOE distance restraining

Summary Application of the weak-coupling scheme to restrain the configurations of a molecular system to a set of NOE distance restraints is investigated using two test systems: (i) a 15-atom chain molecule with one distance restraint; and (ii) a protein molecule with hundreds of NOE distance restraints. Atom-atom distance restraining by the weak-coupling technique is possible, but this method does not produce as good results as the penalty function method normally used to maintain NOE distance restraints.Abbreviations NOE nuclear Overhauser effect - MD molecular dynamics - PDB protein data bank     

Determination of protein global folds using backbone residual dipolar coupling and long-range NOE restraints

We report the determination of the global fold of human ubiquitin using protein backbone NMR residual dipolar coupling and long-range nuclear Overhauser effect (NOE) data as conformational restraints. Specifically, by use of a maximum of three backbone residual dipolar couplings per residue (N_i-H^N _i, N_i-C_i–1, H^N _i - C_i–1) in two tensor frames and only backbone H^N-H^N NOEs, a global fold of ubiquitin can be derived with a backbone root-mean-square deviation of 1.4 Å with respect to the crystal structure. This degree of accuracy is more than adequate for use in databases of structural motifs, and suggests a general approach for the determination of protein global folds using conformational restraints derived only from backbone atoms.     

Protein structure prediction using sparse NOE and RDC restraints with Rosetta in CASP13

Computational methods that produce accurate protein structure models from limited experimental data, for example, from nuclear magnetic resonance (NMR) spectroscopy, hold great potential for biomedical research. The NMR-assisted modeling challenge in CASP13 provided a blind test to explore the capabilities and limitations of current modeling techniques in leveraging NMR data which had high sparsity, ambiguity, and error rate for protein structure prediction. We describe our approach to predict the structure of these proteins leveraging the Rosetta software suite. Protein structure models were predicted de novo using a two-stage protocol. First, low-resolution models were generated with the Rosetta de novo method guided by nonambiguous nuclear Overhauser effect (NOE) contacts and residual dipolar coupling (RDC) restraints. Second, iterative model hybridization and fragment insertion with the Rosetta comparative modeling method was used to refine and regularize models guided by all ambiguous and nonambiguous NOE contacts and RDCs. Nine out of 16 of the Rosetta de novo models had the correct fold (global distance test total score > 45) and in three cases high-resolution models were achieved (root-mean-square deviation < 3.5 å). We also show that a meta-approach applying iterative Rosetta + NMR refinement on server-predicted models which employed non-NMR-contacts and structural templates leads to substantial improvement in model quality. Integrating these data-assisted refinement strategies with innovative non-data-assisted approaches which became possible in CASP13 such as high precision contact prediction will in the near future enable structure determination for large proteins that are outside of the realm of conventional NMR.     

Fast protein fold estimation from NMR-derived distance restraints

PRIDE-NMR is a fast novel method to relate known protein folds to NMR distance restraints. It can be used to obtain a first guess about a structure being determined, as well as to estimate the completeness or verify the correctness of NOE data. AVAILABILITY: The PRIDE-NMR server is available at http://www.icgeb.org/pride     

Parametrisation of time-averaged distance restraints in MD simulations

Summary Time-averaged restraints in molecular dynamics simulations offer a means to account for the averaging that is implicit in NMR spectroscopic data. We present a systematic investigation of the parameters which characterise time-averaged distance restraints. Using previously published data for a small protein, chymotrypsin inhibitor 2, we identify conditions which can lead to undesirable heating or which grossly distort the dynamics of the system.Abbreviations NOE nuclear Overhauser effect - MD molecular dynamics - CI-2 chymotrypsin inhibitor 2     

Systematic evaluation of CS‐Rosetta for membrane protein structure prediction with sparse NOE restraints

