Protein structure elucidation from NMR proton densities

Automated structure determination from NMR spectra

Three-dimensional structures of proteins in solution can be calculated on the basis of conformational restraints derived from NMR measurements. This chapter gives an overview of the computational methods for NMR protein structure analysis highlighting recent automated methods for the assignment of NMR spectra, the collection of conformational restraints, and the structure calculation.

AssignFit: a program for simultaneous assignment and structure refinement from solid-state NMR spectra

AssignFit is a computer program developed within the XPLOR-NIH package for the assignment of dipolar coupling (DC) and chemical shift anisotropy (CSA) restraints derived from the solid-state NMR spectra of protein samples with uniaxial order. The method is based on minimizing the difference between experimentally observed solid-state NMR spectra and the frequencies back calculated from a structural model. Starting with a structural model and a set of DC and CSA restraints grouped only by amino acid type, as would be obtained by selective isotopic labeling, AssignFit generates all of the possible assignment permutations and calculates the corresponding atomic coordinates oriented in the alignment frame, together with the associated set of NMR frequencies, which are then compared with the experimental data for best fit. Incorporation of AssignFit in a simulated annealing refinement cycle provides an approach for simultaneous assignment and structure refinement (SASR) of proteins from solid-state NMR orientation restraints. The methods are demonstrated with data from two integral membrane proteins, one α-helical and one β-barrel, embedded in phospholipid bilayer membranes.

A Bayesian approach for determining protein side-chain rotamer conformations using unassigned NOE data

A major bottleneck in protein structure determination via nuclear magnetic resonance (NMR) is the lengthy and laborious process of assigning resonances and nuclear Overhauser effect (NOE) cross peaks. Recent studies have shown that accurate backbone folds can be determined using sparse NMR data, such as residual dipolar couplings (RDCs) or backbone chemical shifts. This opens a question of whether we can also determine the accurate protein side-chain conformations using sparse or unassigned NMR data. We attack this question by using unassigned nuclear Overhauser effect spectroscopy (NOESY) data, which records the through-space dipolar interactions between protons nearby in three-dimensional (3D) space. We propose a Bayesian approach with a Markov random field (MRF) model to integrate the likelihood function derived from observed experimental data, with prior information (i.e., empirical molecular mechanics energies) about the protein structures. We unify the side-chain structure prediction problem with the side-chain structure determination problem using unassigned NMR data, and apply the deterministic dead-end elimination (DEE) and A* search algorithms to provably find the global optimum solution that maximizes the posterior probability. We employ a Hausdorff-based measure to derive the likelihood of a rotamer or a pairwise rotamer interaction from unassigned NOESY data. In addition, we apply a systematic and rigorous approach to estimate the experimental noise in NMR data, which also determines the weighting factor of the data term in the scoring function derived from the Bayesian framework. We tested our approach on real NMR data of three proteins: the FF Domain 2 of human transcription elongation factor CA150 (FF2), the B1 domain of Protein G (GB1), and human ubiquitin. The promising results indicate that our algorithm can be applied in high-resolution protein structure determination. Since our approach does not require any NOE assignment, it can accelerate the NMR structure determination process.

Protein side-chain resonance assignment and NOE assignment using RDC-defined backbones without TOCSY data

One bottleneck in NMR structure determination lies in the laborious and time-consuming process of side-chain resonance and NOE assignments. Compared to the well-studied backbone resonance assignment problem, automated side-chain resonance and NOE assignments are relatively less explored. Most NOE assignment algorithms require nearly complete side-chain resonance assignments from a series of through-bond experiments such as HCCH-TOCSY or HCCCONH. Unfortunately, these TOCSY experiments perform poorly on large proteins. To overcome this deficiency, we present a novel algorithm, called NASCA: (NOE Assignment and Side-Chain Assignment), to automate both side-chain resonance and NOE assignments and to perform high-resolution protein structure determination in the absence of any explicit through-bond experiment to facilitate side-chain resonance assignment, such as HCCH-TOCSY. After casting the assignment problem into a Markov Random Field (MRF), NASCA: extends and applies combinatorial protein design algorithms to compute optimal assignments that best interpret the NMR data. The MRF captures the contact map information of the protein derived from NOESY spectra, exploits the backbone structural information determined by RDCs, and considers all possible side-chain rotamers. The complexity of the combinatorial search is reduced by using a dead-end elimination (DEE) algorithm, which prunes side-chain resonance assignments that are provably not part of the optimal solution. Then an A* search algorithm is employed to find a set of optimal side-chain resonance assignments that best fit the NMR data. These side-chain resonance assignments are then used to resolve the NOE assignment ambiguity and compute high-resolution protein structures. Tests on five proteins show that NASCA: assigns resonances for more than 90% of side-chain protons, and achieves about 80% correct assignments. The final structures computed using the NOE distance restraints assigned by NASCA: have backbone RMSD 0.8-1.5 Å from the reference structures determined by traditional NMR approaches.

