An improved algorithm for MFR fragment assembly

A method for generating protein backbone models from backbone only NMR data is presented, which is based on molecular fragment replacement (MFR). In a first step, the PDB database is mined for homologous peptide fragments using experimental backbone-only data i.e. backbone chemical shifts (CS) and residual dipolar couplings (RDC). Second, this fragment library is refined against the experimental restraints. Finally, the fragments are assembled into a protein backbone fold using a rigid body docking algorithm using the RDCs as restraints. For improved performance, backbone nuclear Overhauser effects (NOEs) may be included at that stage. Compared to previous implementations of MFR-derived structure determination protocols this model-building algorithm offers improved stability and reliability. Furthermore, relative to CS-ROSETTA based methods, it provides faster performance and straightforward implementation with the option to easily include further types of restraints and additional energy terms.     

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.     

Various strategies of using residual dipolar couplings in NMR-driven protein docking: application to Lys48-linked di-ubiquitin and validation against 15N-relaxation data

When classical, Nuclear Overhauser Effect (NOE)-based approaches fail, it is possible, given high-resolution structures of the free molecules, to model the structure of a complex in solution based solely on chemical shift perturbation (CSP) data in combination with orientational restraints from residual dipolar couplings (RDCs) when available. RDCs can be incorporated into the docking following various strategies: as direct restraints and/or as intermolecular intervector projection angle restraints (Meiler et al., J Biomol NMR 2000;16:245-252). The advantage of the latter for docking is that they directly define the relative orientation of the molecules. A combined protocol in which RDCs are first introduced as intervector projection angle restraints and at a later stage as direct restraints is shown here to give the best performance. This approach, implemented in our information-driven docking approach HADDOCK (Dominguez et al., J Am Chem Soc 2003;125:1731-1737), is used to determine the solution structure of the Lys48-linked di-ubiquitin, for which chemical shift mapping, RDCs, and (15)N-relaxation data have been previously obtained (Varadan et al., J Mol Biol 2002;324:637-647). The resulting structures, derived from CSP and RDC data, are cross-validated using (15)N-relaxation data. The solution structure differs from the crystal structure by a 20 degrees rotation of the two ubiquitin units relative to each other.     

Top-down approach in protein RDC data analysis: <Emphasis Type="Italic">de novo</Emphasis> estimation of the alignment tensor

In solution NMR spectroscopy the residual dipolar coupling (RDC) is invaluable in improving both the precision and accuracy of NMR structures during their structural refinement. The RDC also provides a potential to determine protein structure de novo. These procedures are only effective when an accurate estimate of the alignment tensor has already been made. Here we present a top–down approach, starting from the secondary structure elements and finishing at the residue level, for RDC data analysis in order to obtain a better estimate of the alignment tensor. Using only the RDCs from N–H bonds of residues in α-helices and CA–CO bonds in β-strands, we are able to determine the offset and the approximate amplitude of the RDC modulation-curve for each secondary structure element, which are subsequently used as targets for global minimization. The alignment order parameters and the orientation of the major principal axis of individual helix or strand, with respect to the alignment frame, can be determined in each of the eight quadrants of a sphere. The following minimization against RDC of all residues within the helix or strand segment can be carried out with fixed alignment order parameters to improve the accuracy of the orientation. For a helical protein Bax, the three components A _xx , A _yy and A _zz , of the alignment order can be determined with this method in average to within 2.3% deviation from the values calculated with the available atomic coordinates. Similarly for β-sheet protein Ubiquitin they agree in average to within 8.5%. The larger discrepancy in β-strand parameters comes from both the diversity of the β-sheet structure and the lower precision of CA–CO RDCs. This top-down approach is a robust method for alignment tensor estimation and also holds a promise for providing a protein topological fold using limited sets of RDCs.     

Use of residual dipolar couplings as restraints in ab initio protein structure prediction

NMR residual dipolar couplings (RDCs), in the form of the projection angles between the respective internuclear bond vectors, are used as structural restraints in the ab initio structure prediction of a test set of six proteins. The restraints are applied using a recently developed SICHO (SIde-CHain-Only) lattice protein model that employs a replica exchange Monte Carlo (MC) algorithm to search conformational space. Using a small number of RDC restraints, the quality of the predicted structures is improved as reflected by lower RMSD/dRMSD (root mean square deviation/distance root mean square deviation) values from the corresponding native structures and by the higher correlation of the most cooperative mode of motion of each predicted structure with that of the native structure. The latter, in particular, has possible implications for the structure-based functional analysis of predicted structures.     

