Structure determination of symmetric homo-oligomers by a complete search of symmetry configuration space, using NMR restraints and van der Waals packing

Fat SIRAH: Coarse-Grained Phospholipids To Explore Membrane-Protein Dynamics

The capability to handle highly heterogeneous molecular assemblies in a consistent manner is among the greatest challenges faced when deriving simulation parameters. This is particularly the case for coarse-grained (CG) simulations in which chemical functional groups are lumped into effective interaction centers for which transferability between different chemical environments is not guaranteed. Here, we introduce the parametrization of a set of CG phospholipids compatible with the latest version of the SIRAH force field for proteins. The newly introduced lipid species include different acylic chain lengths and partial unsaturation, as well as polar and acidic head groups that show a very good reproduction of structural membrane determinants, such as areas per lipid, thickness, order parameter, etc., and their dependence with temperature. Simulation of membrane proteins showed unprecedented accuracy in the unbiased description of the thickness-dependent membrane-protein orientation in systems where this information is experimentally available (namely, the SarcoEndoplasmic Reticulum Calcium-SERCA-pump and its regulator Phospholamban). The interactions that lead to this faithful reproduction can be traced down to the single amino acid-lipid interaction level and show full agreement with biochemical data present in the literature. Finally, the present parametrization is implemented in the GROMACS and AMBER simulation packages facilitating its use by a wide portion of the biocomputing community.

An Exhaustive Search Algorithm to Aid NMR-Based Structure Determination of Rotationally Symmetric Transmembrane Oligomers

Nuclear magnetic resonance (NMR) has been an important source of structural restraints for solving structures of oligomeric transmembrane domains (TMDs) of cell surface receptors and viral membrane proteins. In NMR studies, oligomers are assembled using inter-protomer distance restraints. But, for oligomers that are higher than dimer, these distance restraints all have two-fold directional ambiguity, and resolving such ambiguity often requires time-consuming trial-and-error calculations using restrained molecular dynamics (MD) with simulated annealing (SA). We report an Exhaustive Search algorithm for Symmetric Oligomer (ExSSO), which can perform near-complete search of the symmetric conformational space in a very short time. In this approach, the predetermined protomer model is subject to full angular and spatial search within the symmetry space. This approach, which can be applied to any rotationally symmetric oligomers, was validated using the structures of the Fas death receptor, the HIV-1 gp41 fusion protein, the influenza proton channel, and the MCU pore. The algorithm is able to generate approximate oligomer solutions quickly as initial inputs for further refinement using the MD/SA method.

Principles and Overview of Sampling Methods for Modeling Macromolecular Structure and Dynamics

Investigation of macromolecular structure and dynamics is fundamental to understanding how macromolecules carry out their functions in the cell. Significant advances have been made toward this end in silico, with a growing number of computational methods proposed yearly to study and simulate various aspects of macromolecular structure and dynamics. This review aims to provide an overview of recent advances, focusing primarily on methods proposed for exploring the structure space of macromolecules in isolation and in assemblies for the purpose of characterizing equilibrium structure and dynamics. In addition to surveying recent applications that showcase current capabilities of computational methods, this review highlights state-of-the-art algorithmic techniques proposed to overcome challenges posed in silico by the disparate spatial and time scales accessed by dynamic macromolecules. This review is not meant to be exhaustive, as such an endeavor is impossible, but rather aims to balance breadth and depth of strategies for modeling macromolecular structure and dynamics for a broad audience of novices and experts.

Accurate Determination of Conformational Transitions in Oligomeric Membrane Proteins

The structural dynamics governing collective motions in oligomeric membrane proteins play key roles in vital biomolecular processes at cellular membranes. In this study, we present a structural refinement approach that combines solid-state NMR experiments and molecular simulations to accurately describe concerted conformational transitions identifying the overall structural, dynamical, and topological states of oligomeric membrane proteins. The accuracy of the structural ensembles generated with this method is shown to reach the statistical error limit, and is further demonstrated by correctly reproducing orthogonal NMR data. We demonstrate the accuracy of this approach by characterising the pentameric state of phospholamban, a key player in the regulation of calcium uptake in the sarcoplasmic reticulum, and by probing its dynamical activation upon phosphorylation. Our results underline the importance of using an ensemble approach to characterise the conformational transitions that are often responsible for the biological function of oligomeric membrane protein states.