Advances in automated NMR protein structure determination

Around half of all protein structures solved nowadays using solution-state nuclear magnetic resonance (NMR) spectroscopy have been because of automated data analysis. The pervasiveness of computational approaches in general hides, however, a more nuanced view in which the full variety and richness of the field appears. This review is structured around a comparison of methods associated with three NMR observables: classical nuclear Overhauser effect (NOE) constraint gathering in contrast with more recent chemical shift and residual dipole coupling (RDC) based protocols. In each case, the emphasis is placed on the latest research, covering mainly the past 5 years. By describing both general concepts and representative programs, the objective is to map out a field in which--through the very profusion of approaches--it is all too easy to lose one's bearings.

Direct methods and residue type specific isotope labeling in NMR structure determination and model-driven sequential assignment

Direct methods in NMR based structure determination start from an unassigned ensemble of unconnected gaseous hydrogen atoms. Under favorable conditions they can produce low resolution structures of proteins. Usually a prohibitively large number of NOEs is required, to solve a protein structure ab-initio, but even with a much smaller set of distance restraints low resolution models can be obtained which resemble a protein fold. One problem is that at such low resolution and in the absence of a force field it is impossible to distinguish the correct protein fold from its mirror image. In a hybrid approach these ambiguous models have the potential to aid in the process of sequential backbone chemical shift assignment when (13)C(beta) and (13)C' shifts are not available for sensitivity reasons. Regardless of the overall fold they enhance the information content of the NOE spectra. These, combined with residue specific labeling and minimal triple-resonance data using (13)C(alpha) connectivity can provide almost complete sequential assignment. Strategies for residue type specific labeling with customized isotope labeling patterns are of great advantage in this context. Furthermore, this approach is to some extent error-tolerant with respect to data incompleteness, limited precision of the peak picking, and structural errors caused by misassignment of NOEs.

Automated structure determination from NMR spectra

Automated methods for protein structure determination by NMR have increasingly gained acceptance and are now widely used for the automated assignment of distance restraints and the calculation of three-dimensional structures. This review gives an overview of the techniques for automated protein structure analysis by NMR, including both NOE-based approaches and methods relying on other experimental data such as residual dipolar couplings and chemical shifts, and presents the FLYA algorithm for the fully automated NMR structure determination of proteins that is suitable to substitute all manual spectra analysis and thus overcomes a major efficiency limitation of the NMR method for protein structure determination.

Sequence specific resonance assignment via Multicanonical Monte Carlo search using an ABACUS approach

ABACUS [Grishaev et al. (2005) Proteins 61:36-43] is a novel protocol for automated protein structure determination via NMR. ABACUS starts from molecular fragments defined by unassigned J-coupled spin-systems and involves a Monte Carlo stochastic search in assignment space, probabilistic sequence selection, and assembly of fragments into structures that are used to guide the stochastic search. Here, we report further development of the two main algorithms that increase the flexibility and robustness of the method. Performance of the BACUS [Grishaev and Llinás (2004) J Biomol NMR 28:1-101] algorithm was significantly improved through use of sequential connectivities available from through-bond correlated 3D-NMR experiments, and a new set of likelihood probabilities derived from a database of 56 ultra high resolution X-ray structures. A Multicanonical Monte Carlo procedure, Fragment Monte Carlo (FMC), was developed for sequence-specific assignment of spin-systems. It relies on an enhanced assignment sampling and provides the uncertainty of assignments in a quantitative manner. The efficiency of the protocol was validated on data from four proteins of between 68-116 residues, yielding 100% accuracy in sequence specific assignment of backbone and side chain resonances.