A structure refinement protocol combining NMR residual dipolar couplings and small angle scattering restraints

We present the implementation of a target function based on Small Angle Scattering data (Gabel et al. Eur Biophys J 35(4):313-327, 2006) into the Crystallography and NMR Systems (CNS) and demonstrate its utility in NMR structure calculations by simultaneous application of small angle scattering (SAS) and residual dipolar coupling (RDC) restraints. The efficiency and stability of the approach are demonstrated by reconstructing the structure of a two domain region of the 31 kDa nuclear export factor TAP (TIP-associated protein). Starting with the high resolution X-ray structures of the two individual TAP domains, the translational and orientational domain arrangement is refined simultaneously. We tested the stability of the protocol against variations of the SAS target parameters and the number of RDCs and their uncertainties. The activation of SAS restraints results in an improved translational clustering of the domain positions and lifts part of the fourfold degeneracy of their orientations (associated with a single alignment tensor). The resulting ensemble of structures reflects the conformational space that is consistent with the experimental SAS and RDC data. The SAS target function is computationally very efficient. SAS restraints can be activated at different levels of precision and only a limited SAS angular range is required. When combined with additional data from chemical shift perturbation, paramagnetic relaxation enhancement or mutational analysis the SAS refinement is an efficient approach for defining the topology of multi-domain and/or multimeric biomolecular complexes in solution based on available high resolution structures (NMR or X-ray) of the individual domains.     

A polynomial-time algorithm for de novo protein backbone structure determination from nuclear magnetic resonance data.

We describe an efficient algorithm for protein backbone structure determination from solution Nuclear Magnetic Resonance (NMR) data. A key feature of our algorithm is that it finds the conformation and orientation of secondary structure elements as well as the global fold in polynomial time. This is the first polynomial-time algorithm for de novo high-resolution biomacromolecular structure determination using experimentally recorded data from either NMR spectroscopy or X-ray crystallography. Previous algorithmic formulations of this problem focused on using local distance restraints from NMR (e.g., nuclear Overhauser effect [NOE] restraints) to determine protein structure. This approach has been shown to be NP-hard, essentially due to the local nature of the constraints. In practice, approaches such as molecular dynamics and simulated annealing, which lack both combinatorial precision and guarantees on running time and solution quality, are used routinely for structure determination. We show that residual dipolar coupling (RDC) data, which gives global restraints on the orientation of internuclear bond vectors, can be used in conjunction with very sparse NOE data to obtain a polynomial-time algorithm for structure determination. Furthermore, an implementation of our algorithm has been applied to six different real biological NMR data sets recorded for three proteins. Our algorithm is combinatorially precise, polynomialtime, and uses much less NMR data to produce results that are as good or better than previous approaches in terms of accuracy of the computed structure as well as running time.     

Pressure‐induced structural transition of mature HIV‐1 protease from a combined NMR/MD simulation approach

We investigate the pressure‐induced structural changes in the mature human immunodeficiency virus type 1 protease dimer, using residual dipolar coupling (RDC) measurements in a weakly oriented solution. ¹D_NH RDCs were measured under high‐pressure conditions for an inhibitor‐free PR and an inhibitor‐bound complex, as well as for an inhibitor‐free multidrug resistant protease bearing 20 mutations (PR20). While PR20 and the inhibitor‐bound PR were little affected by pressure, inhibitor‐free PR showed significant differences in the RDCs measured at 600 bar compared with 1 bar. The structural basis of such changes was investigated by MD simulations using the experimental RDC restraints, revealing substantial conformational perturbations, specifically a partial opening of the flaps and the penetration of water molecules into the hydrophobic core of the subunits at high pressure. This study highlights the exquisite sensitivity of RDCs to pressure‐induced conformational changes and illustrates how RDCs combined with MD simulations can be used to determine the structural properties of metastable intermediate states on the folding energy landscape. Proteins 2015; 83:2117–2123. Published 2015. This article is a U.S. Government work and is in the public domain in the USA.     

Protein loop closure using orientational restraints from NMR data

Protein loops often play important roles in biological functions. Modeling loops accurately is crucial to determining the functional specificity of a protein. Despite the recent progress in loop prediction approaches, which led to a number of algorithms over the past decade, few rigorous algorithmic approaches exist to model protein loops using global orientational restraints, such as those obtained from residual dipolar coupling (RDC) data in solution nuclear magnetic resonance (NMR) spectroscopy. In this article, we present a novel, sparse data, RDC‐based algorithm, which exploits the mathematical interplay between RDC‐derived sphero‐conics and protein kinematics, and formulates the loop structure determination problem as a system of low‐degree polynomial equations that can be solved exactly, in closed‐form. The polynomial roots, which encode the candidate conformations, are searched systematically, using provable pruning strategies that triage the vast majority of conformations, to enumerate or prune all possible loop conformations consistent with the data; therefore, completeness is ensured. Results on experimental RDC datasets for four proteins, including human ubiquitin, FF2, DinI, and GB3, demonstrate that our algorithm can compute loops with higher accuracy, a three‐ to six‐fold improvement in backbone RMSD, versus those obtained by traditional structure determination protocols on the same data. Excellent results were also obtained on synthetic RDC datasets for protein loops of length 4, 8, and 12 used in previous studies. These results suggest that our algorithm can be successfully applied to determine protein loop conformations, and hence, will be useful in high‐resolution protein backbone structure determination, including loops, from sparse NMR data. Proteins 2012. © 2011 Wiley Periodicals, Inc.     