Structure determination of helical filaments by solid-state NMR spectroscopy

The controlled formation of filamentous protein complexes plays a crucial role in many biological systems and represents an emerging paradigm in signal transduction. The mitochondrial antiviral signaling protein (MAVS) is a central signal transduction hub in innate immunity that is activated by a receptor-induced conversion into helical superstructures (filaments) assembled from its globular caspase activation and recruitment domain. Solid-state NMR (ssNMR) spectroscopy has become one of the most powerful techniques for atomic resolution structures of protein fibrils. However, for helical filaments, the determination of the correct symmetry parameters has remained a significant hurdle for any structural technique and could thus far not be precisely derived from ssNMR data. Here, we solved the atomic resolution structure of helical MAVS(CARD) filaments exclusively from ssNMR data. We present a generally applicable approach that systematically explores the helical symmetry space by efficient modeling of the helical structure restrained by interprotomer ssNMR distance restraints. Together with classical automated NMR structure calculation, this allowed us to faithfully determine the symmetry that defines the entire assembly. To validate our structure, we probed the protomer arrangement by solvent paramagnetic resonance enhancement, analysis of chemical shift differences relative to the solution NMR structure of the monomer, and mutagenesis. We provide detailed information on the atomic contacts that determine filament stability and describe mechanistic details on the formation of signaling-competent MAVS filaments from inactive monomers.

Accurate refinement of docked protein complexes using evolutionary information and deep learning

One of the major challenges for protein docking methods is to accurately discriminate native-like structures from false positives. Docking methods are often inaccurate and the results have to be refined and re-ranked to obtain native-like complexes and remove outliers. In a previous work, we introduced AccuRefiner, a machine learning based tool for refining protein-protein complexes. Given a docked complex, the refinement tool produces a small set of refined versions of the input complex, with lower root-mean-square-deviation (RMSD) of atomic positions with respect to the native structure. The method employs a unique ranking tool that accurately predicts the RMSD of docked complexes with respect to the native structure. In this work, we use a deep learning network with a similar set of features and five layers. We show that a properly trained deep learning network can accurately predict the RMSD of a docked complex with 1.40 Å error margin on average, by approximating the complex relationship between a wide set of scoring function terms and the RMSD of a docked structure. The network was trained on 35000 unbound docking complexes generated by RosettaDock. We tested our method on 25 different putative docked complexes produced also by RosettaDock for five proteins that were not included in the training data. The results demonstrate that the high accuracy of the ranking tool enables AccuRefiner to consistently choose the refinement candidates with lower RMSD values compared to the coarsely docked input structures.

Prediction of the structures of helical membrane proteins based on a minimum unfavorable contacts approach

An understanding of structure-function relationships of membrane proteins continues to be a challenging problem, owing to the difficulty in obtaining their structures experimentally. This study suggests a method for modeling membrane protein structures that can be used to generate a reliable initial conformation prior to the use of other approaches for sampling conformations. It involves optimizing the orientation of hydrophilic residues so as to minimize unfavorable contacts with the hydrophobic tails of the lipid bilayer. Starting with the optimized initial conformation for three different proteins modeled based on this method, two independent approaches have been used for sampling the conformational space of the proteins. Both approaches are able to predict structures reasonably close to experimental structures, indicating that the initial structure enables the sampling of conformations that are close to the native structure. Possible improvements in the method for making it broadly applicable to helical membrane proteins are discussed.

An algorithm to enumerate all possible protein conformations verifying a set of distance constraints

BACKGROUND

The determination of protein structures satisfying distance constraints is an important problem in structural biology. Whereas the most common method currently employed is simulated annealing, there have been other methods previously proposed in the literature. Most of them, however, are designed to find one solution only.

RESULTS

In order to explore exhaustively the feasible conformational space, we propose here an interval Branch-and-Prune algorithm (iBP) to solve the Distance Geometry Problem (DGP) associated to protein structure determination. This algorithm is based on a discretization of the problem obtained by recursively constructing a search space having the structure of a tree, and by verifying whether the generated atomic positions are feasible or not by making use of pruning devices. The pruning devices used here are directly related to features of protein conformations.

CONCLUSIONS

We described the new algorithm iBP to generate protein conformations satisfying distance constraints, that would potentially allows a systematic exploration of the conformational space. The algorithm iBP has been applied on three α-helical peptides.