Deuterated protein folds obtained directly from unassigned nuclear overhauser effect data

We demonstrate the feasibility of determining the global fold of a highly deuterated protein from unassigned experimental NMR nuclear Overhauser effect (NOE) data only. The method relies on the calculation of a spatial configuration of covalently unconnected protons-a "cloud"-directly from unassigned distance restraints derived from 13C- and 15N-edited NOESY spectra. Each proton in the cloud, labeled by its chemical shift and that of the directly bound 13C or 15N, is subsequently mapped to specific atoms in the protein. This is achieved via graph-theoretical protocols that search for connectivities in graphs that encode the structural information within the cloud. The peptidyl HN chain is traced by seeking for all possible routes and selecting the one that yields the minimal sum of sequential distances. Complete proton identification in the cloud is achieved by linking the side-chain protons to proximal main-chain HNs via bipartite graph matching. The identified protons automatically yield the NOE assignments, which in turn are used for structure calculation with RosettaNMR, a protocol that incorporates structural bias derived from protein databases. The method, named Sparse-Constraint CLOUDS, was applied to experimental NOESY data on the 58-residue Z domain of staphylococcal protein A. The generated structures are of similar accuracy to those previously reported, which were derived via a conventional approach involving a larger NMR data set. Additional tests were performed on seven reported protein structures of various folds, using restraint lists simulated from the known atomic coordinates.

ABACUS, a direct method for protein NMR structure computation via assembly of fragments

The ABACUS algorithm obtains the protein NMR structure from unassigned NOESY distance restraints. ABACUS works as an integrated approach that uses the complete set of available NMR experimental information in parallel and yields spin system typing, NOE spin pair identities, sequence specific resonance assignments, and protein structure, all at once. The protocol starts from unassigned molecular fragments (including single amino acid spin systems) derived from triple-resonance (1)H/(13)C/(15)N NMR experiments. Identifications of connected spin systems and NOEs precede the full sequence specific resonance assignments. The latter are obtained iteratively via Monte Carlo-Metropolis and/or probabilistic sequence selections, molecular dynamics structure computation and BACUS filtering (A. Grishaev and M. Llinás, J Biomol NMR 2004;28:1-10). ABACUS starts from scratch, without the requirement of an initial approximate structure, and improves iteratively the NOE identities in a self-consistent fashion. The procedure was run as a blind test on data recorded on mth1743, a 70-amino acid genomic protein from M. thermoautotrophicum. It converges to a structure in ca. 15 cycles of computation on a 3-GHz processor PC. The calculated structures are very similar to the ones obtained via conventional methods (1.22 A backbone RMSD). The success of ABACUS on mth1743 further validates BACUS as a NOESY identification protocol.

Estimation of protein secondary structure content directly from NMR spectra using an improved empirical correlation with averaged chemical shift

We have recently shown that the averaged chemical shift (ACS) of a nucleus in the protein backbone correlates well empirically to its secondary structure content (SSC). This allows the estimation of SSC directly from the NMR spectrum without the time intensive process of chemical shift assignment. Here, we present an empirical correlation that accounts both for contributions to the relevant protein and chemical shift databases made subsequent to the original analysis, and for missing or inconsistently referenced resonances. Our results affirm that this method provides a significant tool for initial structural prediction from NMR data prior to complete chemical shift assignment.

The fumarate sensor DcuS: progress in rapid protein fold elucidation by combining protein structure prediction methods with NMR spectroscopy

We illustrate how moderate resolution protein structures can be rapidly obtained by interlinking computational prediction methodologies with un- or partially assigned NMR data. To facilitate the application of our recently described method of ranking and subsequent refining alternative structural models using unassigned NMR data [Proc. Natl. Acad. Sci. USA 100 (2003) 15404] for such "structural genomics"-type experiments it is combined with protein models from several prediction techniques, enhanced to utilize partial assignments, and applied on a protein with an unknown structure and fold. From the original NMR spectra obtained for the 140 residue fumarate sensor DcuS, 1100 1H, 13C, and 15N chemical shift signals, 3000 1H-1H NOESY cross peak intensities, and 209 backbone residual dipolar couplings were extracted and used to rank models produced by de novo structure prediction and comparative modeling methods. The ranking proceeds in two steps: first, an optimal assignment of the NMR peaks to atoms is found for each model independently, and second, the models are ranked based on the consistency between the NMR data and the model assuming these optimal assignments. The low-resolution model selected using this ranking procedure had the correct overall fold and a global backbone RMSD of 6.0 angstrom, and was subsequently refined to 3.7 angstrom RMSD. With the incorporation of a small number of NOE and residual dipolar coupling constraints available very early in the traditional spectral assignment process, a model with an RMSD of 2.8 angstrom could rapidly be built. The ability to generate moderate resolution models within days of NMR data collection should facilitate large scale NMR structure determination efforts.