NMR structure determination of a membrane protein with two transmembrane helices in micelles: MerF of the bacterial mercury detoxification system

The three-dimensional backbone structure of a membrane protein with two transmembrane helices in micelles was determined using solution NMR methods that rely on the measurement of backbone (1)H-(15)N residual dipolar couplings (RDCs) from samples of two different constructs that align differently in stressed polyacrylamide gels. Dipolar wave fitting to the (1)H-(15)N RDCs determines the helical boundaries based on periodicity and was utilized in the generation of supplemental dihedral restraints for the helical segments. The (1)H-(15)N RDCs and supplemental dihedral restraints enable the determination of the structure of the helix-loop-helix core domain of the mercury transport membrane protein MerF with a backbone RMSD of 0.58 A. Moreover, the fold of this polypeptide demonstrates that the two vicinal pairs of cysteine residues, shown to be involved in the transport of Hg(II) across the membrane, are exposed to the cytoplasm. This finding differs from earlier structural and mechanistic models that were based primarily on the somewhat atypical hydropathy plot for MerF and related transport proteins.     

A target function for quaternary structural refinement from small angle scattering and NMR orientational restraints

We present a novel target function based on atomic coordinates that permits quaternary structural refinement of multi-domain protein–protein or protein–RNA complexes. It requires that the high-resolution structures of the individual domains are known and that small angle scattering (SAS) data as well as NMR orientational restraints from residual dipolar couplings (RDCs) of the complex are available. We show that, when used in combination, the translational and rotational restraints contained in SAS intensities and RDCs, respectively, define a target potential function that permits to determine the overall topology of complexes made up of domains with low internal symmetry. We apply the target function on a modestly anisotropic model system, the Barnase/Barstar complex, and discuss factors that influence the structural refinement such as data errors and the geometrical properties of the individual domains.     

Refined solution structure of the 82-kDa enzyme malate synthase G from joint NMR and synchrotron SAXS restraints

Determination of the accurate three-dimensional structure of large proteins by NMR remains challenging due to a loss in the density of experimental restraints resulting from the often prerequisite perdeuteration. Solution small-angle scattering, which carries long-range translational information, presents an opportunity to enhance the structural accuracy of derived models when used in combination with global orientational NMR restraints such as residual dipolar couplings (RDCs) and residual chemical shift anisotropies (RCSAs). We have quantified the improvements in accuracy that can be obtained using this strategy for the 82 kDa enzyme Malate Synthase G (MSG), currently the largest single chain protein solved by solution NMR. Joint refinement against NMR and scattering data leads to an improvement in structural accuracy as evidenced by a decrease from approximately 4.5 to approximately 3.3 A of the backbone rmsd between the derived model and the high-resolution X-ray structure, PDB code 1D8C. This improvement results primarily from medium-angle scattering data, which encode the overall molecular shape, rather than the lowest angle data that principally determine the radius of gyration and the maximum particle dimension. The effect of the higher angle data, which are dominated by internal density fluctuations, while beneficial, is also found to be relatively small. Our results demonstrate that joint NMR/SAXS refinement can yield significantly improved accuracy in solution structure determination and will be especially well suited for the study of systems with limited NMR restraints such as large proteins, oligonucleotides, or their complexes.     

Solution structure of tRNA<Superscript>Val</Superscript> from refinement of homology model against residual dipolar coupling and SAXS data

A procedure is presented for refinement of a homology model of E. coli tRNA^Val, originally based on the X-ray structure of yeast tRNA^Phe, using experimental residual dipolar coupling (RDC) and small angle X-ray scattering (SAXS) data. A spherical sampling algorithm is described for refinement against SAXS data that does not require a globbic approximation, which is particularly important for nucleic acids where such approximations are less appropriate. Substantially higher speed of the algorithm also makes its application favorable for proteins. In addition to the SAXS data, the structure refinement employed a sparse set of NMR data consisting of 24 imino N–H^N RDCs measured with Pf1 phage alignment, and 20 imino N–H^N RDCs obtained from magnetic field dependent alignment of tRNA^Val. The refinement strategy aims to largely retain the local geometry of the 58% identical tRNA^Phe by ensuring that the atomic coordinates for short, overlapping segments of the ribose-phosphate backbone and the conserved base pairs remain close to those of the starting model. Local coordinate restraints are enforced using the non-crystallographic symmetry (NCS) term in the XPLOR-NIH or CNS software package, while still permitting modest movements of adjacent segments. The RDCs mainly drive the relative orientation of the helical arms, whereas the SAXS restraints ensure an overall molecular shape compatible with experimental scattering data. The resulting structure exhibits good cross-validation statistics (jack-knifed Q _free = 14% for the Pf1 RDCs, compared to 25% for the starting model) and exhibits a larger angle between the two helical arms than observed in the X-ray structure of tRNA^Phe, in agreement with previous NMR-based tRNA^Val models. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Enhancement of bound-state residual dipolar couplings: conformational analysis of lactose bound to Galectin-3