Systematic solution to homo-oligomeric structures determined by NMR

Protein structure determination by NMR has predominantly relied on simulated annealing-based conformational search for a converged fold using primarily distance constraints, including constraints derived from nuclear Overhauser effects, paramagnetic relaxation enhancement, and cysteine crosslinkings. Although there is no guarantee that the converged fold represents the global minimum of the conformational space, it is generally accepted that good convergence is synonymous to the global minimum. Here, we show such a criterion breaks down in the presence of large numbers of ambiguous constraints from NMR experiments on homo-oligomeric protein complexes. A systematic evaluation of the conformational solutions that satisfy the NMR constraints of a trimeric membrane protein, DAGK, reveals 9 distinct folds, including the reported NMR and crystal structures. This result highlights the fundamental limitation of global fold determination for homo-oligomeric proteins using ambiguous distance constraints and provides a systematic solution for exhaustive enumeration of all satisfying solutions.

Stoichiometries and affinities of interacting proteins from concentration series of solution scattering data: decomposition by least squares and quadratic optimization

In studying interacting proteins, complementary insights are provided by analyzing both the association model (the stoichiometry and affinity constants of the intermediate and final complexes) and the quaternary structure of the resulting complexes. Many current methods for analyzing protein interactions either give a binary answer to the question of association and no information about quaternary structure or at best provide only part of the complete picture. Presented here is a method to extract both types of information from X-ray or neutron scattering data for a series of equilibrium mixtures containing the initial components at different concentrations. The method determines the association pathway and constants, along with the scattering curves of the individual members of the mixture, so as to best explain the scattering data for the mixtures. The derived curves then enable reconstruction of the intermediate and final complexes. Using simulated solution scattering data for four hetero-oligomeric complexes with different structures, molecular weights and association models, it is demonstrated that this method accurately determines the simulated association model and scattering profiles for the initial components and complexes. Recognizing that experimental mixtures contain static contaminants and nonspecific complexes with the lowest affinities (inter-particle interference) as well as the desired specific complex(es), a new analytical method is also employed to extend this approach to evaluating the association models and scattering curves in the presence of static contaminants, testing both a nonparticipating monomer and a large homo-oligomeric aggregate. It is demonstrated that the method is robust to both random noise and systematic noise from such contaminants, and the treatment of nonspecific complexes is discussed. Finally, it is shown that this method is applicable over a large range of weak association constants typical of specific but transient protein-protein complexes.

A conservation and biophysics guided stochastic approach to refining docked multimeric proteins

Background

We introduce a protein docking refinement method that accepts complexes consisting of any number of monomeric units. The method uses a scoring function based on a tight coupling between evolutionary conservation, geometry and physico-chemical interactions. Understanding the role of protein complexes in the basic biology of organisms heavily relies on the detection of protein complexes and their structures. Different computational docking methods are developed for this purpose, however, these methods are often not accurate and their results need to be further refined to improve the geometry and the energy of the resulting complexes. Also, despite the fact that complexes in nature often have more than two monomers, most docking methods focus on dimers since the computational complexity increases exponentially due to the addition of monomeric units.

Results

Our results show that the refinement scheme can efficiently handle complexes with more than two monomers by biasing the results towards complexes with native interactions, filtering out false positive results. Our refined complexes have better IRMSDs with respect to the known complexes and lower energies than those initial docked structures.

Conclusions

Evolutionary conservation information allows us to bias our results towards possible functional interfaces, and the probabilistic selection scheme helps us to escape local energy minima. We aim to incorporate our refinement method in a larger framework which also enables docking of multimeric complexes given only monomeric structures.

AN EVOLUTIONARY CONSERVATION-BASED METHOD FOR REFINING AND RERANKING PROTEIN COMPLEX STRUCTURES

Detection of protein complexes and their structures is crucial for understanding their role in the basic biology of organisms. Computational docking methods can provide researchers with a good starting point for the analysis of protein complexes. However, these methods are often not accurate and their results need to be further refined to improve interface packing. In this paper, we introduce a refinement method that incorporates evolutionary information into a novel scoring function by employing Evolutionary Trace (ET)-based scores. Our method also takes Van der Waals interactions into account to avoid atomic clashes in refined structures. We tested our method on docked candidates of eight protein complexes and the results suggest that the proposed scoring function helps bias the search toward complexes with native interactions. We show a strong correlation between evolutionary-conserved residues and correct interface packing. Our refinement method is able to produce structures with better lRMSD (least RMSD) with respect to the known complexes and lower energies than initial docked structures. It also helps to filter out false-positive complexes generated by docking methods, by detecting little or no conserved residues on false interfaces. We believe this method is a step toward better ranking and prediction of protein complexes.