Protein Structure Elucidation from Minimal NMR Data: The CLOUDS Approach

In this chapter we review automated methods of protein NMR data analysis and expand on the assignment-independent CLOUDS approach. As presented, given a set of reliable NOEs it is feasible to derive a spatial H-atom distribution that provides a low-resolution image of the protein structure. In order to generate such a list of unambiguous NOEs, a probabilistic assessment of the NOE identities (in terms of frequency-labeled H-atom sources) was developed on the basis of Bayesian inference. The methodology, encompassing programs SPI and BACUS, provides a list of "clean" NOEs that does not hinge on prior knowledge of sequence-specific resonance assignments or a preliminary structural model. As such, the combined SPI/BACUS approach, intrinsically adaptable to include 13C- and/or 15N-edited experiments, affords a useful tool for the analysis of NMR data irrespective of whether the adopted structure calculation protocol is assignment-dependent.

BACUS: A Bayesian protocol for the identification of protein NOESY spectra via unassigned spin systems

NMR frequency assignments are usually considered a prerequisite for the analysis of NOESY spectra, in turn required for the calculation of biomolecular structures. In contrast, as we propose here, relatively high numbers of unambiguous NOE identities can be consistently achieved in an automated manner by relying only on grouping resonances into connected spin systems. To achieve this goal, we have developed for proteins two protocols, SPI and BACUS, based on Bayesian inference. SPI (Grishaev and Llinás, 2002c) produces a list of the (1)H resonance frequencies from homo- and hetero-nuclear multidimensional spectra, grouped into effective spin systems. BACUS automatically establishes probabilistic identities of NOESY cross-peaks in terms of the chemical shifts provided by SPI. BACUS requires neither assignment of resonances nor an initial structural model. It successfully copes with chemical shift overlap and does so without cycling through 3D structure calculations. The method exploits the self-consistency of the NOESY graph by taking advantage of a network of J- as well as NOE-connected "reporter" protons sorted via SPI. BACUS was validated by tests on experimental NOESY data recorded for the col 2 and kringle 2 domains.

Rapid protein fold determination using unassigned NMR data

Experimental structure determination by x-ray crystallography and NMR spectroscopy is slow and time-consuming compared with the rate at which new protein sequences are being identified. NMR spectroscopy has the advantage of rapidly providing the structurally relevant information in the form of unassigned chemical shifts (CSs), intensities of NOESY crosspeaks [nuclear Overhauser effects (NOEs)], and residual dipolar couplings (RDCs), but use of these data are limited by the time and effort needed to assign individual resonances to specific atoms. Here, we develop a method for generating low-resolution protein structures by using unassigned NMR data that relies on the de novo protein structure prediction algorithm, rosetta [Simons, K. T., Kooperberg, C., Huang, E. & Baker, D. (1997) J. Mol. Biol. 268, 209-225] and a Monte Carlo procedure that searches for the assignment of resonances to atoms that produces the best fit of the experimental NMR data to a candidate 3D structure. A large ensemble of models is generated from sequence information alone by using rosetta, an optimal assignment is identified for each model, and the models are then ranked based on their fit with the NMR data assuming the identified assignments. The method was tested on nine protein sequences between 56 and 140 amino acids and published CS, NOE, and RDC data. The procedure yielded models with rms deviations between 3 and 6 A, and, in four of the nine cases, the partial assignments obtained by the method could be used to refine the structures to high resolution (0.6-1.8 A) by repeated cycles of structure generation guided by the partial assignments, followed by reassignment using the newly generated models.

Information content of molecular structures

For a completely enumerated set of conformers of a macromolecule or for exhaustive lattice walks of model polymers it is straightforward to use Shannon information theory to deduce the information content of the ensemble. It is also practicable to develop numerical measures of the information content of sets of exact distance constraints applied to specific conformational ensembles. We examine the effects of experimental uncertainties by considering "noisy" constraints. The introduction of noise requires additional assumptions about noise distribution and conformational clustering protocols that make the problem of measuring information content more complex. We make use of a standard concept in communication theory, the "noise sphere," to link uncertainty in measurements to information loss. Most of our numerical results are derived from two-dimensional lattice ensembles. Expressing results in terms of information per degree of freedom removes almost all of the chain length dependence. We also explore off-lattice polyalanine chains that yield surprisingly similar results.

Functional sites in protein families uncovered via an objective and automated graph theoretic approach