We critically test and validate the CS‐Rosetta methodology for de novo structure prediction of ‐helical membrane proteins (MPs) from NMR data, such as chemical shifts and NOE distance restraints. By systematically reducing the number and types of NOE restraints, we focus on determining the regime in which MP structures can be reliably predicted and pinpoint the boundaries of the approach. Five MPs of known structure were used as test systems, phototaxis sensory rhodopsin II (pSRII), a subdomain of pSRII, disulfide binding protein B (DsbB), microsomal prostaglandin E2 synthase‐1 (mPGES‐1), and translocator protein (TSPO). For pSRII and DsbB, where NMR and X‐ray structures are available, resolution‐adapted structural recombination (RASREC) CS‐Rosetta yields structures that are as close to the X‐ray structure as the published NMR structures if all available NMR data are used to guide structure prediction. For mPGES‐1 and Bacillus cereus TSPO, where only X‐ray crystal structures are available, highly accurate structures are obtained using simulated NMR data. One main advantage of RASREC CS‐Rosetta is its robustness with respect to even a drastic reduction of the number of NOEs. Close‐to‐native structures were obtained with one randomly picked long‐range NOEs for every 14, 31, 38, and 8 residues for full‐length pSRII, the pSRII subdomain, TSPO, and DsbB, respectively, in addition to using chemical shifts. For mPGES‐1, atomically accurate structures could be predicted even from chemical shifts alone. Our results show that atomic level accuracy for helical membrane proteins is achievable with CS‐Rosetta using very sparse NOE restraint sets to guide structure prediction. Proteins 2017; 85:812–826. © 2016 Wiley Periodicals, Inc.     

Modeling helix-turn-helix protein-induced DNA bending with knowledge-based distance restraints.

A crucial element of many gene functions is protein-induced DNA bending. Computer-generated models of such bending have generally been derived by using a presumed bending angle for DNA. Here we describe a knowledge-based docking strategy for modeling the structure of bent DNA recognized by a major groove-inserting alpha-helix of proteins with a helix-turn-helix (HTH) motif. The method encompasses a series of molecular mechanics and dynamics simulations and incorporates two experimentally derived distance restraints: one between the recognition helix and DNA, the other between respective sites of protein and DNA involved in chemical modification-enabled nuclease scissions. During simulation, a DNA initially placed at a distance was "steered" by these restraints to dock with the binding protein and bends. Three prototype systems of dimerized HTH DNA binding were examined: the catabolite gene activator protein (CAP), the phage 434 repressor (Rep), and the factor for inversion stimulation (Fis). For CAP-DNA and Rep-DNA, the root mean square differences between model and x-ray structures in nonhydrogen atoms of the DNA core domain were 2.5 A and 1.6 A, respectively. An experimental structure of Fis-DNA is not yet available, but the predicted asymmetrical bending and the bending angle agree with results from a recent biochemical analysis.     

A method for determining overall protein fold from NMR distance restraints

Summary We describe a simple method for determining the overall fold of a polypeptide chain from NOE-derived distance restraints. The method uses a reduced representation consisting of two particles per residue, and a force field containing pseudo-bond and pseudo-angle terms, an electrostatic term, but no van der Waals or hard shell repulsive terms. The method is fast and robust, requiring relatively few distance restraints to approximate the correct fold, and the correct mirror image is readily determined. The method is easily implemented using commercially available molecular modeling software.     

Alpha-helical topology prediction and generation of distance restraints in membrane proteins

The field of protein structure prediction has seen significant advances in recent years. Researchers have followed a multitude of approaches, including methods based on comparative modeling, fold recognition and threading, and first-principles techniques. It is noteworthy that the structure prediction of membrane proteins is comparatively less studied by researchers in the field. A membrane protein is characterized by a protein structure that extends into or through the lipid-lipid bilayer of a cell. The structure is influenced by the combination of the hydrophobic bilayer region, the direct interaction with the bilayer, and the aqueous external environment. Due to the difficulty in obtaining reliable experimental structures, accurate computational prediction of membrane proteins is of paramount importance. An optimization model has been developed to predict the interhelical interactions in α-helical membrane proteins. A database of α-helical membrane proteins of known structure and limited sequence identity can be constructed to develop interaction probabilities. By then maximizing the occurrence of highly probable pairwise or three-residue interactions, realistic contacts can be predicted by imposing a number of geometrical constraints. The development of these low distance contacts can provide additional distance restraints for first principles-based approaches to the tertiary structure prediction problem. The proposed approach is shown to successfully predict interhelical contacts in several membrane protein systems, including bovine rhodopsin and the recently released human β2 adrenergic receptor protein structure.     