SQUEEZE-E: The Optimal Solution for Molecular Simulations with Periodic Boundary Conditions

In molecular simulations of macromolecules, it is desirable to limit the amount of solvent in the system to avoid spending computational resources on uninteresting solvent-solvent interactions. As a consequence, periodic boundary conditions are commonly used, with a simulation box chosen as small as possible, for a given minimal distance between images. Here, we describe how such a simulation cell can be set up for ensembles, taking into account a priori available or estimable information regarding conformational flexibility. Doing so ensures that any conformation present in the input ensemble will satisfy the distance criterion during the simulation. This helps avoid periodicity artifacts due to conformational changes. The method introduces three new approaches in computational geometry: (1) The first is the derivation of an optimal packing of ensembles, for which the mathematical framework is described. (2) A new method for approximating the α-hull and the contact body for single bodies and ensembles is presented, which is orders of magnitude faster than existing routines, allowing the calculation of packings of large ensembles and/or large bodies. 3. A routine is described for searching a combination of three vectors on a discretized contact body forming a reduced base for a lattice with minimal cell volume. The new algorithms reduce the time required to calculate packings of single bodies from minutes or hours to seconds. The use and efficacy of the method is demonstrated for ensembles obtained from NMR, MD simulations, and elastic network modeling. An implementation of the method has been made available online at http://haddock.chem.uu.nl/services/SQUEEZE/ and has been made available as an option for running simulations through the weNMR GRID MD server at http://haddock.science.uu.nl/enmr/services/GROMACS/main.php .

A geometric arrangement algorithm for structure determination of symmetric protein homo-oligomers from NOEs and RDCs

Nuclear magnetic resonance (NMR) spectroscopy is a primary tool to perform structural studies of proteins in physiologically-relevant solution conditions. Restraints on distances between pairs of nuclei in the protein, derived from the nuclear Overhauser effect (NOE), provide information about the structure of the protein in its folded state. NMR studies of symmetric protein homo-oligomers present a unique challenge. Using X-filtered NOESY experiments, it is possible to determine whether an NOE restrains a pair of protons across different subunits or within a single subunit, but current experimental techniques are unable to determine in which subunits the restrained protons lie. Consequently, it is difficult to assign NOEs to particular pairs of subunits with certainty, thus hindering the structural analysis of the oligomeric state. Computational approaches are needed to address this subunit ambiguity, but traditional solutions often rely on stochastic search coupled with simulated annealing and simulations of simplified molecular dynamics, which have many tunable parameters that must be chosen carefully and can also fail to report structures consistent with the experimental restraints. In addition, these traditional approaches rarely provide guarantees on running time or solution quality. We reduce the structure determination of homo-oligomers with cyclic symmetry to computing geometric arrangements of unions of annuli in a plane. Our algorithm, disco, runs in expected O(n²) time, where n is the number of distance restraints, potentially assigned ambiguously. disco is guaranteed to report the exact set of oligomer structures consistent with the distance restraints and also with orientational restraints from residual dipolar couplings (RDCs). We demonstrate our method using two symmetric protein complexes: the trimeric E. coli diacylglycerol kinase (DAGK) and a dimeric mutant of the immunoglobulin-binding domain B1 of streptococcal protein G (GB1). In both cases, disco computes oligomer structures with high precision and also finds distance restraints that are either mutually inconsistent or inconsistent with the RDCs. The entire protocol DISCO has been completely automated in a software package that is freely available and open-source at www.cs.duke.edu/donaldlab/software.php.