We report a method for detection of recurring side-chain patterns (DRESPAT) using an unbiased and automated graph theoretic approach. We first list all structural patterns as sub-graphs where the protein is represented as a graph. The patterns from proteins are compared pair-wise to detect patterns common to a protein pair based on content and geometry criteria. The recurring pattern is then detected using an automated search algorithm from the all-against-all pair-wise comparison data of proteins. Intra-protein pattern comparison data are used to enable detection of patterns recurring within a protein. A method has been proposed for empirical calculation of statistical significance of recurring pattern. The method was tested on 17 protein sets of varying size, composed of non-redundant representatives from SCOP superfamilies. Recurring patterns in serine proteases, cysteine proteases, lipases, cupredoxin, ferredoxin, ferritin, cytochrome c, aspartoyl proteases, peroxidases, phospholipase A2, endonuclease, SH3 domain, EF-hand and lectins show additional residues conserved in the vicinity of the known functional sites. On the basis of the recurring patterns in ferritin, EF-hand and lectins, we could separate proteins or domains that are structurally similar yet different in metal ion-binding characteristics. In addition, novel recurring patterns were observed in glutathione-S-transferase, phospholipase A2 and ferredoxin with potential structural/functional roles. The results are discussed in relation to the known functional sites in each family. Between 2000 and 50,000 patterns were enumerated from each protein with between ten and 500 patterns detected as common to an evolutionarily related protein pair. Our results show that unbiased extraction of functional site pattern is not feasible from an evolutionarily related protein pair but is feasible from protein sets comprising five or more proteins. The DRESPAT method does not require a user-defined pattern, size or location of the pattern and therefore, has the potential to uncover new functional sites in protein families.

MONTE: An automated Monte Carlo based approach to nuclear magnetic resonance assignment of proteins

A general-purpose Monte Carlo assignment program has been developed to aid in the assignment of NMR resonances from proteins. By virtue of its flexible data requirements the program is capable of obtaining assignments of both heavily deuterated and fully protonated proteins. A wide variety of source data, such as inter-residue scalar connectivity, inter-residue dipolar (NOE) connectivity, and residue specific information, can be utilized in the assignment process. The program can also use known assignments from one form of a protein to facilitate the assignment of another form of the protein. This attribute is useful for assigning protein-ligand complexes when the assignments of the unliganded protein are known. The program can be also be used as an interactive research tool to assist in the choice of additional experimental data to facilitate completion of assignments. The assignment of a deuterated 45 kDa homodimeric Glutathione-S-transferase illustrates the principal features of the program.

Sorting signals from protein NMR spectra: SPI, a Bayesian protocol for uncovering spin systems

Grouping of spectral peaks into J-connected spin systems is essential in the analysis of macromolecular NMR data as it provides the basis for disentangling chemical shift degeneracies. It is a mandatory step before resonance and NOESY cross-peak identities can be established. We have developed SPI, a computational protocol that scrutinizes peak lists from homo- and hetero-nuclear multidimensional NMR spectra and progressively assembles sets of resonances into consensus J- and/or NOE-connected spin systems. SPI estimates the likelihood of nuclear spin resonances appearing at defined frequencies given sets of cross-peaks measured from multi-dimensional experiments. It quantifies spin system matching probabilities via Bayesian inference. The protocol takes advantage of redundancies in the number of connectivities revealed by suites of diverse NMR experiments, systematically tracking the adequacy of each grouping hypothesis. SPI was tested on 2D homonuclear and 2D/3D(15)N-edited data recorded from two protein modules, the col 2 domain of matrix metalloproteinase-2 (MMP-2) and the kringle 2 domain of plasminogen, of 60 and 83 amino acid residues, respectively. For these protein domains SPI identifies approximately 95% unambiguous resonance frequencies, a relatively good performance vis-à-vis the reported 'manual' (interactive) analyses. Abbreviations and Acronyms: SPI, SPin Identification; BMRB, BioMagResBank (Madison, WI).

CLOUDS, a protocol for deriving a molecular proton density via NMR

We demonstrate the feasibility of computing realistic spatial proton distributions for proteins in solution from experimental NMR nuclear Overhauser effect data only and with minimal assignments. The method, CLOUDS, relies on precise and abundant interproton distance restraints calculated via a relaxation matrix analysis of sets of experimental nuclear Overhauser effect spectroscopy crosspeaks. The MIDGE protocol was adapted for this purpose. A gas of unassigned, unconnected H atoms is condensed into a structured proton distribution (cloud) via a molecular dynamics simulated-annealing scheme in which the internuclear distances and van der Waals repulsive terms are the only active restraints. Proton densities are generated by combining a large number of such clouds, each computed from a different trajectory. After filtering by reference to the cloud closest to the mean, a minimal dispersion proton density (foc) is identified. The latter affords a quasi-continuous hydrogen-only probability distribution that conveys immediate information on the protein surface topology (grooves, protrusions, potential binding site cavities, etc.), directly related to the molecular structure. Feasibility of the method was tested on NMR data measured on two globular protein domains of low regular secondary structure content, the col 2 domain of human matrix metalloproteinase-2 and the kringle 2 domain of human plasminogen, of 60 and 83 amino acid residues, respectively.