Computer simulations of protein folding with a small number of distance restraints

A high coordination lattice model was used to represent the protein chain. Lattice points correspond to amino-acid side groups. A complicated force field was designed in order to reproduce a protein-like behavior of the chain. Long-distance tertiary restraints were also introduced into the model. The Replica Exchange Monte Carlo method was applied to find the lowest energy states of the folded chain and to solve the problem of multiple minima. In this method, a set of replicas of the model chain was simulated independently in different temperatures with the exchanges of replicas allowed. The model chains, which consisted of up to 100 residues, were folded to structures whose root-mean-square deviation (RMSD) from their native state was between 2.5 and 5 A. Introduction of restrain based on the positions of the backbone hydrogen atoms led to an improvement in the number of successful simulation runs. A small improvement (about 0.5 A) was also achieved in the RMSD of the folds. The proposed method can be used for the refinement of structures determined experimentally from NMR data.     

Strategy for supplementing structure calculations using limited data with hydrophobic distance restraints

Introductory biochemistry texts often note that the fold of a protein is completely defined when the dihedral angles phi and psi are known for each amino acid. This assertion was examined with torsion angle dynamics and simulated annealing (TAD/SA) calculations of protein G using only dihedral angle restraints. When all dihedral angles were restrained to within 1 degrees of the values of the X-ray structure, the TAD/SA structures gave a backbone root mean square deviation to the target of 4 A. Factors that contributed to divergence from the correct solution include deviations of peptide bonds from planarity, internal conflicts resulting from the nonuniform energies of different phi, psi combinations, and relaxation to extended conformations in the absence of long-range constraints. Simulations including hydrogen-bond restraints showed that even a few long-range contacts constrain the fold better than a complete set of accurate dihedral restraints. A procedure is described for TAD/SA calculations using hydrogen-bond restraints, idealized dihedral restraints for residues in regular secondary structures, and "hydrophobic distance restraints" derived from the positions of hydrophobic residues in the amino acid sequence. The hydrogen-bond restraints are treated as inviolable, whereas violated hydrophobic restraints are removed following reduction of restraint upper bounds from 2 to 1 times the predicted radius of gyration. The strategy was tested with simulated restraints from X-ray structures of proteins from different fold classes and NMR data for cold shock protein A that included only backbone chemical shifts and hydrogen bonds obtained from a long-range HNCO experiment.     

Methodology for rigorous modeling of protein conformational changes by Rosetta using DEER distance restraints

We describe an approach for integrating distance restraints from Double Electron-Electron Resonance (DEER) spectroscopy into Rosetta with the purpose of modeling alternative protein conformations from an initial experimental structure. Fundamental to this approach is a multilateration algorithm that harnesses sets of interconnected spin label pairs to identify optimal rotamer ensembles at each residue that fit the DEER decay in the time domain. Benchmarked relative to data analysis packages, the algorithm yields comparable distance distributions with the advantage that fitting the DEER decay and rotamer ensemble optimization are coupled. We demonstrate this approach by modeling the protonation-dependent transition of the multidrug transporter PfMATE to an inward facing conformation with a deviation to the experimental structure of less than 2Å C_α RMSD. By decreasing spin label rotamer entropy, this approach engenders more accurate Rosetta models that are also more closely clustered, thus setting the stage for more robust modeling of protein conformational changes.     

Algorithm for selection of optimized EPR distance restraints for de novo protein structure determination

A hybrid protein structure determination approach combining sparse Electron Paramagnetic Resonance (EPR) distance restraints and Rosetta de novo protein folding has been previously demonstrated to yield high quality models (Alexander et al. (2008)). However, widespread application of this methodology to proteins of unknown structures is hindered by the lack of a general strategy to place spin label pairs in the primary sequence. In this work, we report the development of an algorithm that optimally selects spin labeling positions for the purpose of distance measurements by EPR. For the α-helical subdomain of T4 lysozyme (T4L), simulated restraints that maximize sequence separation between the two spin labels while simultaneously ensuring pairwise connectivity of secondary structure elements yielded vastly improved models by Rosetta folding. 54% of all these models have the correct fold compared to only 21% and 8% correctly folded models when randomly placed restraints or no restraints are used, respectively. Moreover, the improvements in model quality require a limited number of optimized restraints, which is determined by the pairwise connectivities of T4L α-helices. The predicted improvement in Rosetta model quality was verified by experimental determination of distances between spin labels pairs selected by the algorithm. Overall, our results reinforce the rationale for the combined use of sparse EPR distance restraints and de novo folding. By alleviating the experimental bottleneck associated with restraint selection, this algorithm sets the stage for extending computational structure determination to larger, traditionally elusive protein topologies of critical structural and biochemical importance.