NMR structural inference of symmetric homo-oligomers

Symmetric homo-oligomers represent a majority of proteins, and determining their structures helps elucidate important biological processes, including ion transport, signal transduction, and transcriptional regulation. In order to account for the noise and sparsity in the distance restraints used in Nuclear Magnetic Resonance (NMR) structure determination of cyclic (C(n)) symmetric homo-oligomers, and the resulting uncertainty in the determined structures, we develop a Bayesian structural inference approach. In contrast to traditional NMR structure determination methods, which identify a small set of low-energy conformations, the inferential approach characterizes the entire posterior distribution of conformations. Unfortunately, traditional stochastic techniques for inference may under-sample the rugged landscape of the posterior, missing important contributions from high-quality individual conformations and not accounting for the possible aggregate effects on inferred quantities from numerous unsampled conformations. However, by exploiting the geometry of symmetric homo-oligomers, we develop an algorithm that provides provable guarantees for the posterior distribution and the inferred mean atomic coordinates. Using experimental restraints for three proteins, we demonstrate that our approach is able to objectively characterize the structural diversity supported by the data. By simulating spurious and missing restraints, we further demonstrate that our approach is robust, degrading smoothly with noise and sparsity.

A graphical method for analyzing distance restraints using residual dipolar couplings for structure determination of symmetric protein homo-oligomers

High-resolution structure determination of homo-oligomeric protein complexes remains a daunting task for NMR spectroscopists. Although isotope-filtered experiments allow separation of intermolecular NOEs from intramolecular NOEs and determination of the structure of each subunit within the oligomeric state, degenerate chemical shifts of equivalent nuclei from different subunits make it difficult to assign intermolecular NOEs to nuclei from specific pairs of subunits with certainty, hindering structural analysis of the oligomeric state. Here, we introduce a graphical method, DISCO, for the analysis of intermolecular distance restraints and structure determination of symmetric homo-oligomers using residual dipolar couplings. Based on knowledge that the symmetry axis of an oligomeric complex must be parallel to an eigenvector of the alignment tensor of residual dipolar couplings, we can represent distance restraints as annuli in a plane encoding the parameters of the symmetry axis. Oligomeric protein structures with the best restraint satisfaction correspond to regions of this plane with the greatest number of overlapping annuli. This graphical analysis yields a technique to characterize the complete set of oligomeric structures satisfying the distance restraints and to quantitatively evaluate the contribution of each distance restraint. We demonstrate our method for the trimeric E. coli diacylglycerol kinase, addressing the challenges in obtaining subunit assignments for distance restraints. We also demonstrate our method on a dimeric mutant of the immunoglobulin-binding domain B1 of streptococcal protein G to show the resilience of our method to ambiguous atom assignments. In both studies, DISCO computed oligomer structures with high accuracy despite using ambiguously assigned distance restraints.

An allosteric mechanism inferred from molecular dynamics simulations on phospholamban pentamer in lipid membranes

Phospholamban functions as a regulator of Ca(2+) concentration of cardiac muscle cells by triggering the bioactivity of sarcoplasmic reticulum Ca(2+)-ATPase. In order to understand its dynamic mechanism in the environment of bilayer surroundings, we performed long time-scale molecular dynamic simulations based on the high-resolution NMR structure of phospholamban pentamer. It was observed from the molecular dynamics trajectory analyses that the conformational transitions between the "bellflower" and "pinwheel" modes were detected for phospholamban. Particularly, the two modes became quite similar to each other after phospholamban was phosphorylated at Ser16. Based on these findings, an allosteric mechanism was proposed to elucidate the dynamic process of phospholamban interacting with Ca(2+)-ATPase.

Phosphorylation and mutation of phospholamban alter physical interactions with the sarcoplasmic reticulum calcium pump

Phospholamban physically interacts with the sarcoplasmic reticulum calcium pump (SERCA) and regulates contractility of the heart in response to adrenergic stimuli. We studied this interaction using electron microscopy of 2D crystals of SERCA in complex with phospholamban. In earlier studies, phospholamban oligomers were found interspersed between SERCA dimer ribbons and a 3D model was constructed to show interactions with SERCA. In this study, we examined the oligomeric state of phospholamban and the effects of phosphorylation and mutation of phospholamban on the interaction with SERCA in the 2D crystals. On the basis of projection maps from negatively stained and frozen-hydrated crystals, phosphorylation of Ser16 selectively disordered the cytoplasmic domain of wild type phospholamban. This was not the case for a pentameric gain-of-function mutant (Lys27Ala), which retained inhibitory activity and remained ordered in the phosphorylated state. A partial loss-of-function mutation that altered the charge state of phospholamban (Arg14Ala) retained an ordered state, while a complete loss-of-function mutation (Asn34Ala) was also disordered. The functional state of phospholamban was correlated with an order-to-disorder transition of the phospholamban cytoplasmic domain in the 2D co-crystals. Furthermore, co-crystals of the gain-of-function mutant (Lys27Ala) facilitated data collection from frozen-hydrated crystals. An improved projection map was calculated to a resolution of 8 Å, which supports the pentamer as the oligomeric state of phospholamban in the crystals. The 2D co-crystals with SERCA require a functional pentameric form of phospholamban, which physically interacts with SERCA at an accessory site distinct from that used by the phospholamban monomer for the inhibitory association.

