Estimating the accuracy of protein structures using residual dipolar couplings

A method for validating the accuracy of NMR protein structures

We present a method that measures the accuracy of NMR protein structures. It compares random coil index [RCI] against local rigidity predicted by mathematical rigidity theory, calculated from NMR structures [FIRST], using a correlation score (which assesses secondary structure), and an RMSD score (which measures overall rigidity). We test its performance using: structures refined in explicit solvent, which are much better than unrefined structures; decoy structures generated for 89 NMR structures; and conventional predictors of accuracy such as number of restraints per residue, restraint violations, energy of structure, ensemble RMSD, Ramachandran distribution, and clashscore. Restraint violations and RMSD are poor measures of accuracy. Comparisons of NMR to crystal structures show that secondary structure is equally accurate, but crystal structures are typically too rigid in loops, whereas NMR structures are typically too floppy overall. We show that the method is a useful addition to existing measures of accuracy.

Chemical shifts-based similarity restraints improve accuracy of RNA structures determined via NMR

Determination of structure of RNA via NMR is complicated in large part by the lack of a precise parameterization linking the observed chemical shifts to the underlying geometric parameters. In contrast to proteins, where numerous high-resolution crystal structures serve as coordinate templates for this mapping, such models are rarely available for smaller oligonucleotides accessible via NMR, or they exhibit crystal packing and counter-ion binding artifacts that prevent their use for the chemical shifts analysis. On the other hand, NMR-determined structures of RNA often are not solved at the density of restraints required to precisely define the variable degrees of freedom. In this study we sidestep the problems of direct parameterization of the RNA chemical shifts/structure relationship and examine the effects of imposing local fragmental coordinate similarity restraints based on similarities of the experimental secondary ribose ¹³C/¹H chemical shifts instead. The effect of such chemical shift similarity (CSS) restraints on the structural accuracy is assessed via residual dipolar coupling (RDC)-based cross-validation. Improvements in the coordinate accuracy are observed for all of the six RNA constructs considered here as test cases, which argues for routine inclusion of these terms during NMR-based oligonucleotide structure determination. Such accuracy improvements are expected to facilitate derivation of the chemical shift/structure relationships for RNA.

Molecular Dynamics model of peptide-protein conjugation: case study of covalent complex between Sos1 peptide and N-terminal SH3 domain from Grb2

We have investigated covalent conjugation of VPPPVPPRRRX′ peptide (where X′ denotes N^ε-chloroacetyl lysine) to N-terminal SH3 domain from adapter protein Grb2. Our experimental results confirmed that the peptide first binds to the SH3 domain noncovalently before establishing a covalent linkage through reaction of X′ with the target cysteine residue C32. We have also confirmed that this reaction involves a thiolate-anion form of C32 and follows the S_N2 mechanism. For this system, we have developed a new MD-based protocol to model the formation of covalent conjugate. The simulation starts with the known coordinates of the noncovalent complex. When two reactive groups come into contact during the course of the simulation, the reaction is initiated. The reaction is modeled via gradual interpolation between the two sets of force field parameters that are representative of the noncovalent and covalent complexes. The simulation proceeds smoothly, with no appreciable perturbations to temperature, pressure or volume, and results in a high-quality MD model of the covalent complex. The validity of this model is confirmed using the experimental chemical shift data. The new MD-based approach offers a valuable tool to explore the mechanics of protein-peptide conjugation and build accurate models of covalent complexes.

Modern Technologies of Solution Nuclear Magnetic Resonance Spectroscopy for Three-dimensional Structure Determination of Proteins Open Avenues for Life Scientists

Nuclear magnetic resonance (NMR) spectroscopy is a powerful technique for structural studies of chemical compounds and biomolecules such as DNA and proteins. Since the NMR signal sensitively reflects the chemical environment and the dynamics of a nuclear spin, NMR experiments provide a wealth of structural and dynamic information about the molecule of interest at atomic resolution. In general, structural biology studies using NMR spectroscopy still require a reasonable understanding of the theory behind the technique and experience on how to recorded NMR data. Owing to the remarkable progress in the past decade, we can easily access suitable and popular analytical resources for NMR structure determination of proteins with high accuracy. Here, we describe the practical aspects, workflow and key points of modern NMR techniques used for solution structure determination of proteins. This review should aid NMR specialists aiming to develop new methods that accelerate the structure determination process, and open avenues for non-specialist and life scientists interested in using NMR spectroscopy to solve protein structures.