Residual dipolar couplings (RDCs) have proven to be a valuable NMR tool that can provide long-range constraints for molecular structure determination. The constraints are orientational in nature and are, thus, highly complementary to conventional distance constraints from NOE data. This complementarity would seem to extend to the study of the geometry of ligands bound to proteins. However, unlike transferred NOEs, where collection, even with a large excess of free ligand, results in measurements dominated by bound contributions, RDCs of exchanging ligands can be dominated by free-state contributions. Here we present a strategy for enhancement of RDCs from bound states that is based on specifically enhancing the alignment of the protein to which a ligand will bind. The protein is modified by addition of a hydrophobic alkyl tail that anchors it to the bicelles that are a part of the ordering medium needed for RDC measurement. As an illustration, we have added a propyl chain to the C terminus of the carbohydrate recognition domain of the protein, Galectin-3, and report enhanced RDCs that prove consistent with known bound-ligand geometries for this protein.     

Integrating NOE and RDC using sum-of-squares relaxation for protein structure determination

We revisit the problem of protein structure determination from geometrical restraints from NMR, using convex optimization. It is well-known that the NP-hard distance geometry problem of determining atomic positions from pairwise distance restraints can be relaxed into a convex semidefinite program (SDP). However, often the NOE distance restraints are too imprecise and sparse for accurate structure determination. Residual dipolar coupling (RDC) measurements provide additional geometric information on the angles between atom-pair directions and axes of the principal-axis-frame. The optimization problem involving RDC is highly non-convex and requires a good initialization even within the simulated annealing framework. In this paper, we model the protein backbone as an articulated structure composed of rigid units. Determining the rotation of each rigid unit gives the full protein structure. We propose solving the non-convex optimization problems using the sum-of-squares (SOS) hierarchy, a hierarchy of convex relaxations with increasing complexity and approximation power. Unlike classical global optimization approaches, SOS optimization returns a certificate of optimality if the global optimum is found. Based on the SOS method, we proposed two algorithms—RDC-SOS and RDC–NOE-SOS, that have polynomial time complexity in the number of amino-acid residues and run efficiently on a standard desktop. In many instances, the proposed methods exactly recover the solution to the original non-convex optimization problem. To the best of our knowledge this is the first time SOS relaxation is introduced to solve non-convex optimization problems in structural biology. We further introduce a statistical tool, the Cramér–Rao bound (CRB), to provide an information theoretic bound on the highest resolution one can hope to achieve when determining protein structure from noisy measurements using any unbiased estimator. Our simulation results show that when the RDC measurements are corrupted by Gaussian noise of realistic variance, both SOS based algorithms attain the CRB. We successfully apply our method in a divide-and-conquer fashion to determine the structure of ubiquitin from experimental NOE and RDC measurements obtained in two alignment media, achieving more accurate and faster reconstructions compared to the current state of the art.     

Residual dipolar coupling constants and structure determination of large DNA duplexes

Several NMR works have shown that long-range information provided by residual dipolar couplings (RDCs) significantly improve the global structure definition of RNAs and DNAs. Most of these are based on the use of a large set of RDCs, the collect of which requires samples labeled with ¹³C, ¹⁵N, and sometimes, ²H. Here, we carried out torsion-angle dynamics simulations on a non-self complementary DNA fragment of 17 base-pairs, d(GGAAAATATCTAGCAGT).(ACTGCTAGAGATTTTCC). This reproduces the U5 LTR distal end of the HIV-1 cDNA that contains the enzyme integrase binding site. Simulations aimed at evaluating the impact of RDCs on the structure definition of long oligonucleotides, were performed in incorporating (i) nOe-distances at both < 4.5 Å and < 5 Å; (ii) a small set of ¹³C-¹H RDCs, easily detectable at the natural abundance, and (iii) a larger set of RDCs only accessible through the ¹³C labeling of DNAs. Agreement between a target structure and a simulated structure was measured in terms of precision and accuracy. Results allowed to define conditions in which accurate DNA structures can be determined. We confirmed the strong impact of RDCs on the structure determination, and, above all, we found that a small set of RDC constraints (ca. 50) detectable at the natural abundance is sufficient to accurately derive the global and local DNA duplex structures when used in conjunction with nOe-distances < 5 Å.