The RCSB Protein Data Bank: redesigned web site and web services

The RCSB Protein Data Bank (RCSB PDB) web site (http://www.pdb.org) has been redesigned to increase usability and to cater to a larger and more diverse user base. This article describes key enhancements and new features that fall into the following categories: (i) query and analysis tools for chemical structure searching, query refinement, tabulation and export of query results; (ii) web site customization and new structure alerts; (iii) pair-wise and representative protein structure alignments; (iv) visualization of large assemblies; (v) integration of structural data with the open access literature and binding affinity data; and (vi) web services and web widgets to facilitate integration of PDB data and tools with other resources. These improvements enable a range of new possibilities to analyze and understand structure data. The next generation of the RCSB PDB web site, as described here, provides a rich resource for research and education.

High-resolution protein structure determination starting with a global fold calculated from exact solutions to the RDC equations

We present a novel structure determination approach that exploits the global orientational restraints from RDCs to resolve ambiguous NOE assignments. Unlike traditional approaches that bootstrap the initial fold from ambiguous NOE assignments, we start by using RDCs to compute accurate secondary structure element (SSE) backbones at the beginning of structure calculation. Our structure determination package, called RDC-PANDA: (RDC-based SSE PAcking with NOEs for Structure Determination and NOE Assignment), consists of three modules: (1) RDC-EXACT: ; (2) PACKER: ; and (3) HANA: (HAusdorff-based NOE Assignment). RDC-EXACT: computes the global optimal solution of backbone dihedral angles for each secondary structure element by exactly solving a system of quartic RDC equations derived by Wang and Donald (Proceedings of the IEEE computational systems bioinformatics conference (CSB), Stanford, CA, 2004a; J Biomol NMR 29(3):223-242, 2004b), and systematically searching over the roots, each of which is a backbone dihedral varphi- or psi-angle consistent with the RDC data. Using a small number of unambiguous inter-SSE NOEs extracted using only chemical shift information, PACKER: performs a systematic search for the core structure, including all SSE backbone conformations. HANA: uses a Hausdorff-based scoring function to measure the similarity between the experimental spectra and the back-computed NOE pattern for each side-chain from a statistically-diverse rotamer library, and drives the selection of optimal position-specific rotamers for filtering ambiguous NOE assignments. Finally, a local minimization approach is used to compute the loops and refine side-chain conformations by fixing the core structure as a rigid body while allowing movement of loops and side-chains. RDC-PANDA: was applied to NMR data for the FF Domain 2 of human transcription elongation factor CA150 (RNA polymerase II C-terminal domain interacting protein), human ubiquitin, the ubiquitin-binding zinc finger domain of the human Y-family DNA polymerase Eta (pol eta UBZ), and the human Set2-Rpb1 interacting domain (hSRI). These results demonstrated the efficiency and accuracy of our algorithm, and show that RDC-PANDA: can be successfully applied for high-resolution protein structure determination using only a limited set of NMR data by first computing RDC-defined backbones.

RDC-assisted modeling of symmetric protein homo-oligomers

Protein oligomerization serves an important function in biological processes, yet solving structures of protein oligomers has always been a challenge. For solution NMR, the challenge arises both from the increased size of these systems and, in the case of homo-oligomers, from ambiguities in assignment of intra- as opposed to intersubunit NOEs. In this study, we present a residual dipolar coupling (RDC)-assisted method for constructing models of homo-oligomers with purely rotational symmetry. Utilizing the fact that one of the principal axes of the tensor describing the alignment needed for RDC measurement is always parallel to the oligomer symmetry axis, it is possible to greatly restrict possible models for the oligomer. Here, it is shown that, if the monomer structure is known, all allowed dimer models can be constructed using a grid search algorithm and evaluated based on RDC simulations and the quality of the interface between the subunits. Using the Bacillus subtilis protein YkuJ as an example, it is shown that the evaluation criteria based on just two sets of NH RDCs are very selective and can unambiguously produce a model in good agreement with an existing X-ray structure of YkuJ.