Ensemble MD simulations restrained via crystallographic data: accurate structure leads to accurate dynamics

Currently, the best existing molecular dynamics (MD) force fields cannot accurately reproduce the global free-energy minimum which realizes the experimental protein structure. As a result, long MD trajectories tend to drift away from the starting coordinates (e.g., crystallographic structures). To address this problem, we have devised a new simulation strategy aimed at protein crystals. An MD simulation of protein crystal is essentially an ensemble simulation involving multiple protein molecules in a crystal unit cell (or a block of unit cells). To ensure that average protein coordinates remain correct during the simulation, we introduced crystallography-based restraints into the MD protocol. Because these restraints are aimed at the ensemble-average structure, they have only minimal impact on conformational dynamics of the individual protein molecules. So long as the average structure remains reasonable, the proteins move in a native-like fashion as dictated by the original force field. To validate this approach, we have used the data from solid-state NMR spectroscopy, which is the orthogonal experimental technique uniquely sensitive to protein local dynamics. The new method has been tested on the well-established model protein, ubiquitin. The ensemble-restrained MD simulations produced lower crystallographic R factors than conventional simulations; they also led to more accurate predictions for crystallographic temperature factors, solid-state chemical shifts, and backbone order parameters. The predictions for (15) N R1 relaxation rates are at least as accurate as those obtained from conventional simulations. Taken together, these results suggest that the presented trajectories may be among the most realistic protein MD simulations ever reported. In this context, the ensemble restraints based on high-resolution crystallographic data can be viewed as protein-specific empirical corrections to the standard force fields.

Subtle dynamics of holo glutamine binding protein revealed with a rigid paramagnetic probe

Bacterial periplasmic binding proteins (PBPs) are involved in the translocation of small molecules in the periplasm. To unload, the two domains of a PBP open up, allowing the ligand to exit. However, it is not clear whether there are dynamics near the binding site which can facilitate the rapid dissociation of a ligand. To visualize such dynamics, we utilized paramagnetic relaxation enhancement (PRE) NMR and introduced a rigid paramagnetic probe to a PBP, glutamine-binding protein (QBP) with its cognate ligand bound. A paramagnetic Cu(II) ion is sandwiched between an engineered di-histidine motif at a helix and an NTA capping molecule. The afforded paramagnetic probe is so rigid that PRE values calculated from a single structure of holo QBP largely agree with the observed values. The remaining PRE discrepancies, however, manifest dynamics of a loop in the opposite domain from the paramagnetic probe. This loop packs against the glutamine ligand in the holo QBP and undergoes fluctuations upon ligand dissociation, as assessed by steered molecular dynamics simulations. As such, the loop dynamics, occurring for a small population in nanosecond to microsecond time scale, may be related to the ligand dissociation process. The rigid paramagnetic probe described herein can be grafted to other protein systems for structure and dynamics studies.

Domain cooperativity in multidomain proteins: what can we learn from molecular alignment in anisotropic media?

Many proteins have modular design with multiple globular domains connected via flexible linkers. As a simple model of such system, we study a tandem construct consisting of two identical SH3 domains and a variable-length Gly/Ser linker. When the linker is short, this construct represents a dumbbell-shaped molecule with limited amount of domain-domain mobility. Due to its elongated shape, this molecule efficiently aligns in steric alignment media. As the length of the linker increases, the two domains become effectively uncoupled and begin to behave as independent entities. Consequently, their degree of alignment drops, approaching that found in the (near-spherical) isolated SH3 domains. To model the dependence of alignment parameters on the length of the interdomain linker, we have generated in silico a series of conformational ensembles representing SH3 tandems with different linker length. These ensembles were subsequently used as input for alignment prediction software PALES. The predicted alignment tensors were compared with the results of experimental measurements using a series of tandem-SH3 samples in PEG/hexanol alignment media. This comparison broadly confirmed the expected trends. At the same time, it has been found that the isolated SH3 domain aligns much stronger than expected. This finding can be attributed to complex morphology of the PEG/hexanol media and/or to weak site-specific interactions between the protein and the media. In the latter case, there are strong indications that electrostatic interactions may play a role. The fact that PEG/hexanol does not behave as a simple steric media should serve as a caution for studies that use PALES as a quantitative prediction tool (especially for disordered proteins). Further progress in this area depends on our ability to accurately model the anisotropic media and its site-specific interactions with protein molecules. Once this ability is improved, it should be possible to use the alignment parameters as a measure of domain-domain cooperativity, thus identifying the situations where two domains transiently interact with each other or become coupled through a partially structured linker.

Assessing the accuracy of protein structures by quantum mechanical computations of 13C(alpha) chemical shifts

Two major techniques have been used to determine the three-dimensional structures of proteins: X-ray diffraction and NMR spectroscopy. In particular, the validation of NMR-derived protein structures is one of the most challenging problems in NMR spectroscopy. Therefore, researchers have proposed a plethora of methods to determine the accuracy and reliability of protein structures. Despite these proposals, there is a growing need for more sophisticated, physics-based structure validation methods. This approach will enable us to (a) characterize the "quality" of the NMR-derived ensemble as a whole by a single parameter, (b) unambiguously identify flaws in the sequence at a residue level, and (c) provide precise information, such as sets of backbone and side-chain torsional angles, that we can use to detect local flaws. Rather than reviewing all of the existing validation methods, this Account describes the contributions of our research group toward a solution of the long-standing problem of both global and local structure validation of NMR-derived protein structures. We emphasize a recently introduced physics-based methodology that makes use of observed and computed (13)C(alpha) chemical shifts (at the density functional theory (DFT) level of theory) for an accurate validation of protein structures in solution and in crystals. By assessing the ability of computed (13)C(alpha) chemical shifts to reproduce observed (13)C(alpha) chemical shifts of a single structure or ensemble of structures in solution and in crystals, we accomplish a global validation by using the conformationally averaged root-mean-square deviation, ca-rmsd, as a scoring function. In addition, the method enables us to provide local validation by identifying a set of individual amino acid conformations for which the computed and observed (13)C(alpha) chemical shifts do not agree within a certain error range and may represent a nonreliable fold of the protein model. Although it is computationally intensive, our validation method has several advantages, which we illustrate through a series of applications. This method makes use of the (13)C(alpha) chemical shifts, not shielding, that are ubiquitous to proteins and can be computed precisely from the phi, psi, and chi torsional angles. There is no need for a priori knowledge of the oligomeric state of the protein, and no knowledge-based information or additional NMR data are required. The primary limitation at this point is the computational cost of such calculations. However, we anticipate that enhancements in the speed of calculating these chemical shifts coupled with the ever-increasing computational power should soon make this a standard method accessible to the general NMR community.

Structure discrimination for the C-terminal domain of Escherichia coli trigger factor in solution

NMR measurements can give important information on solution structure, without the necessity for a full-scale solution structure determination. The C-terminal protein binding domain of the ribosome-associated chaperone protein trigger factor is composed of non-contiguous parts of the polypeptide chain, with an interpolated prolyl isomerase domain. A construct of the C-terminal domain of Escherichia coli trigger factor containing residues 113-149 and 247-432, joined by a Gly-Ser-Gly-Ser linker, is well folded and gives excellent NMR spectra in solution. We have used NMR measurements on this construct, and on a longer construct that includes the prolyl isomerase domain, to distinguish between two possible structures for the C-terminal domain of trigger factor, and to assess the behavior of the trigger factor C-terminal domain in solution. Two X-ray crystal structures, of intact trigger factor from E. coli (Ferbitz et al., Nature 431:590-596, 2004), and of a truncated trigger factor from Vibrio cholerae (Ludlam et al., Proc Natl Acad Sci USA 101:13436-13441, 2004) showed significant differences in the structure of the C-terminal domain, such that the two structures could not be superimposed. We show using NMR chemical shifts and long range nuclear Overhauser effects that the secondary and tertiary structure of the E. coli C-terminal domain in solution is consistent with the crystal structure of the E. coli trigger factor and not with the V. cholerae protein. Given the similarity of the amino acid sequences of the E. coli and V. cholerae proteins, it appears likely that the structure of the V. cholerae protein has been distorted as a result of truncation of a 44-amino acid segment at the C-terminus. Analysis of residual dipolar coupling measurements shows that the overall topology of the solution structure is completely inconsistent with both structures. Dynamics analysis of the C-terminal domain using T1, T2 and heteronuclear NOE parameters show that the protein is overall rather flexible. These results indicate that the structure of this domain in solution resembles the X-ray crystal structure of the E. coli protein in secondary structure and at least some tertiary contacts, but that the overall topology differs in solution, probably due to structural fluctuation.