Structure-based protein NMR assignments using native structural ensembles

An important step in NMR protein structure determination is the assignment of resonances and NOEs to corresponding nuclei. Structure-based assignment (SBA) uses a model structure ("template") for the target protein to expedite this process. Nuclear vector replacement (NVR) is an SBA framework that combines multiple sources of NMR data (chemical shifts, RDCs, sparse NOEs, amide exchange rates, TOCSY) and has high accuracy when the template is close to the target protein's structure (less than 2 A backbone RMSD). However, a close template may not always be available. We extend the circle of convergence of NVR for distant templates by using an ensemble of structures. This ensemble corresponds to the low-frequency perturbations of the given template and is obtained using normal mode analysis (NMA). Our algorithm assigns resonances and sparse NOEs using each of the structures in the ensemble separately, and aggregates the results using a voting scheme based on maximum bipartite matching. Experimental results on human ubiquitin, using four distant template structures show an increase in the assignment accuracy. Our algorithm also improves the robustness of NVR with respect to structural noise. We provide a confidence measure for each assignment using the percentage of the structures that agree on that assignment. We use this measure to assign a subset of the peaks with even higher accuracy. We further validate our algorithm on data for two additional proteins with NVR. We then show the general applicability of our approach by applying our NMA ensemble-based voting scheme to another SBA tool, MARS. For three test proteins with corresponding templates, including the 370-residue maltose binding protein, we increase the number of reliable assignments made by MARS. Finally, we show that our voting scheme is sound and optimal, by proving that it is a maximum likelihood estimator of the correct assignments.

Analysis of self-associating proteins by singular value decomposition of solution scattering data

We describe a method by which a single experiment can reveal both association model (pathway and constants) and low-resolution structures of a self-associating system. Small-angle scattering data are collected from solutions at a range of concentrations. These scattering data curves are mass-weighted linear combinations of the scattering from each oligomer. Singular value decomposition of the data yields a set of basis vectors from which the scattering curve for each oligomer is reconstructed using coefficients that depend on the association model. A search identifies the association pathway and constants that provide the best agreement between reconstructed and observed data. Using simulated data with realistic noise, our method finds the correct pathway and association constants. Depending on the simulation parameters, reconstructed curves for each oligomer differ from the ideal by 0.05-0.99% in median absolute relative deviation. The reconstructed scattering curves are fundamental to further analysis, including interatomic distance distribution calculation and low-resolution ab initio shape reconstruction of each oligomer in solution. This method can be applied to x-ray or neutron scattering data from small angles to moderate (or higher) resolution. Data can be taken under physiological conditions, or particular conditions (e.g., temperature) can be varied to extract fundamental association parameters (DeltaH(ass), DeltaS(ass)).

A complete algorithm to resolve ambiguity for intersubunit NOE assignment in structure determination of symmetric homo-oligomers

Assignment of nuclear Overhauser effect (NOE) data is a key bottleneck in structure determination by NMR. NOE assignment resolves the ambiguity as to which pair of protons generated the observed NOE peaks, and thus should be restrained in structure determination. In the case of intersubunit NOEs in symmetric homo-oligomers, the ambiguity includes both the identities of the protons within a subunit, and the identities of the subunits to which they belong. This paper develops an algorithm for simultaneous intersubunit NOE assignment and C(n) symmetric homo-oligomeric structure determinations, given the subunit structure. By using a configuration space framework, our algorithm guarantees completeness, in that it identifies structures representing, to within a user-defined similarity level, every structure consistent with the available data (ambiguous or not). However, while our approach is complete in considering all conformations and assignments, it avoids explicit enumeration of the exponential number of combinations of possible assignments. Our algorithm can draw two types of conclusions not possible under previous methods: (1) that different assignments for an NOE would lead to different structural classes, or (2) that it is not necessary to uniquely assign an NOE, since it would have little impact on structural precision. We demonstrate on two test proteins that our method reduces the average number of possible assignments per NOE by a factor of 2.6 for MinE and 4.2 for CCMP. It results in high structural precision, reducing the average variance in atomic positions by factors of 1.5 and 3.6, respectively.