Predicting 13Calpha chemical shifts for validation of protein structures

The (13)C(alpha) chemical shifts for 16,299 residues from 213 conformations of four proteins (experimentally determined by X-ray crystallography and Nuclear Magnetic Resonance methods) were computed by using a combination of approaches that includes, but is not limited to, the use of density functional theory. Initially, a validation test of this methodology was carried out by a detailed examination of the correlation between computed and observed (13)C(alpha) chemical shifts of 10,564 (of the 16,299) residues from 139 conformations of the human protein ubiquitin. The results of this validation test on ubiquitin show agreement with conclusions derived from computation of the chemical shifts at the ab initio Hartree-Fock level. Further, application of this methodology to 5,735 residues from 74 conformations of the three remaining proteins that differ in their number of amino acid residues, sequence and three-dimensional structure, together with a new scoring function, namely the conformationally averaged root-mean-square-deviation, enables us to: (a) offer a criterion for an accurate assessment of the quality of NMR-derived protein conformations; (b) examine whether X-ray or NMR-solved structures are better representations of the observed (13)C(alpha) chemical shifts in solution; (c) provide evidence indicating that the proposed methodology is more accurate than automated predictors for validation of protein structures; (d) shed light as to whether the agreement between computed and observed (13)C(alpha) chemical shifts is influenced by the identity of an amino acid residue or its location in the sequence; and (e) provide evidence confirming the presence of dynamics for proteins in solution, and hence showing that an ensemble of conformations is a better representation of the structure in solution than any single conformation.

Methyl rotation barriers in proteins from 2H relaxation data. Implications for protein structure

Side-chain 2H and backbone 15N relaxation data have been collected at multiple temperatures in the samples of the SH3 domain from alpha-spectrin. Combined analyses of the data allowed for determination of the temperature-dependent correlation times tauf characterizing fast methyl motion. Molecular dynamics simulations confirmed that tauf are dominated by methyl rotation; the corresponding activation energies approximate methyl rotation barriers. For 33 methyl groups in the alpha-spectrin SH3 domain the average barrier height was thus determined to be 2.8 +/- 0.9 kcal/mol. This value is deemed representative of the "fluid" hydrophobic protein core where some barriers are increased and others are lowered because of the contacts with surrounding atoms, but there is no local order that could produce systematically higher (lower) barriers. For comparison, the MD simulation predicts the average barrier of 3.1 kcal/mol (calculated via the potential of mean force) or 3.4-3.5 kcal/mol (rigid barriers after appropriate averaging over multiple MD snapshots). The latter result prompted us to investigate rigid methyl rotation barriers in a series of NMR structures from the Protein Databank. In most cases the barriers proved to be higher than expected, 4-6 kcal/mol. To a certain degree, this is caused by tight packing of the side chains in the NMR structures and stems from the structure calculation procedure where the coordinates are first annealed toward the temperature of 0 K and then subjected to energy minimization. In several cases the barriers >10 kcal/mol are indicative of van der Waals violations. The notable exceptions are (i) the structures solved using the GROMOS force field where tight methyl packing is avoided (3.0-3.6 kcal/mol) and (ii) the structure solved by means of the dynamic ensemble refinement method (Lindorff-Larsen, K.; Best, R. B.; DePristo, M. A.; Dobson, C. M.; Vendruscolo, M. Nature 2005, 433, 128) (3.5 kcal/mol). These results demonstrate that methyl rotation barriers, derived from the experiments that are traditionally associated with studies of protein dynamics, can be also used in the context of structural work. This is particularly interesting in view of the recent efforts to incorporate dynamics data in the process of protein structure elucidation.

Weak alignment NMR: a hawk-eyed view of biomolecular structure

Imposing a very slight deviation from the isotropic random distribution of macromolecules in solution in an NMR sample tube permits the measurement of residual internuclear dipolar couplings (RDCs). Such interactions are very sensitive functions of the time-averaged orientation of the corresponding internuclear vectors and thereby offer highly precise structural information. In recent years, advances have been made both in the technology to measure RDCs and in the computational procedures that integrate this information in the structure determination process. The exceptional precision with which RDCs can be measured under weakly aligned conditions is also starting to reveal the mostly, but not universally, subtle effects of internal protein dynamics. Importantly, RDCs potentially can reveal motions taking place on a timescale slower than rotational diffusion and analysis is uniquely sensitive to the direction of motion, not just its amplitude.